Texte d'oral de modélisation - Agrégation Option Informatique

Préparation à l'agrégation - ENS de Rennes, 2016-17

Date : 7 avril 2017
Auteur : Lilian Besson
Texte: Annale 2009, "Contraintes temporelles"

À propos de ce document

Ceci est une proposition de correction, partielle et probablement non-optimale, pour la partie implémentation d'un texte d'annale de l'agrégation de mathématiques, option informatique.
Ce document est un notebook Jupyter, et est open-source sous Licence MIT sur GitHub, comme les autres solutions de textes de modélisation que j'ai écrite cette année.
L'implémentation sera faite en OCaml, version 4+ :



In [2]:

    
Sys.command "ocaml -version";;









    



The OCaml toplevel, version 4.04.2






    Out[2]:





- : int = 0

Notez que certaines fonctions des modules usuels List et Array ne sont pas disponibles en OCaml 3.12. J'essaie autant que possible de ne pas les utiliser, ou alors de les redéfinir si je m'en sers.

Question de programmation

La question de programmation pour ce texte était donnée en question 1 en page 9 :

"Programmer l'algorithme PC. Faites le tourner sur l'exemple de réseau non distributif."

La consigne était très courte, mais avec aucune indication. Notez qu'il est rare que le texte exige un exemple particulier.

Réponse à l'exercice requis

Ça va être assez long, en fait...

D'abord, il faut définir les types de données avec lesquels on va travailler,
Ensuite, implémenter les deux opérations $\oplus$ et $\otimes$ sur les ensembles d'intervalles,
Puis implémenter l'algorithme PC (similaire à Floyd-Warshall),
Et enfin, l'exécuter sur l'exemple de réseau non distributif donné en page 8.

Si possible, on va essayer de faire des tests pour chaque fonction intermédiaire, et un exemple de plus à la fin.

Un des problèmes que l'on va rencontrer est le fait que l'on doit manipuler $-\infty$ et $+\infty$, pour pouvoir gérer une contrainte qui n'est pas une contrainte, à savoir l'interavalle $(-\infty, +\infty)$.

Structures de données

On va travailler avec des valeurs entières ou $\pm\infty$. En écrivant nous même les opérations arithmétiques ($+,max$) sur les entiers "étendus" on obtiendra ce qu'on veut.



In [75]:

    
type entier_etendu = MInf | PInf | E of int;;









    Out[75]:





type entier_etendu = MInf | PInf | E of int

On se restreint aux intervalles à coordonnées entières, et on considère des listes d'intervalles. Tous les intervalles sont fermés à gauche et à droite.



In [76]:

    
type intervalle = (entier_etendu * entier_etendu);;  (* (a, b) représente l'intervalle [a, b] *)









    Out[76]:





type intervalle = entier_etendu * entier_etendu



In [77]:

    
type intervalles = intervalle list;;









    Out[77]:





type intervalles = intervalle list

On définit tout de suite deux exemples, $T_a$ et $S_a$ tirés de la Figure 2.a) et $T_b,S_b$ de la Figure 2.b). Cela permettra de vérifier les opérations $\oplus$ et $\otimes$.

$T_a = \{ [1, 4], [6, 8] \}$ et $S_a = \{ [0, 1], [3, 5], [6, 7] \}$.



In [78]:

    
let t_a : intervalles = [
    (E(1), E(4));
    (E(6), E(8))
];;

let s_a : intervalles = [
    (E(0), E(1));
    (E(3), E(5));
    (E(6), E(7))
];;









    Out[78]:





val t_a : intervalles = [(E 1, E 4); (E 6, E 8)]







    Out[78]:





val s_a : intervalles = [(E 0, E 1); (E 3, E 5); (E 6, E 7)]

$T_b = \{ [-1, 0], [2, 4] \}$ et $S_b = \{ [0, 1], [4, 4] \}$.



