public void ArgumentExceptionInAddEdge()
{
var fg = new FlowGraph(2);
Assert.Throws <ArgumentException>(() => fg.AddEdge(0, 0, -1));
Assert.Throws <ArgumentException>(() => fg.AddEdge(0, 0, 0, -1));
}
/// <summary>
/// Berechnet zu einem Flussgraphen den Residual-Graphen.
/// </summary>
/// <typeparam name="T">Der Datentyp des Graphen.</typeparam>
/// <param name="graph">Der Graph.</param>
/// <returns>Der Residualgraph.</returns>
public static FlowGraph <T> GetResidualGraph <T> (this FlowGraph <T> graph)
{
if (graph.Edges.Where(e => !e.Capacity.HasValue).Any())
{
throw new ArgumentException("In dem Graphen muss für jede Kante eine Kapazität definiert sein.");
}
// Sicherstellen, dass der Fluss bei allen Kanten initialisiert ist.
foreach (Edge <T> e in graph.Edges.Where(e => !e.Flow.HasValue))
{
e.Flow = 0;
}
FlowGraph <T> residualGraph = new FlowGraph <T>(graph.Source.Value, graph.Target.Value, graph.Vertices.Select(v => v.Value), isDirected: true);
foreach (Edge <T> e in graph.Edges)
{
if ((e.Capacity - e.Flow) > 0)
{
residualGraph.AddEdge(e.From, e.To, capacity: e.Capacity.Value, flow: e.Capacity.Value - e.Flow.Value);
}
if (e.Flow > 0)
{
residualGraph.AddEdge(e.To, e.From, capacity: e.Capacity.Value, flow: e.Flow.Value * (-1));
}
}
return(residualGraph);
}
public void MaxFlowTwiceTest()
{
var fg = new FlowGraph(3);
Assert.That(fg.AddEdge(0, 1, 1), Is.Zero);
Assert.That(fg.AddEdge(0, 2, 1), Is.EqualTo(1));
Assert.That(fg.AddEdge(1, 2, 1), Is.EqualTo(2));
Assert.That(fg.MaxFlow(0, 2), Is.EqualTo(2));
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, 2, 1, 1)));
Assert.That(fg.GetEdge(2), Is.EqualTo(new FlowGraph.Edge(1, 2, 1, 1)));
fg.ChangeEdge(0, 100, 10);
Assert.That(fg.GetEdge(0), Is.EqualTo(new FlowGraph.Edge(0, 1, 100, 10)));
Assert.That(fg.MaxFlow(0, 2), Is.Zero);
Assert.That(fg.MaxFlow(0, 1), Is.EqualTo(90));
Assert.That(fg.GetEdge(0), Is.EqualTo(new FlowGraph.Edge(0, 1, 100, 100)));
Assert.That(fg.GetEdge(1), Is.EqualTo(new FlowGraph.Edge(0, 2, 1, 1)));
Assert.That(fg.GetEdge(2), Is.EqualTo(new FlowGraph.Edge(1, 2, 1, 1)));
Assert.That(fg.MaxFlow(2, 0), Is.EqualTo(2));
Assert.That(fg.GetEdge(0), Is.EqualTo(new FlowGraph.Edge(0, 1, 100, 99)));
Assert.That(fg.GetEdge(1), Is.EqualTo(new FlowGraph.Edge(0, 2, 1, 0)));
Assert.That(fg.GetEdge(2), Is.EqualTo(new FlowGraph.Edge(1, 2, 1, 0)));
}
public static void Solve()
{
var(N, G, E) = Scanner.Scan <int, int, int>();
if (G == 0)
{
Console.WriteLine(0); return;
}
var P = Scanner.ScanEnumerable <int>().ToArray();
var fg = new FlowGraph(N + 1);
foreach (var p in P)
{
fg.AddEdge(p, N, 1);
}
for (var i = 0; i < E; i++)
{
var(a, b) = Scanner.Scan <int, int>();
fg.AddEdge(a, b, 1);
fg.AddEdge(b, a, 1);
}
var answer = fg.MaxFlow(0, N);
Console.WriteLine(answer);
}
public void ArgumentOutOfRangeExceptionInChangeEdge([Values(-1, 3)] int v)
