-
Notifications
You must be signed in to change notification settings - Fork 2.4k
Expand file tree
/
Copy pathflow_api.cc
More file actions
96 lines (87 loc) · 3.68 KB
/
flow_api.cc
File metadata and controls
96 lines (87 loc) · 3.68 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
// Copyright 2010-2025 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.
#include <cstdlib>
#include "ortools/base/init_google.h"
#include "ortools/base/logging.h"
#include "ortools/graph/generic_max_flow.h"
#include "ortools/graph/graph.h"
#include "ortools/graph/min_cost_flow.h"
namespace operations_research {
using Graph = ::util::ReverseArcListGraph<>;
using NodeIndex = Graph::NodeIndex;
using ArcIndex = Graph::ArcIndex;
using CostValue = GenericMinCostFlow<Graph>::CostValue;
using FlowQuantity = GenericMinCostFlow<Graph>::FlowQuantity;
// ----- Min Cost Flow -----
// Test on a 4x4 matrix. Example taken from
// http://www.ee.oulu.fi/~mpa/matreng/eem1_2-1.htm
void MinCostFlowOn4x4Matrix() {
LOG(INFO) << "Min Cost Flow on 4x4 Matrix";
const int kNumSources = 4;
const int kNumTargets = 4;
const CostValue kCost[kNumSources][kNumTargets] = {{90, 75, 75, 80},
{35, 85, 55, 65},
{125, 95, 90, 105},
{45, 110, 95, 115}};
const CostValue kExpectedCost = 275;
Graph graph(kNumSources + kNumTargets, kNumSources * kNumTargets);
GenericMinCostFlow<Graph> min_cost_flow(&graph);
for (NodeIndex source = 0; source < kNumSources; ++source) {
for (NodeIndex target = 0; target < kNumTargets; ++target) {
ArcIndex arc = graph.AddArc(source, kNumSources + target);
min_cost_flow.SetArcUnitCost(arc, kCost[source][target]);
min_cost_flow.SetArcCapacity(arc, 1);
}
}
for (NodeIndex source = 0; source < kNumSources; ++source) {
min_cost_flow.SetNodeSupply(source, 1);
}
for (NodeIndex target = 0; target < kNumTargets; ++target) {
min_cost_flow.SetNodeSupply(kNumSources + target, -1);
}
CHECK(min_cost_flow.Solve());
CHECK_EQ(GenericMinCostFlow<Graph>::OPTIMAL, min_cost_flow.status());
CostValue total_flow_cost = min_cost_flow.GetOptimalCost();
CHECK_EQ(kExpectedCost, total_flow_cost);
}
// ----- Max Flow -----
void MaxFeasibleFlow() {
LOG(INFO) << "Max Feasible Flow";
const int kNumNodes = 6;
const int kNumArcs = 9;
const NodeIndex kTail[kNumArcs] = {0, 0, 0, 0, 1, 2, 3, 3, 4};
const NodeIndex kHead[kNumArcs] = {1, 2, 3, 4, 3, 4, 4, 5, 5};
const FlowQuantity kCapacity[kNumArcs] = {5, 8, 5, 3, 4, 5, 6, 6, 4};
const FlowQuantity kExpectedFlow[kNumArcs] = {1, 1, 5, 3, 1, 1, 0, 6, 4};
const FlowQuantity kExpectedTotalFlow = 10;
Graph graph(kNumNodes, kNumArcs);
GenericMaxFlow<Graph> max_flow(&graph, 0, kNumNodes - 1);
for (int i = 0; i < kNumArcs; ++i) {
ArcIndex arc = graph.AddArc(kTail[i], kHead[i]);
max_flow.SetArcCapacity(arc, kCapacity[i]);
}
CHECK(max_flow.Solve());
CHECK_EQ(MaxFlowStatusClass::OPTIMAL, max_flow.status());
FlowQuantity total_flow = max_flow.GetOptimalFlow();
CHECK_EQ(total_flow, kExpectedTotalFlow);
for (int i = 0; i < kNumArcs; ++i) {
CHECK_EQ(kExpectedFlow[i], max_flow.Flow(i)) << " i = " << i;
}
}
} // namespace operations_research
int main(int argc, char** argv) {
InitGoogle(argv[0], &argc, &argv, true);
operations_research::MinCostFlowOn4x4Matrix();
operations_research::MaxFeasibleFlow();
return EXIT_SUCCESS;
}