text: #   Copyright 2010 Pierre Schaus pschaus@gmail.com, lperron@google.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.
  
  import argparse
  from ortools.constraint_solver import pywrapcp
  
  parser = argparse.ArgumentParser()
  parser.add_argument('--data', default = 'data/steel_mill/steel_mill_slab.txt',
                      help = 'path to data file')
  parser.add_argument('--time_limit', default = 20000, type = int,
                      help = 'global time limit')
  
  #----------------helper for binpacking posting----------------
  
  
  def BinPacking(solver, binvars, weights, loadvars):
    '''post the load constraint on bins.
  
    constraints forall j: loadvars[j] == sum_i (binvars[i] == j) * weights[i])
    '''
    pack = solver.Pack(binvars, len(binvars))
    pack.AddWeightedSumEqualVarDimension(weights, loadvars)
    solver.Add(pack)
    solver.Add(solver.SumEquality(loadvars, sum(weights)))
  
  #------------------------------data reading-------------------
  
  
  def ReadData(filename):
    """Read data from <filename>."""
    f = open(filename)
    capacity = [int(nb) for nb in f.readline().split()]
    capacity.pop(0)
    capacity = [0] + capacity
    max_capacity = max(capacity)
    nb_colors = int(f.readline())
    nb_slabs = int(f.readline())
    wc = [[int(j) for j in f.readline().split()] for i in range(nb_slabs)]
    weights = [x[0] for x in wc]
    colors = [x[1] for x in wc]
    loss = [min(filter(lambda x: x >= c, capacity)) - c
            for c in range(max_capacity + 1)]
    color_orders = [filter(lambda o: colors[o] == c, range(nb_slabs))
                    for c in range(1, nb_colors + 1)]
    print 'Solving steel mill with', nb_slabs, 'slabs'
    return (nb_slabs, capacity, max_capacity, weights, colors, loss, color_orders)
  
  #------------------dedicated search for this problem-----------
  
  
  class SteelDecisionBuilder(pywrapcp.PyDecisionBuilder):
    '''Dedicated Decision Builder for steel mill slab.
  
    Search for the steel mill slab problem with Dynamic Symmetry
    Breaking during search is an adaptation (for binary tree) from the
    paper of Pascal Van Hentenryck and Laurent Michel CPAIOR-2008.
  
    The value heuristic comes from the paper
    Solving Steel Mill Slab Problems with Constraint-Based Techniques:
      CP, LNS, and CBLS,
    Schaus et. al. to appear in Constraints 2010
    '''
  
    def __init__(self, x, nb_slabs, weights, losstab, loads):
      pywrapcp.PyDecisionBuilder.__init__(self)
      self.__x = x
      self.__nb_slabs = nb_slabs
      self.__weights = weights
      self.__losstab = losstab
      self.__loads = loads
      self.__maxcapa = len(losstab) - 1
  
    def Next(self, solver):
      var, weight = self.NextVar()
      if var:
        v = self.MaxBound()
        if v + 1 == var.Min():
          # Symmetry breaking. If you need to assign to a new bin,
          # select the first one.
          solver.Add(var == v + 1)
          return self.Next(solver)
        else:
          # value heuristic (important for difficult problem):
          #   try first to place the order in the slab that will induce
          #   the least increase of the loss
          loads = self.getLoads()
          l, v = min((self.__losstab[loads[i] + weight], i)
                     for i in range(var.Min(), var.Max() + 1)
                     if var.Contains(i) and loads[i] + weight <= self.__maxcapa)
          decision = solver.AssignVariableValue(var, v)
          return decision
      else:
        return None
  
    def getLoads(self):
      load = [0] * len(self.__loads)
      for w, x in zip(self.__weights, self.__x):
        if x.Bound():
          load[x.Min()] += w
      return load
  
    def MaxBound(self):
      """ returns the max value bound to a variable, -1 if no variables bound"""
      return max([-1] + [self.__x[o].Min()
                         for o in range(self.__nb_slabs)
                         if self.__x[o].Bound()])
  
    def NextVar(self):
      """ mindom size heuristic with tie break on the weights of orders """
      res = [(self.__x[o].Size(), -self.__weights[o], self.__x[o])
             for o in range(self.__nb_slabs)
             if self.__x[o].Size() > 1]
      if res:
        res.sort()
        return res[0][2], -res[0][1]  # returns the order var and its weight
      else:
        return None, None
  
    def DebugString(self):
      return 'SteelMillDecisionBuilder(' + str(self.__x) + ')'
  
  
  def main(args):
    #------------------solver and variable declaration-------------
    (nb_slabs, capacity, max_capacity, weights, colors, loss, color_orders) =\
        ReadData(args.data)
    nb_colors = len(color_orders)
    solver = pywrapcp.Solver('Steel Mill Slab')
    x = [solver.IntVar(0, nb_slabs - 1, 'x' + str(i))
         for i in range(nb_slabs)]
    load_vars = [solver.IntVar(0, max_capacity - 1, 'load_vars' + str(i))
                 for i in range(nb_slabs)]
  
    #-------------------post of the constraints--------------
  
    # Bin Packing.
    BinPacking(solver, x, weights, load_vars)
    # At most two colors per slab.
    for s in range(nb_slabs):
      solver.Add(solver.SumLessOrEqual(
          [solver.Max([solver.IsEqualCstVar(x[c], s) for c in o])
           for o in color_orders], 2))
  
    #----------------Objective-------------------------------
  
    objective_var = \
        solver.Sum([load_vars[s].IndexOf(loss) for s in range(nb_slabs)]).Var()
    objective = solver.Minimize(objective_var, 1)
  
    #------------start the search and optimization-----------
  
    db = SteelDecisionBuilder(x, nb_slabs, weights, loss, load_vars)
    search_log = solver.SearchLog(100000, objective_var)
    global_limit = solver.TimeLimit(args.time_limit)
    solver.NewSearch(db, [objective, search_log, global_limit])
    while solver.NextSolution():
      print 'Objective:', objective_var.Value(),\
          'check:', sum(loss[load_vars[s].Min()] for s in range(nb_slabs))
    solver.EndSearch()
  
  
  if __name__ == '__main__':
    main(parser.parse_args())
  