{
var fg = new FlowGraph(3);
fg.AddEdge(0, 1, 100);
fg.AddEdge(1, 2, 100);
Assert.Throws <ArgumentOutOfRangeException>(() => fg.ChangeEdge(v, 100, 10));
}
public void ArgumentExceptionInChangeEdge([Values(-10, 100)] int newFlow)
{
var fg = new FlowGraph(3);
fg.AddEdge(0, 1, 100);
fg.AddEdge(1, 2, 100);
Assert.Throws <ArgumentException>(() => fg.ChangeEdge(1, 10, newFlow));
}
public void ArgumentOutOfRangeExceptionInMaxFlow(int u, int v)
{
var fg = new FlowGraph(3);
fg.AddEdge(0, 1, 100);
fg.AddEdge(1, 2, 100);
Assert.Throws <ArgumentOutOfRangeException>(() => fg.MaxFlow(u, v));
}
public void ArgumentOutOfRangeExceptionInAddEdgeAndGetEdge([Values(-1, 3)] int v)
{
var fg = new FlowGraph(3);
Assert.Throws <ArgumentOutOfRangeException>(() => fg.AddEdge(v, 1, 10));
Assert.Throws <ArgumentOutOfRangeException>(() => fg.AddEdge(0, v, 10));
Assert.Throws <ArgumentOutOfRangeException>(() => fg.GetEdge(v));
}
public void ArgumentExceptionInMaxFlow()
{
var fg = new FlowGraph(3);
fg.AddEdge(0, 1, 100);
fg.AddEdge(1, 2, 100);
Assert.Throws <ArgumentException>(() => fg.MaxFlow(0, 0));
Assert.Throws <ArgumentException>(() => fg.MaxFlow(0, 0, 0));
}
public void MinCostFlowSameCostPathsTest()
{
var fg = new FlowGraph(3);
Assert.That(fg.AddEdge(0, 1, 1, 1), Is.Zero);
Assert.That(fg.AddEdge(1, 2, 1), Is.EqualTo(1));
Assert.That(fg.AddEdge(0, 2, 2, 1), Is.EqualTo(2));
var actual = fg.MinCostSlope(0, 2).ToArray();
Assert.That(actual[0], Is.EqualTo((0, 0)));
Assert.That(actual[1], Is.EqualTo((3, 3)));
}
public void MinCostFlowSelfLoopTest()
{
var fg = new FlowGraph(3);
Assert.That(fg.AddEdge(0, 0, 100, 123), Is.Zero);
Assert.That(fg.GetEdge(0), Is.EqualTo(new FlowGraph.Edge(0, 0, 100, 0, 123)));
}
public void MaxFlowSimpleTest()
{
var fg = new FlowGraph(4);
Assert.That(fg.AddEdge(0, 1, 1), Is.Zero);
Assert.That(fg.AddEdge(0, 2, 1), Is.EqualTo(1));
Assert.That(fg.AddEdge(1, 3, 1), Is.EqualTo(2));
Assert.That(fg.AddEdge(2, 3, 1), Is.EqualTo(3));
Assert.That(fg.AddEdge(1, 2, 1), Is.EqualTo(4));
Assert.That(fg.MaxFlow(0, 3), Is.EqualTo(2));
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, 2, 1, 1)));
Assert.That(fg.GetEdge(2), Is.EqualTo(new FlowGraph.Edge(1, 3, 1, 1)));
Assert.That(fg.GetEdge(3), Is.EqualTo(new FlowGraph.Edge(2, 3, 1, 1)));
Assert.That(fg.GetEdge(4), Is.EqualTo(new FlowGraph.Edge(1, 2, 1, 0)));
}
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 MinCostFlowSimpleTest()
{
var fg = new FlowGraph(4);
fg.AddEdge(0, 1, 1, 1);
fg.AddEdge(0, 2, 1, 1);
fg.AddEdge(1, 3, 1, 1);
fg.AddEdge(2, 3, 1, 1);
fg.AddEdge(1, 2, 1, 1);
var actual = fg.MinCostSlope(0, 3, 10).ToArray();
Assert.That(actual[0], Is.EqualTo((0, 0)));
Assert.That(actual[1], Is.EqualTo((2, 4)));
Assert.That(fg.GetEdge(0), Is.EqualTo(new FlowGraph.Edge(0, 1, 1, 1, 1)));
Assert.That(fg.GetEdge(1), Is.EqualTo(new FlowGraph.Edge(0, 2, 1, 1, 1)));
