# Copyright 2011 Hakan Kjellerstrand hakank@bonetmail.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.

"""

  3 jugs problem using MIP in Google or-tools.

  A.k.a. water jugs problem.

  Problem from Taha 'Introduction to Operations Research',
  page 245f .

  Compare with the CP model:
     http://www.hakank.org/google_or_tools/3_jugs_regular

  This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
  Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
"""
import sys
from linear_solver import pywraplp

def main(sol = 'GLPK'):

  # Create the solver.

  print 'Solver: ', sol

  # using GLPK
  if sol == 'GLPK':
    solver = pywraplp.Solver('CoinsGridGLPK',
                             pywraplp.Solver.GLPK_MIXED_INTEGER_PROGRAMMING)
  else:
  # Using CLP
      solver = pywraplp.Solver('CoinsGridCLP',
                               pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)


  #
  # data
  #
  n = 15
  start = 0 # start node
  end = 14  # end node
  M = 999   # a large number

  nodes = ['8,0,0', # start
           '5,0,3',
           '5,3,0',
           '2,3,3',
           '2,5,1',
           '7,0,1',
           '7,1,0',
           '4,1,3',
           '3,5,0',
           '3,2,3',
           '6,2,0',
           '6,0,2',
           '1,5,2',
           '1,4,3',
           '4,4,0'  # goal!
          ]

  # distance
  d = [[M, 1, M, M, M, M, M, M, 1, M, M, M, M, M, M],
       [M, M, 1, M, M, M, M, M, M, M, M, M, M, M, M],
       [M, M, M, 1, M, M, M, M, 1, M, M, M, M, M, M],
       [M, M, M, M, 1, M, M, M, M, M, M, M, M, M, M],
       [M, M, M, M, M, 1, M, M, 1, M, M, M, M, M, M],
       [M, M, M, M, M, M, 1, M, M, M, M, M, M, M, M],
       [M, M, M, M, M, M, M, 1, 1, M, M, M, M, M, M],
       [M, M, M, M, M, M, M, M, M, M, M, M, M, M, 1],
       [M, M, M, M, M, M, M, M, M, 1, M, M, M, M, M],
       [M, 1, M, M, M, M, M, M, M, M, 1, M, M, M, M],
       [M, M, M, M, M, M, M, M, M, M, M, 1, M, M, M],
       [M, 1, M, M, M, M, M, M, M, M, M, M, 1, M, M],
       [M, M, M, M, M, M, M, M, M, M, M, M, M, 1, M],
       [M, 1, M, M, M, M, M, M, M, M, M, M, M, M, 1],
       [M, M, M, M, M, M, M, M, M, M, M, M, M, M, M]]


  #
  # variables
  #

  # requirements (right hand statement)
  rhs = [solver.IntVar(-1, 1, 'rhs[%i]' % i) for i in range(n)]

  x = {}
  for i in range(n):
    for j in range(n):
        x[i,j] = solver.IntVar(0, 1, 'x[%i,%i]' % (i, j))

  out_flow = [solver.IntVar(0, 1, 'out_flow[%i]' % i) for i in range(n)]
  in_flow = [solver.IntVar(0, 1, 'in_flow[%i]' % i) for i in range(n)]

  # length of path, to be minimized
  z = solver.Sum([d[i][j]*x[i,j]
                               for i in range(n)
                               for j in range(n) if d[i][j] < M])

  #
  # constraints
  #


  for i in range(n):
    if i == start:
      solver.Add(rhs[i] == 1)
    elif i == end:
      solver.Add(rhs[i] == -1)
    else:
      solver.Add(rhs[i] == 0)


  # outflow constraint
  for i in range(n):
    solver.Add(out_flow[i] == solver.Sum([x[i,j]
                                          for j in range(n)
                                          if d[i][j] < M]))

  # inflow constraint
  for j in range(n):
    solver.Add(in_flow[j] == solver.Sum([x[i,j]
                                         for i in range(n)
                                         if d[i][j] < M]))

  # inflow = outflow
  for i in range(n):
     solver.Add(out_flow[i]-in_flow[i] == rhs[i])


  # objective
  objective = solver.Minimize(z)


  #
  # solution and search
  #
  solver.Solve()

  print
  print 'z: ', int(solver.ObjectiveValue())

  t = start
  while t != end:
    print nodes[t], '->',
    for j in range(n):
      if x[t,j].SolutionValue() == 1:
        print nodes[j]
        t = j
        break

  print
  print 'walltime  :', solver.WallTime(), 'ms'
  if sol == 'CBC':
    print 'iterations:', solver.Iterations()


if __name__ == '__main__':

  sol = 'GLPK'
  if len(sys.argv) > 1:
    sol = sys.argv[1]
    if sol != 'GLPK' and sol != 'CBC':
      print 'Solver must be either GLPK or CBC'
      sys.exit(1)

  main(sol)