In [80]:

    
let t_b : intervalles = [
    (E(-1), E(0));
    (E(2), E(4))
];;

let s_b : intervalles = [
    (E(0), E(1));
    (E(4), E(4))  (* Intervalle de longueur nulle *)
];;









    Out[80]:





val t_b : intervalles = [(E (-1), E 0); (E 2, E 4)]







    Out[80]:





val s_b : intervalles = [(E 0, E 1); (E 4, E 4)]

Et la contrainte vide, $T = \{[-\infty, +\infty\}$ :



In [79]:

    
let t_vide : intervalles = [
    (MInf, PInf)
];;









    Out[79]:





val t_vide : intervalles = [(MInf, PInf)]

Arithmétiques sur nos entiers étendus

Max/min



In [81]:

    
let max_ee x y =
    match x, y with
    | MInf, _ -> y
    | PInf, _ -> PInf
    | _, MInf -> x
    | _, PInf -> PInf
    | E(vx), E(vy) -> E(max vx vy)
;;









    Out[81]:





val max_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>



In [86]:

    
max_ee MInf (E(10));;
max_ee PInf (E(10));;
max_ee (E(10)) MInf;;
max_ee (E(10)) PInf;;
max_ee (E(-10)) (E(10));;
max_ee (E(10)) (E(-10));;









    Out[86]:





- : entier_etendu = E 10







    Out[86]:





- : entier_etendu = PInf







    Out[86]:





- : entier_etendu = E 10







    Out[86]:





- : entier_etendu = PInf







    Out[86]:





- : entier_etendu = E 10







    Out[86]:





- : entier_etendu = E 10



In [87]:

    
let min_ee x y =
    match x, y with
    | PInf, _ -> y
    | MInf, _ -> MInf
    | _, PInf -> x
    | _, MInf -> MInf
    | E(vx), E(vy) -> E(min vx vy)
;;









    Out[87]:





val min_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>



In [90]:

    
min_ee MInf (E(10));;
min_ee PInf (E(10));;
min_ee (E(10)) MInf;;
min_ee (E(10)) PInf;;
min_ee (E(-10)) (E(10));;
min_ee (E(10)) (E(-10));;









    Out[90]:





- : entier_etendu = MInf







    Out[90]:





- : entier_etendu = E 10







    Out[90]:





- : entier_etendu = MInf







    Out[90]:





- : entier_etendu = E 10







    Out[90]:





- : entier_etendu = E (-10)







    Out[90]:





- : entier_etendu = E (-10)

On peut utiliser la fonction minimum pour trier deux entiers étendus :



In [115]:

    
let pluspetiteq_ee x y =
    let m = min_ee x y in
    m = x || x = y
;;









    Out[115]:





val pluspetiteq_ee : entier_etendu -> entier_etendu -> bool = <fun>



In [116]:

    
let pluspetit_ee x y =
    let m = min_ee x y in
    m = x && x != y
;;









    Out[116]:





val pluspetit_ee : entier_etendu -> entier_etendu -> bool = <fun>

Somme/produit



In [88]:

    
let plus_ee x y =
    match x, y with
    | MInf, PInf -> failwith "-inf + +inf = ?"
    | PInf, MInf -> failwith "-inf + +inf = ?"
    | PInf, _ -> PInf
    | MInf, _ -> MInf
    | _, MInf -> MInf
    | _, PInf -> PInf
    | E(vx), E(vy) -> E(vx + vy)
;;









    Out[88]:





val plus_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>



In [92]:

    
plus_ee MInf (E(10));;
plus_ee PInf (E(10));;
plus_ee (E(10)) MInf;;
plus_ee (E(10)) PInf;;
plus_ee (E(-10)) (E(10));;
plus_ee (E(10)) (E(-10));;
plus_ee (E(10)) (E(10));;
plus_ee (E(-10)) (E(-10));;









    Out[92]:





- : entier_etendu = MInf







    Out[92]:





- : entier_etendu = PInf







    Out[92]:





- : entier_etendu = MInf







    Out[92]:





- : entier_etendu = PInf







    Out[92]:





- : entier_etendu = E 0







    Out[92]:





- : entier_etendu = E 0







    Out[92]:





- : entier_etendu = E 20







    Out[92]:





- : entier_etendu = E (-20)



In [93]:

    
let produit_ee x y =
    match x, y with
    | MInf, PInf -> MInf
    | PInf, MInf -> PInf
    | PInf, E(vy) when vy < 0 -> MInf
    | PInf, _ -> PInf
    | MInf, E(vy) when vy < 0 -> PInf
    | MInf, _ -> MInf
    | E(vx), PInf when vx < 0 -> MInf
    | _, PInf -> PInf
    | E(vx), MInf when vx < 0 -> PInf
    | _, MInf -> MInf
    | E(vx), E(vy) -> E(vx * vy)
;;