Assert.That(fg.GetEdge(2), Is.EqualTo(new FlowGraph.Edge(1, 3, 1, 1, 1)));
Assert.That(fg.GetEdge(3), Is.EqualTo(new FlowGraph.Edge(2, 3, 1, 1, 1)));
Assert.That(fg.GetEdge(4), Is.EqualTo(new FlowGraph.Edge(1, 2, 1, 0, 1)));
}
public static void Solve()
{
var NK = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();
var(N, K) = (NK[0], NK[1]);
var A = new long[N][].Select(x =>
Console.ReadLine().Split(" ").Select(long.Parse).ToArray())
.ToArray();
var fg = new FlowGraph(N * 2 + 2);
var s = N * 2;
var t = N * 2 + 1;
const long inf = (long)1e9;
fg.AddEdge(s, t, N * K, inf);
for (var i = 0; i < N; i++)
{
fg.AddEdge(s, i, K);
fg.AddEdge(N + i, t, K);
}
for (var i = 0; i < N; i++)
{
for (var j = 0; j < N; j++)
{
fg.AddEdge(i, N + j, 1, inf - A[i][j]);
}
}
var result = fg.MinCostFlow(s, t, N * K);
Console.WriteLine(inf * N * K - result.Item2);
var G = new char[N][].Select(x => Enumerable.Repeat('.', N).ToArray()).ToArray();
foreach (var edge in fg.GetEdges().Where(x => x.From != s && x.To != t && x.Flow != 0))
{
G[edge.From][edge.To - N] = 'X';
}
Console.WriteLine(string.Join("\n", G.Select(x => new string(x))));
}
public void UsageTest()
{
var fg = new FlowGraph(2);
fg.AddEdge(0, 1, 1, 2);
Assert.That(fg.MinCostFlow(0, 1), Is.EqualTo((1, 2)));
fg = new FlowGraph(2);
fg.AddEdge(0, 1, 1, 2);
var actual = fg.MinCostSlope(0, 1).ToArray();
Assert.That(actual[0], Is.EqualTo((0, 0)));
Assert.That(actual[1], Is.EqualTo((1, 2)));
}
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 Copy_must_work()
{
Vertex<string> source = new Vertex<string>("s");
Vertex<string> target = new Vertex<string>("t");
FlowGraph<string> flowGraph = new FlowGraph<string>(source, target, new List<Vertex<string>>() { source, target });
flowGraph.AddVertex("a");
flowGraph.AddVertex("b");
flowGraph.AddEdge("s", "a", 5, 2);
flowGraph.AddEdge("s", "b", 8, 4);
flowGraph.AddEdge("a", "b", 3, 0);
flowGraph.AddEdge("a", "t", 4, 2);
flowGraph.AddEdge("b", "t", 6, 4);
FlowGraph<string> flowGraphCopy = flowGraph.Copy();
Assert.IsFalse(ReferenceEquals(flowGraph.Vertices, flowGraphCopy.Vertices));
Assert.IsFalse(ReferenceEquals(flowGraph.Edges, flowGraphCopy.Edges));
Assert.IsFalse(ReferenceEquals(flowGraph.Vertices[0], flowGraphCopy.Vertices[0]));
Assert.IsFalse(ReferenceEquals(flowGraph.Edges[0], flowGraphCopy.Edges[0]));
}
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);
}
public void FordFulkerson_must_work()
{
// Quelle und Senke erstellen.
Vertex <string> source = new Vertex <string>("s");
Vertex <string> target = new Vertex <string>("t");
// alle weiteren Knoten des Graphens erstellen.
Vertex <string> vA = new Vertex <string>("a");
Vertex <string> vB = new Vertex <string>("b");
Vertex <string> vC = new Vertex <string>("c");
Vertex <string> vD = new Vertex <string>("d");
// Den Graphen erstellen.
