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In [1]:

    
l = [1, 4, 3];



In [2]:

    
l









    Out[2]:





[1, 4, 3]



In [4]:

    
l.append(6)



In [5]:

    
l









    Out[5]:





[1, 4, 3, 6]



In [6]:

    
l+l









    Out[6]:





[1, 4, 3, 6, 1, 4, 3, 6]



In [7]:

    
3*l









    Out[7]:





[1, 4, 3, 6, 1, 4, 3, 6, 1, 4, 3, 6]



In [8]:

    
l









    Out[8]:





[1, 4, 3, 6]



In [9]:

    
range(10)









    Out[9]:





[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]



In [11]:

    
range(3, 10, 2)









    Out[11]:





[3, 5, 7, 9]



In [15]:

    
def listb(n):
    if n == 0:
        return [[]]
    rec = listb(n-1)
    return [ [0]+l for l in rec ] + [ [1] + l for l in rec ]



In [16]:

    
listb(4)









    Out[16]:





[[0, 0, 0, 0],
 [0, 0, 0, 1],
 [0, 0, 1, 0],
 [0, 0, 1, 1],
 [0, 1, 0, 0],
 [0, 1, 0, 1],
 [0, 1, 1, 0],
 [0, 1, 1, 1],
 [1, 0, 0, 0],
 [1, 0, 0, 1],
 [1, 0, 1, 0],
 [1, 0, 1, 1],
 [1, 1, 0, 0],
 [1, 1, 0, 1],
 [1, 1, 1, 0],
 [1, 1, 1, 1]]



In [17]:

    
[len(listb(i)) for i in range(10)]









    Out[17]:





[1, 2, 4, 8, 16, 32, 64, 128, 256, 512]



In [19]:

    
p = Primes()



In [20]:

    
p









    Out[20]:





Set of all prime numbers: 2, 3, 5, 7, ...



In [22]:

    
l = [3,2,5,6]



In [23]:

    
it = iter(l)



In [24]:

    
it









    Out[24]:





<listiterator object at 0x7f0c12639550>



In [25]:

    
it.next()









    Out[25]:





3



In [26]:

    
it.next()









    Out[26]:





2



In [27]:

    
it.next()









    Out[27]:





5



In [28]:

    
it.next()









    Out[28]:





6



In [29]:

    
it.next()









    



---------------------------------------------------------------------------
StopIteration                             Traceback (most recent call last)
<ipython-input-29-24d6ab57088b> in <module>()
----> 1 it.next()

StopIteration:



In [30]:

    
def listCompo(n):
    if n == 0:
        return [[]]
    res = []
    for k in range(1, n+1):
        res.extend([[k] + l for l in listCompo(n-k)])
    return res



In [31]:

    
listCompo(0)









    Out[31]:





[[]]



In [32]:

    
listCompo(1)









    Out[32]:





[[1]]



In [33]:

    
listCompo(2)









    Out[33]:





[[1, 1], [2]]



In [34]:

    
listCompo(3)









    Out[34]:





[[1, 1, 1], [1, 2], [2, 1], [3]]



In [35]:

    
listCompo(4)









    Out[35]:





[[1, 1, 1, 1], [1, 1, 2], [1, 2, 1], [1, 3], [2, 1, 1], [2, 2], [3, 1], [4]]



In [36]:

    
[len(listCompo(i)) for i in range(11)]









    Out[36]:





[1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512]



In [38]:

    
def ajoute1(l):
    res = list(l) # copie l
    res[0]+=1
    return res



In [40]:

    
l = [4,3,1,2]; ajoute1(l), l









    Out[40]:





([5, 3, 1, 2], [4, 3, 1, 2])



In [43]:

    
def listC(n):
    if n == 0:
        return [[]]
    if n == 1:
        return [[1]]
    rec = listC(n-1)
    return [[1] + l for l in rec] + [ajoute1(l) for l in rec]



In [46]:

    
listC(6)









    Out[46]:





[[1, 1, 1, 1, 1, 1],
 [1, 1, 1, 1, 2],
 [1, 1, 1, 2, 1],
 [1, 1, 1, 3],
 [1, 1, 2, 1, 1],
 [1, 1, 2, 2],
 [1, 1, 3, 1],
 [1, 1, 4],
 [1, 2, 1, 1, 1],
 [1, 2, 1, 2],
 [1, 2, 2, 1],
 [1, 2, 3],
 [1, 3, 1, 1],
 [1, 3, 2],
 [1, 4, 1],
 [1, 5],
 [2, 1, 1, 1, 1],
 [2, 1, 1, 2],
 [2, 1, 2, 1],
 [2, 1, 3],
 [2, 2, 1, 1],
 [2, 2, 2],
 [2, 3, 1],
 [2, 4],
 [3, 1, 1, 1],
 [3, 1, 2],
 [3, 2, 1],
 [3, 3],
 [4, 1, 1],
 [4, 2],
 [5, 1],
 [6]]

Iteration et Yield en Python



In [47]:

    
def demoyield():
    yield 1
    yield "toto"
    yield 7



In [48]:

    
it = demoyield()



In [49]:

    
it









    Out[49]:





<generator object demoyield at 0x7f0c12763460>



In [50]:

    
it.next()









    Out[50]:





1



In [51]:

    
it.next()









    Out[51]:





'toto'



In [52]:

    
it.next()









    Out[52]:





7



In [53]:

    
it.next()









    



---------------------------------------------------------------------------
StopIteration                             Traceback (most recent call last)
<ipython-input-53-24d6ab57088b> in <module>()
----> 1 it.next()

StopIteration:



In [54]:

    
def bla(n):
    for i in range(n):
        yield i



In [55]:

    
it = bla(5)



In [56]:

    
it.next()









    Out[56]:





0



In [57]:

    
it.next()









    Out[57]:





1



In [58]:

    
list(it)









    Out[58]:





[2, 3, 4]



In [60]:

    
def genBin(n):
    if n == 0:
        yield []
    else:
        for l in genBin(n-1):
            yield [0] + l
        for l in genBin(n-1):
            yield [1] + l



In [61]:

    
it = genBin(4)



In [62]:

    
it.next()









    Out[62]:





[0, 0, 0, 0]



In [63]:

    
it.next()









    Out[63]:





[0, 0, 0, 1]



In [64]:

    
list(it)









    Out[64]:





[[0, 0, 1, 0],
 [0, 0, 1, 1],
 [0, 1, 0, 0],
 [0, 1, 0, 1],
 [0, 1, 1, 0],
 [0, 1, 1, 1],
 [1, 0, 0, 0],
 [1, 0, 0, 1],
 [1, 0, 1, 0],
 [1, 0, 1, 1],
 [1, 1, 0, 0],
 [1, 1, 0, 1],
 [1, 1, 1, 0],
 [1, 1, 1, 1]]

Memoization



In [68]:

    
@cached_function
def binom(n, k):
    if k == 0:
        return 1
    if k == n: 
        return 1
    return binom(n-1, k) + binom(n-1, k-1)



In [69]:

    
binom(100, 50)









    Out[69]:





100891344545564193334812497256



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