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# Copyright 2010-2018 Google LLC
# 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.
# [START program]
"""From Bradley, H. and M., 'Applied Mathematical Programming', figure 8.1."""
# [START import]
from __future__ import print_function
from ortools.graph import pywrapgraph
# [END import]


"""MinCostFlow simple interface example."""
# [START data]
# Define four parallel arrays: sources, destinations, capacities,
# and unit costs between each pair. For instance, the arc from node 0
# to node 1 has a capacity of 15.
start_nodes = [0, 0, 1, 1, 1, 2, 2, 3, 4]
end_nodes = [1, 2, 2, 3, 4, 3, 4, 4, 2]
capacities = [15, 8, 20, 4, 10, 15, 4, 20, 5]
unit_costs = [4, 4, 2, 2, 6, 1, 3, 2, 3]

# Define an array of supplies at each node.
supplies = [20, 0, 0, -5, -15]
# [END data]

# [START constraints]
# Instantiate a SimpleMinCostFlow solver.
min_cost_flow = pywrapgraph.SimpleMinCostFlow()

# Add each arc.
for arc in zip(start_nodes, end_nodes, capacities, unit_costs):
    min_cost_flow.AddArcWithCapacityAndUnitCost(arc[0], arc[1], arc[2],
                                                arc[3])

# Add node supplies.
for count, supply in enumerate(supplies):
    min_cost_flow.SetNodeSupply(count, supply)
# [END constraints]

# [START solve]
# Find the min cost flow.
solve_status = min_cost_flow.Solve()
# [END solve]

# [START print_solution]
if solve_status == min_cost_flow.OPTIMAL:
    print('Minimum cost: ', min_cost_flow.OptimalCost())
    print('')
    print(' Arc   Flow / Capacity  Cost')
    for i in range(min_cost_flow.NumArcs()):
        cost = min_cost_flow.Flow(i) * min_cost_flow.UnitCost(i)
        print('%1s -> %1s    %3s   / %3s   %3s' %
              (min_cost_flow.Tail(i), min_cost_flow.Head(i),
               min_cost_flow.Flow(i), min_cost_flow.Capacity(i), cost))
else:
    print('Solving the min cost flow problem failed. Solver status: ',
          solve_status)
# [END print_solution]