    Out[93]:





val produit_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>



In [94]:

    
produit_ee MInf (E(10));;
produit_ee PInf (E(10));;
produit_ee (E(10)) MInf;;
produit_ee (E(10)) PInf;;
produit_ee (E(-10)) (E(10));;
produit_ee (E(10)) (E(-10));;
produit_ee (E(10)) (E(10));;
produit_ee (E(-10)) (E(-10));;









    Out[94]:





- : entier_etendu = MInf







    Out[94]:





- : entier_etendu = PInf







    Out[94]:





- : entier_etendu = MInf







    Out[94]:





- : entier_etendu = PInf







    Out[94]:





- : entier_etendu = E (-100)







    Out[94]:





- : entier_etendu = E (-100)







    Out[94]:





- : entier_etendu = E 100







    Out[94]:





- : entier_etendu = E 100

Opérations de base, $\oplus$ et $\otimes$

On peut écrire des opérations d'intersection et de composition sur deux intervalles, ensuite il suffira de les généraliser à un ensemble d'intervalle.

On suit les définitions de l'énoncé.

Intersection

$$ \forall T = (I_1,\dots,I_l), \forall S = (J_1,\dots,J_m),\\ T \oplus S := \{ K_1, \dots, K_n\} \;\;\text{Où}\;\; K_k = I_i \cap J_j. $$

Notez que $n \leq l + m$ ici.

Pour l'intersection de deux intervalles, l'intervalle vide $\emptyset$ peut être obtenu, donc la fonction suivante renvoie un type intervalle option : soit None si $I \cap J = \emptyset$, soit Some (x, y) si $I \cap J = [x, y]$.



In [96]:

    
let intersection (i : intervalle) (j : intervalle) : intervalle option =
    let a = fst i and b = snd i in
    let c = fst j and d = snd j in
    if pluspetit_ee b c || pluspetit_ee d a then
        None
    else
        Some (max_ee a c, min_ee b d)
;;









    Out[96]:





val intersection : intervalle -> intervalle -> intervalle option = <fun>

Ensuite, il suffit d'explorer tous les couples $(I, J)$ possible, et de ne garder que ceux qui donnent un intervalle. On supprimera les doublons en vérifiant au fur et à mesure (ça a la même complexité que si on le fait à la fin).

En manipulant une liste d'intervalle option, on doit ruser un peu pour n'ajouter que ceux qui ne sont pas dans acc et qui sont des vrais intervalles.



In [98]:

    
let ajoute_nouveaux_option (acc : intervalles) (liste_option : intervalle option list) =
    List.map
    (fun i -> match i with Some i2 -> i2 | None -> (MInf, PInf))
    (List.filter (fun i ->
        match i with
        | None -> false
        | Some i2 -> not (List.mem i2 acc)
    ) liste_option)
;;









    Out[98]:





val ajoute_nouveaux_option :
  intervalles -> intervalle option list -> intervalle list = <fun>

Avec tout ça, on a une belle fonction récursive, avec un accumulateur acc qui contient la liste des intervalles dans $T \oplus S$, construite en considérant les intervalles de $S$ les un après les autres.

On s'assure de n'avoir ni intervalles vide, ni doublon, grâce à ajoute_nouveaux_option.



In [101]:

    
let intersections (t : intervalles) (s : intervalles) : intervalles =
    let rec inter_aux acc tx sx =
        match sx with
        | [] -> acc    (* Plus rien à ajouter *)
        | j :: s2 ->   (* On traite j, puis récursivement la suite de s *)
            let t_inter_j = List.map (intersection j) tx in
            inter_aux ((ajoute_nouveaux_option acc t_inter_j) @ acc) tx s2
    in
    List.sort compare (inter_aux [] t s)
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;









    Out[101]:





val intersections : intervalles -> intervalles -> intervalles = <fun>

Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci : $$ T \oplus S = \texttt{t ++ s}.$$



In [102]:

    
let ( ++ ) = intersections;;









    Out[102]:





val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>

Composition

Ce sera plus facile. $$ \forall T = (I_1,\dots,I_l), \forall S = (J_1,\dots,J_m),\\ T \otimes S := \{ K_1, \dots, K_n\} \;\;\text{Où}\;\; K_k = [a + c, b + d], \;\text{si}\; I_i = [a, b], J_j = [c, d]. $$ Notez que $n \leq l \times m$ ici.

