public void MaxFlowStressTest()
{
for (var ph = 0; ph < 10000; ph++)
{
var n = Utilities.RandomInteger(2, 20);
var m = Utilities.RandomInteger(1, 100);
var(s, t) = Utilities.RandomPair(0, n - 1);
if (Utilities.RandomBool())
{
(s, t) = (t, s);
}
var fg = new FlowGraph(n);
for (var i = 0; i < m; i++)
{
var u = Utilities.RandomInteger(0, n - 1);
var v = Utilities.RandomInteger(0, n - 1);
var c = Utilities.RandomInteger(0, 10000);
fg.AddEdge(u, v, c);
}
var flow = fg.MaxFlow(s, t);
var dual = 0L;
var minCut = fg.MinCut(s);
var flows = new long[n];
foreach (var edge in fg.GetEdges())
{
flows[edge.From] -= edge.Flow;
flows[edge.To] += edge.Flow;
if (minCut[edge.From] && !minCut[edge.To])
{
dual += edge.Capacity;
}
}
Assert.That(dual, Is.EqualTo(flow));
Assert.That(flows[s], Is.EqualTo(-flow));
Assert.That(flows[t], Is.EqualTo(flow));
for (var i = 0; i < n; i++)
{
if (i == s || i == t)
{
continue;
}
Assert.That(flows[i], Is.Zero);
}
}
}
public void MaxFlowMinCutTest()
{
var fg = new FlowGraph(3);
Assert.That(fg.AddEdge(0, 1, 2), Is.Zero);
Assert.That(fg.AddEdge(1, 2, 1), Is.EqualTo(1));
Assert.That(fg.MaxFlow(0, 2), Is.EqualTo(1));
Assert.That(fg.GetEdge(0), Is.EqualTo(new FlowGraph.Edge(0, 1, 2, 1)));
Assert.That(fg.GetEdge(1), Is.EqualTo(new FlowGraph.Edge(1, 2, 1, 1)));
var minCut = fg.MinCut(0);
Assert.That(minCut[0], Is.True);
Assert.That(minCut[1], Is.True);
Assert.That(minCut[2], Is.False);
}
public void MaxFlowComplexTest()
{
var fg = new FlowGraph(2);
Assert.That(fg.AddEdge(0, 1, 1), Is.Zero);
Assert.That(fg.AddEdge(0, 1, 2), Is.EqualTo(1));
Assert.That(fg.AddEdge(0, 1, 3), Is.EqualTo(2));
Assert.That(fg.AddEdge(0, 1, 4), Is.EqualTo(3));
Assert.That(fg.AddEdge(0, 1, 5), Is.EqualTo(4));
Assert.That(fg.AddEdge(0, 0, 6), Is.EqualTo(5));
Assert.That(fg.AddEdge(1, 1, 7), Is.EqualTo(6));
Assert.That(fg.MaxFlow(0, 1), Is.EqualTo(15));
Assert.That(fg.GetEdge(0), Is.EqualTo(new FlowGraph.Edge(0, 1, 1, 1)));
Assert.That(fg.GetEdge(1), Is.EqualTo(new FlowGraph.Edge(0, 1, 2, 2)));
Assert.That(fg.GetEdge(2), Is.EqualTo(new FlowGraph.Edge(0, 1, 3, 3)));
Assert.That(fg.GetEdge(3), Is.EqualTo(new FlowGraph.Edge(0, 1, 4, 4)));
Assert.That(fg.GetEdge(4), Is.EqualTo(new FlowGraph.Edge(0, 1, 5, 5)));
var minCut = fg.MinCut(0);
Assert.That(minCut[0], Is.True);
Assert.That(minCut[1], Is.False);
}