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# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""

  Nurse rostering in Google CP Solver.

  This is a simple nurse rostering model using a DFA and
  my decomposition of regular constraint.

  The DFA is from MiniZinc Tutorial, Nurse Rostering example:
  - one day off every 4 days
  - no 3 nights in a row.


  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models:
  http://www.hakank.org/google_or_tools/

"""
from __future__ import print_function
from ortools.constraint_solver import pywrapcp
from collections import defaultdict

#
# Global constraint regular
#
# This is a translation of MiniZinc's regular constraint (defined in
# lib/zinc/globals.mzn), via the Comet code refered above.
# All comments are from the MiniZinc code.
# '''
# The sequence of values in array 'x' (which must all be in the range 1..S)
# is accepted by the DFA of 'Q' states with input 1..S and transition
# function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
# (which must be in 1..Q) and accepting states 'F' (which all must be in
# 1..Q).  We reserve state 0 to be an always failing state.
# '''
#
# x : IntVar array
# Q : number of states
# S : input_max
# d : transition matrix
# q0: initial state
# F : accepting states


def regular(x, Q, S, d, q0, F):

  solver = x[0].solver()

  assert Q > 0, 'regular: "Q" must be greater than zero'
  assert S > 0, 'regular: "S" must be greater than zero'

  # d2 is the same as d, except we add one extra transition for
  # each possible input;  each extra transition is from state zero
  # to state zero.  This allows us to continue even if we hit a
  # non-accepted input.

  # Comet: int d2[0..Q, 1..S]
  d2 = []
  for i in range(Q + 1):
    row = []
    for j in range(S):
      if i == 0:
        row.append(0)
      else:
        row.append(d[i - 1][j])
    d2.append(row)

  d2_flatten = [d2[i][j] for i in range(Q + 1) for j in range(S)]

  # If x has index set m..n, then a[m-1] holds the initial state
  # (q0), and a[i+1] holds the state we're in after processing
  # x[i].  If a[n] is in F, then we succeed (ie. accept the
  # string).
  x_range = list(range(0, len(x)))
  m = 0
  n = len(x)

  a = [solver.IntVar(0, Q + 1, 'a[%i]' % i) for i in range(m, n + 1)]

  # Check that the final state is in F
  solver.Add(solver.MemberCt(a[-1], F))
  # First state is q0
  solver.Add(a[m] == q0)
  for i in x_range:
    solver.Add(x[i] >= 1)
    solver.Add(x[i] <= S)

    # Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
    solver.Add(
        a[i + 1] == solver.Element(d2_flatten, ((a[i]) * S) + (x[i] - 1)))



# Create the solver.
solver = pywrapcp.Solver('Nurse rostering using regular')

#
# data
#

# Note: If you change num_nurses or num_days,
#       please also change the constraints
#       on nurse_stat and/or day_stat.
num_nurses = 7
num_days = 14

day_shift = 1
night_shift = 2
off_shift = 3
shifts = [day_shift, night_shift, off_shift]

# the DFA (for regular)
n_states = 6
input_max = 3
initial_state = 1  # 0 is for the failing state
accepting_states = [1, 2, 3, 4, 5, 6]

transition_fn = [
    # d,n,o
    [2, 3, 1],  # state 1
    [4, 4, 1],  # state 2
    [4, 5, 1],  # state 3
    [6, 6, 1],  # state 4
    [6, 0, 1],  # state 5
    [0, 0, 1]  # state 6
]

days = ['d', 'n', 'o']  # for presentation

#
# declare variables
#
x = {}
for i in range(num_nurses):
  for j in range(num_days):
    x[i, j] = solver.IntVar(shifts, 'x[%i,%i]' % (i, j))

x_flat = [x[i, j] for i in range(num_nurses) for j in range(num_days)]

# summary of the nurses
nurse_stat = [
    solver.IntVar(0, num_days, 'nurse_stat[%i]' % i)
    for i in range(num_nurses)
]

# summary of the shifts per day
day_stat = {}
for i in range(num_days):
  for j in shifts:
    day_stat[i, j] = solver.IntVar(0, num_nurses, 'day_stat[%i,%i]' % (i, j))

day_stat_flat = [day_stat[i, j] for i in range(num_days) for j in shifts]

#
# constraints
#
for i in range(num_nurses):
  reg_input = [x[i, j] for j in range(num_days)]
  regular(reg_input, n_states, input_max, transition_fn, initial_state,
          accepting_states)

#
# Statistics and constraints for each nurse
#
for i in range(num_nurses):
  # number of worked days (day or night shift)
  b = [
      solver.IsEqualCstVar(x[i, j], day_shift) + solver.IsEqualCstVar(
          x[i, j], night_shift) for j in range(num_days)
  ]
  solver.Add(nurse_stat[i] == solver.Sum(b))

  # Each nurse must work between 7 and 10
  # days during this period
  solver.Add(nurse_stat[i] >= 7)
  solver.Add(nurse_stat[i] <= 10)

#
# Statistics and constraints for each day
#
for j in range(num_days):
  for t in shifts:
    b = [solver.IsEqualCstVar(x[i, j], t) for i in range(num_nurses)]
    solver.Add(day_stat[j, t] == solver.Sum(b))

  #
  # Some constraints for this day:
  #
  # Note: We have a strict requirements of
  #       the number of shifts.
  #       Using atleast constraints is much harder
  #       in this model.
  #
  if j % 7 == 5 or j % 7 == 6:
    # special constraints for the weekends
    solver.Add(day_stat[j, day_shift] == 2)
    solver.Add(day_stat[j, night_shift] == 1)
    solver.Add(day_stat[j, off_shift] == 4)
  else:
    # workdays:

    # - exactly 3 on day shift
    solver.Add(day_stat[j, day_shift] == 3)
    # - exactly 2 on night
    solver.Add(day_stat[j, night_shift] == 2)
    # - exactly 1 off duty
    solver.Add(day_stat[j, off_shift] == 2)

#
# solution and search
#
db = solver.Phase(day_stat_flat + x_flat + nurse_stat,
                  solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)

solver.NewSearch(db)

num_solutions = 0
while solver.NextSolution():
  num_solutions += 1

  for i in range(num_nurses):
    print('Nurse%i: ' % i, end=' ')
    this_day_stat = defaultdict(int)
    for j in range(num_days):
      d = days[x[i, j].Value() - 1]
      this_day_stat[d] += 1
      print(d, end=' ')
    print(
        ' day_stat:', [(d, this_day_stat[d]) for d in this_day_stat], end=' ')
    print('total:', nurse_stat[i].Value(), 'workdays')
  print()

  print('Statistics per day:')
  for j in range(num_days):
    print('Day%2i: ' % j, end=' ')
    for t in shifts:
      print(day_stat[j, t].Value(), end=' ')
    print()
  print()

  # We just show 2 solutions
  if num_solutions >= 2:
    break

solver.EndSearch()
print()
print('num_solutions:', num_solutions)
print('failures:', solver.Failures())
print('branches:', solver.Branches())
print('WallTime:', solver.WallTime(), 'ms')