Pour la composition de deux intervalles, il n'y pas de difficulté particulière :



In [103]:

    
let composition (i : intervalle) (j : intervalle) : intervalle =
    let a = fst i and b = snd i in
    let c = fst j and d = snd j in
    (* (a + c, b + d) *)
    ((plus_ee a c), (plus_ee d b))
;;









    Out[103]:





val composition : intervalle -> intervalle -> intervalle = <fun>

Et on les combine facilement, en gardant la même architecture que pour intersections.



In [104]:

    
let ajoute_nouveaux (acc : intervalles) (liste : intervalles) : intervalles =
    List.filter (fun i -> not (List.mem i acc)) liste
;;









    Out[104]:





val ajoute_nouveaux : intervalles -> intervalles -> intervalles = <fun>



In [105]:

    
let compositions (t : intervalles) (s : intervalles) : intervalles =
    let rec compo_aux acc tx sx =
        match sx with
        | [] -> acc    (* Plus rien à ajouter *)
        | j :: s2 ->   (* On traite j, puis récursivement la suite de s *)
            let t_compo_j = List.map (composition j) tx in
            compo_aux ((ajoute_nouveaux acc t_compo_j) @ acc) tx s2
    in
    List.sort compare (compo_aux [] t s)
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;









    Out[105]:





val compositions : intervalles -> intervalles -> intervalles = <fun>

Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci : $$ T \otimes S = \texttt{t ** s}.$$



In [106]:

    
let ( ** ) = compositions;;









    Out[106]:





val ( ** ) : intervalles -> intervalles -> intervalles = <fun>

Union

On peut aussi rapidement définier $T \cup S$, pour l'union. C'est très facile.



In [107]:

    
let union (t : intervalles) (s : intervalles) : intervalles =
    List.append t s
;;









    Out[107]:





val union : intervalles -> intervalles -> intervalles = <fun>

Exemples

On aimerait reproduire les exemples de la Figure 2 du texte.

Pour les deux intervalles de la Figure 2.a) : $T_a = \{ [1, 4], [6, 8] \}$ et $S_a = \{ [0, 1], [3, 5], [6, 7] \}$.



In [108]:

    
t_a ++ s_a;;









    Out[108]:





- : intervalles = [(E 3, E 4); (E 6, E 7)]

On retrouve bien le résultat de la Figure 2.a).



In [109]:

    
t_a ** s_a;;
union t_a s_a;;









    Out[109]:





- : intervalles =
[(E 1, E 5); (E 4, E 9); (E 6, E 9); (E 7, E 11); (E 9, E 13); (E 12, E 15)]







    Out[109]:





- : intervalles =
[(E 1, E 4); (E 6, E 8); (E 0, E 1); (E 3, E 5); (E 6, E 7)]

Pour les deux intervalles de la Figure 2.b) : $T_b = \{ [-1, 0], [2, 4] \}$ et $S_b = \{ [0, 1], [4, 4] \}$.



In [110]:

    
t_b ** s_b;;









    Out[110]:





- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 3, E 4); (E 6, E 8)]

On retrouve bien le résultat de la Figure 2.b).

L'intervalle $[3, 4]$ est inclus dans $[2, 5]$, donc on devrait ajouter une étape de nettoyage pour donner une forme canonique aux intervalles produit par composition. On le fait plus bas.



In [113]:

    
t_b;;
s_b;;









    Out[113]:





- : intervalles = [(E (-1), E 0); (E 2, E 4)]







    Out[113]:





- : intervalles = [(E 0, E 1); (E 4, E 4)]



In [114]:

    
t_b ++ s_b;;
union t_b s_b;;









    Out[114]:





- : intervalles = []







    Out[114]:





- : intervalles = [(E (-1), E 0); (E 2, E 4); (E 0, E 1); (E 4, E 4)]

On remarque que les intervalles sont bien donnés dans l'ordre croissant, puisqu'on a pensé à trier la sortie des deux fonctions, mais ça ne change rien.

Une étape de plus : ne pas inclure des intervalles inclus dans ceux déjà présents

On va raffiner les fonctions définis ci-dessus en ajoutant un test, sur leur résultat final.

est_inclus i j teste si $I \subseteq J$.



In [119]:

    
let est_inclus (i : intervalle) (j : intervalle) : bool =
    let a = fst i and b = snd i in
    let c = fst j and d = snd j in
    (* on peut aussi écrire directement
    let a, b = i and c, d = j in
    pour extraire les valeurs d'un coupe i=(a,b) et j=(c,d)
    *)
    (* c <= a && b <= d *)
    (pluspetiteq_ee c a) && (pluspetiteq_ee b d)
;;









    Out[119]:





val est_inclus : intervalle -> intervalle -> bool = <fun>



In [121]:

    
est_inclus (E(3), E(4)) (E(2), E(5));; (* true *)
est_inclus (E(2), E(5)) (E(3), E(4));; (* false *)
est_inclus (E(1), E(1)) (E(1), E(1));; (* true *)









    Out[121]:





- : bool = true







    Out[121]:





- : bool = false







    Out[121]:





- : bool = true

est_inclus_dans_un i acc teste si $I \subseteq J$ pour un $J \neq I \in \mathrm{Acc}$.



In [122]:

    
let est_inclus_dans_un (i : intervalle) (acc : intervalles) : bool =
    List.exists (fun j -> (i != j) && (est_inclus i j)) acc
;;









    Out[122]:





val est_inclus_dans_un : intervalle -> intervalles -> bool = <fun>

On peut écrire une fonction filtre qui retire les intervalles inclus dans d'autres, puis retire les doublons.



In [123]:

    
let retire_les_inclus (liste : intervalles) : intervalles =
    List.filter (fun i -> not (est_inclus_dans_un i liste)) liste
;;

let retire_les_doublons (liste : intervalles) : intervalles =
    let reponse = ref [] in
    List.iter (fun i ->
        if not (List.mem i !reponse) then
        reponse := i :: !reponse
    ) liste;
    !reponse
;;

let filtre liste =
    retire_les_doublons (retire_les_inclus liste)
;;









    Out[123]:





val retire_les_inclus : intervalles -> intervalles = <fun>







    Out[123]:





val retire_les_doublons : intervalles -> intervalles = <fun>







    Out[123]:





val filtre : intervalles -> intervalles = <fun>

L'intersection ne devrait pas être impactée.



In [124]:

    
let intersections2 (t : intervalles) (s : intervalles) : intervalles =
    List.sort compare (filtre (intersections t s))
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;









    Out[124]:





val intersections2 : intervalles -> intervalles -> intervalles = <fun>



In [125]:

    
let ( ++ ) = intersections2;;

t_a ++ s_a;;









    Out[125]:





val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>







    Out[125]:





- : intervalles = [(E 3, E 4); (E 6, E 7)]

Mais la composition va donner la bonne réponse désormais pour l'exemple de la figure 2.b).



In [126]:

    
let compositions2 (t : intervalles) (s : intervalles) : intervalles =
    List.sort compare (filtre (compositions t s))
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;









    Out[126]:





val compositions2 : intervalles -> intervalles -> intervalles = <fun>



In [127]:

    
let ( ** ) = compositions2;;

t_b ** s_b;;









    Out[127]:





val ( ** ) : intervalles -> intervalles -> intervalles = <fun>







    Out[127]:





- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 6, E 8)]

C'était un peu long, mais c'est propre au moins.

Notez que pour obtenir une vraie forme canonique, il faudrait aussi rassembler les intervalles consécutifs ($\{ [0, 1], [1, 2] \} \rightarrow \{ [0, 1] \}$) et se recoupant ($\{ [0, 3], [2, 4] \} \rightarrow \{ [0, 4] \}$).

Ça prendrait trop de temps. Et ce n'était pas exigé.

L'algorithme PC

Structure de données pour les réseaux STP

On a besoin désormais de considérer des réseaux STP, qui sont des graphes dont les sommets sont des entiers, et dont les arêtes sont étiquetées par des listes (non vides) d'intervalles.

L'algorithme PC demande de pouvoir accéder rapidement et facilement à l'arête entre deux sommets $x,y$, $T_{x,y}$. Ainsi, la structure de matrice d'adjacence semble appropriée. Les arêtes inexistantes dans le réseau auront simplement $T_{x,y} = \emptyset$, c'est-à-dire [] (liste vide).

On supposera que toutes les matrices données aux différentes fonctions définies plus bas sont carrées, on ne le vérifie pas (mais ce serait facile).



In [128]:

    
type sommet = int;;
type arete = intervalles;; (* c'est l'idée *)

type reseauSTP = intervalles array array;;









    Out[128]:





type sommet = int







    Out[128]:





type arete = intervalles







    Out[128]:





type reseauSTP = intervalles array array

On essaie tout de suite notre structure de données avec l'exemple du réseau STP de la figure 4 :



In [235]:

    
let t_01 : intervalles = [(E(0), E(1)); (E(10), E(20))];;
let t_12 : intervalles = [(E(0), E(10))];;
let t_13 : intervalles = [(E(25), E(50))];;
let t_23 : intervalles = [(E(0), E(20)); (E(40), E(40))];;

let t_vide = [(MInf, PInf)];;

let stp_4 : reseauSTP = [|
    [| t_vide; t_01;   t_vide; t_vide |];
    [| t_vide; t_vide; t_12;   t_13 |];
    [| t_vide; t_vide; t_vide; t_23 |];
    [| t_vide; t_vide; t_vide; t_vide |];
|];;









    Out[235]:





val t_01 : intervalles = [(E 0, E 1); (E 10, E 20)]







    Out[235]:





val t_12 : intervalles = [(E 0, E 10)]







    Out[235]:





val t_13 : intervalles = [(E 25, E 50)]







    Out[235]:





val t_23 : intervalles = [(E 0, E 20); (E 40, E 40)]







    Out[235]:





val t_vide : (entier_etendu * entier_etendu) list = [(MInf, PInf)]







    Out[235]:





val stp_4 : reseauSTP =
  [|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(E 0, E 20); (E 40, E 40)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]

On peut vérifier qu'il n'est pas distributif, en prenant l'exemple du texte (fin page 8) :



In [236]:

    
let s_13 = t_12 ** t_23;;

t_13 ++ s_13;;
t_01 ** (t_13 ++ s_13);;  (* 1er cas *)

t_01 ** t_13;;
t_01 ** s_13;;
(t_01 ** t_13) ++ (t_01 ** s_13);; (* 2nd cas *)









    Out[236]:





val s_13 : intervalles = [(E 0, E 30); (E 40, E 50)]







    Out[236]:





- : intervalles = [(E 25, E 30); (E 40, E 50)]







    Out[236]:





- : intervalles = [(E 25, E 31); (E 35, E 50); (E 40, E 51); (E 50, E 70)]







    Out[236]:





- : intervalles = [(E 25, E 51); (E 35, E 70)]







    Out[236]:





- : intervalles = [(E 0, E 31); (E 10, E 50); (E 40, E 51); (E 50, E 70)]







    Out[236]:





- : intervalles = [(E 25, E 50); (E 50, E 70)]

En simplifiant, on obtient :

$T_{01} \otimes (T_{13} \oplus S_{13} = \{ [25, 31], [35, 70] \}$,
$(T_{01} \otimes T_{13}) \oplus (T_{01} \otimes S_{13}) = \{ [25, 70] \}$,

qui sont bien différents.

Enfin, on peut rapidement vérifier si la matrice d'un graphe est bien carrée :



In [237]:

    
let est_carree matrice =
    let n = Array.length matrice in
    Array.fold_left (fun b x -> b && (n = (Array.length x))) true matrice
;;









    Out[237]:





val est_carree : 'a array array -> bool = <fun>



In [238]:

    
est_carree stp_4;;









    Out[238]:





- : bool = true

L'algorithme PC

Ça semble être un bon choix. Maintenant, passons à l'algorithme PC.

Il n'y a pas de boucle until en Caml, mais avec une boucle while on arrivera presque à la même chose.



In [239]:

    
exception Fini;; (* Pour faire le [exit]. *)









    Out[239]:





exception Fini

On peut l'écrire avant pour la rendre plus claire, mais l'étape clé de l'algorithme PC (et Floyd-Warshall) est une opération dite de relaxation : $$ T_{i,j} \oplus (T_{i,k} \otimes T_{k,j}).$$



In [240]:

    
let relaxe (reseau : reseauSTP) i j k =
    let t_ij = reseau.(i).(j)
    and t_ik = reseau.(i).(k)
    and t_kj = reseau.(k).(j)
    in t_ij ++ (t_ik ** t_kj)
;;









    Out[240]:





val relaxe : reseauSTP -> int -> int -> int -> intervalles = <fun>

On a tout ce qu'il faut pour écrire l'algorithme. Mais comme il ne marche pas encore, on va le débogguer.



In [241]:

    
let string_of_entieretendu = function
    | MInf -> "-oo"
    | PInf -> "+oo"
    | E(x) -> string_of_int x
;;









    Out[241]:





val string_of_entieretendu : entier_etendu -> string = <fun>



In [242]:

    
let print_intervalle (une_contrainte : intervalle) =
    let a, b = une_contrainte in
    Printf.printf "(%s, %s) " (string_of_entieretendu a) (string_of_entieretendu b)
;;









    Out[242]:





val print_intervalle : intervalle -> unit = <fun>



In [243]:

    
let print_intervalles (contraintes : intervalles) =
    List.iter print_intervalle contraintes
;;









    Out[243]:





val print_intervalles : intervalles -> unit = <fun>



In [244]:

    
let flush_force () =
    Printf.printf "\n";
    flush_all();
    Printf.printf "\n";
    flush_all();
    Printf.printf "\n";
    flush_all();
;;









    Out[244]:





val flush_force : unit -> unit = <fun>



In [245]:

    
let print_reseau (reseau : reseauSTP) : unit =
    flush_force ();
    Printf.printf "\nReseau =\n";
    Array.iteri (fun i ligne ->
        Array.iteri (fun j case ->
            if case != [(MInf, PInf)] then begin
            Printf.printf "\n    T[i=%i, j=%i] = [" i j;
            print_intervalles case;
            Printf.printf "]";
        end) ligne
    ) reseau;
    flush_all ();
;;









    Out[245]:





val print_reseau : reseauSTP -> unit = <fun>



In [246]:

    
stp_4;;









    Out[246]:





- : reseauSTP =
[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
    [(MInf, PInf)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
    [(E 0, E 20); (E 40, E 40)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]



In [247]:

    
flush_force();;









    



    T[i=3, j=3] = [(-oo, +oo) ]








    Out[247]:





- : unit = ()



In [248]:

    
print_reseau stp_4;;









    






Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]






    Out[248]:





- : unit = ()

On est prêt à écrire l'algorithme :



In [249]:

    
let algorithmePC ?(max_etape=10) (reseau : reseauSTP) : (reseauSTP * intervalles list) =
    let resT = Array.map Array.copy reseau in (* on ne modifie pas l'entrée *)
    let resS = ref [||] in
    let n = Array.length resT in
    let allseen = ref [] in (* Pour débogguer, je veux la liste des Tij vus *)
    let etape = ref 0 in
    begin
        try begin
        while !etape < max_etape && !resS != resT do
            incr etape;
            resS := Array.map Array.copy resT; (* S := T *)
            for k = 0 to n - 1 do
                for i = 0 to n - 1 do
                    for j = 0 to n - 1 do
                        Printf.printf "\n\nEtape %i, k = %i, i = %i, j = %i.\n" !etape k i j;
                        print_string "Contraintes :";
                        print_reseau resT;
                        resT.(i).(j) <- relaxe resT i j k;
                        allseen := (resT.(i).(j)) :: !allseen; (* on l'ajoute *)
                        if resT.(i).(j) = [] then
                            raise Fini
                    done
                done
            done
        done;
        end
        with Fini -> () (* On ignore l'exception, on a juste terminé. *)
    end;
    resT, !allseen
;;









    Out[249]:





val algorithmePC :
  ?max_etape:int -> reseauSTP -> reseauSTP * intervalles list = <fun>

Exemple de réseau non distributif

On va traiter l'exemple de la Figure 4 du texte, comme défini plus haut :



In [250]:

    
stp_4;;









    Out[250]:





- : reseauSTP =
[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
    [(MInf, PInf)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
    [(E 0, E 20); (E 40, E 40)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]



In [251]:

    
relaxe stp_4 1 2 3;;









    Out[251]:





- : intervalles = [(E 0, E 10)]



In [252]:

    
stp_4.(1).(3)









    Out[252]:





- : intervalles = [(E 25, E 50)]



In [ ]:



In [253]:

    
algorithmePC stp_4;;









    



    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]






    Out[253]:





- : reseauSTP * intervalles list =
([|[|[]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
     [(E 0, E 20); (E 40, E 40)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|],
 [[]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(E 0, E 20); (E 40, E 40)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(MInf, PInf)]; [(E 25, E 50)]; [(E 0, E 10)]; [(MInf, PInf)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)];
  [(MInf, PInf)]])

Je ne suis pas sûr de comment interprêter ce résultat...

soit j'ai fait une erreur dans l'implémentation,

soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple...

D'autres exemples

On peut étudier le STP de la Figure 1., en enlevant la contrainte $[60, \infty)$, qui ne rentre pas dans notre implémentation.



In [254]:

    
let t_01 : intervalles = [(E(10), E(20))];;
let t_12 : intervalles = [(E(30), E(40))];;
let t_32 : intervalles = [(E(10), E(20))];;
let t_34 : intervalles = [(E(20), E(30)); (E(40), E(50))];;
let t_40 : intervalles = [(E(60), E(70))];;

let stp_1 : reseauSTP = [|
    [| t_vide; t_01; t_vide; t_vide; t_vide |];
    [| t_vide; t_vide; t_12; t_vide; t_vide |];
    [| t_vide; t_vide; t_vide; t_vide; t_vide   |];
    [| t_vide; t_vide; t_32; t_vide; t_34 |];
    [| t_40; t_vide; t_vide; t_vide; t_vide |];
|];;









    Out[254]:





val t_01 : intervalles = [(E 10, E 20)]







    Out[254]:





val t_12 : intervalles = [(E 30, E 40)]







    Out[254]:





val t_32 : intervalles = [(E 10, E 20)]







    Out[254]:





val t_34 : intervalles = [(E 20, E 30); (E 40, E 50)]







    Out[254]:





val t_40 : intervalles = [(E 60, E 70)]







    Out[254]:





val stp_1 : reseauSTP =
  [|[|[(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)];
      [(E 20, E 30); (E 40, E 50)]|];
    [|[(E 60, E 70)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(MInf, PInf)]|]|]



In [255]:

    
print_reseau stp_1;;









    Out[255]:





- : unit = ()







    



    T[i=3, j=3] = [(-oo, +oo) ]



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]



In [256]:

    
algorithmePC stp_1;;









    



    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(80, 100) (100, 120) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(80, 100) (100, 120) ]
    T[i=3, j=1] = [(90, 120) (110, 140) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]






    Out[256]:





- : reseauSTP * intervalles list =
([|[|[(MInf, PInf)]; [(E 10, E 20)]; [(E 40, E 60)]; [(MInf, PInf)];
     [(MInf, PInf)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];
     [(MInf, PInf)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
     [(MInf, PInf)]|];
   [|[(E 80, E 100); (E 100, E 120)]; [(E 90, E 120); (E 110, E 140)]; 
     []; [(MInf, PInf)]; [(E 20, E 30); (E 40, E 50)]|];
   [|[(E 60, E 70)]; [(E 70, E 90)]; [(E 100, E 130)]; [(MInf, PInf)];
     [(MInf, PInf)]|]|],
 [[]; [(E 90, E 120); (E 110, E 140)]; [(E 80, E 100); (E 100, E 120)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(E ...); ...]; ...])

Je ne suis pas sûr de comment interprêter ce résultat...

soit j'ai fait une erreur dans l'implémentation,

soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple...

Conclusion

Voilà pour la question obligatoire de programmation :

on a décomposé le problème en sous-fonctions,
on a essayé d'être fainéant, en réutilisant les sous-fonctions,
on a fait des exemples et on les garde dans ce qu'on présente au jury,
on a testé la fonction exigée sur de petits exemples et sur un exemple de taille réelle (venant du texte)

Et on a essayé de faire un peu plus, en implémentant la vérification d'une contrainte de plus.

Bien-sûr, ce petit notebook ne se prétend pas être une solution optimale, ni exhaustive.

Table of Contents

Texte d'oral de modélisation - Agrégation Option Informatique

Préparation à l'agrégation - ENS de Rennes, 2016-17

À propos de ce document

Question de programmation

Réponse à l'exercice requis

Structures de données

Arithmétiques sur nos entiers étendus

Max/min

Somme/produit

Opérations de base, $\oplus$ et $\otimes$

Intersection

Composition

Union

Exemples

Une étape de plus : ne pas inclure des intervalles inclus dans ceux déjà présents

L'algorithme PC

Structure de données pour les réseaux STP

L'algorithme PC

Exemple de réseau non distributif

D'autres exemples

Conclusion