FlowGraph <string> flowGraph = new FlowGraph <string>(source, target, new List <Vertex <string> >()
{
source, vA, vB, vC, vD, target
});
// Die Kanten des Graphens erstellen.
flowGraph.AddEdge("s", "a", capacity: 5, flow: 5);
flowGraph.AddEdge("s", "b", capacity: 7, flow: 3);
flowGraph.AddEdge("a", "b", capacity: 7, flow: 3);
flowGraph.AddEdge("a", "c", capacity: 4, flow: 2);
flowGraph.AddEdge("b", "c", capacity: 3, flow: 3);
flowGraph.AddEdge("b", "d", capacity: 3, flow: 3);
flowGraph.AddEdge("c", "d", capacity: 4, flow: 0);
flowGraph.AddEdge("c", "t", capacity: 5, flow: 5);
flowGraph.AddEdge("d", "t", capacity: 6, flow: 3);
FlowGraph <string> maxFlowGraph = flowGraph.FordFulkerson();
// Die Flüsse über die Kanten überprüfen.
Assert.AreEqual(5, maxFlowGraph.Edges[0].Flow);
Assert.AreEqual(5, maxFlowGraph.Edges[1].Flow);
Assert.AreEqual(1, maxFlowGraph.Edges[2].Flow);
Assert.AreEqual(4, maxFlowGraph.Edges[3].Flow);
Assert.AreEqual(3, maxFlowGraph.Edges[4].Flow);
Assert.AreEqual(3, maxFlowGraph.Edges[5].Flow);
Assert.AreEqual(2, maxFlowGraph.Edges[6].Flow);
Assert.AreEqual(5, maxFlowGraph.Edges[7].Flow);
Assert.AreEqual(5, maxFlowGraph.Edges[8].Flow);
// Die Kantenflüsse für den nächsten Test auf 0 setzen.
flowGraph.Edges.ForEach(e =>
{
e.Flow = 0;
});
maxFlowGraph = flowGraph.FordFulkerson();
// Die Flüsse über die Kanten überprüfen.
Assert.AreEqual(4, maxFlowGraph.Edges[0].Flow);
Assert.AreEqual(6, maxFlowGraph.Edges[1].Flow);
Assert.AreEqual(0, maxFlowGraph.Edges[2].Flow);
Assert.AreEqual(4, maxFlowGraph.Edges[3].Flow);
Assert.AreEqual(3, maxFlowGraph.Edges[4].Flow);
Assert.AreEqual(3, maxFlowGraph.Edges[5].Flow);
Assert.AreEqual(2, maxFlowGraph.Edges[6].Flow);
Assert.AreEqual(5, maxFlowGraph.Edges[7].Flow);
Assert.AreEqual(5, maxFlowGraph.Edges[8].Flow);
}
public void MinCostFlowStressTest()
{
for (var ph = 0; ph < 1000; 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 mfg = new FlowGraph(n);
var mcfg = 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 cap = Utilities.RandomInteger(0, 10);
var cost = Utilities.RandomInteger(0, 10000);
mcfg.AddEdge(u, v, cap, cost);
mfg.AddEdge(u, v, cap);
}
var(flow, cost1) = mcfg.MinCostFlow(s, t);
Assert.That(flow, Is.EqualTo(mfg.MaxFlow(s, t)));
var cost2 = 0L;
var capacities = new long[n];
foreach (var edge in mcfg.GetEdges())
{
capacities[edge.From] -= edge.Flow;
capacities[edge.To] += edge.Flow;
cost2 += edge.Flow * edge.Cost;
}
Assert.That(cost1, Is.EqualTo(cost2));
for (var i = 0; i < n; i++)
{
if (i == s)
{
Assert.That(capacities[i], Is.EqualTo(-flow));
}
else if (i == t)
{
Assert.That(capacities[i], Is.EqualTo(flow));
}
else
{
Assert.That(capacities[i], Is.EqualTo(0));
}
}
Assert.DoesNotThrow(() =>
{
var dist = new long[n];
while (true)
{
var update = false;
foreach (var edge in mcfg.GetEdges())
{
if (edge.Flow < edge.Capacity)
{
var ndist = dist[edge.From] + edge.Cost;
if (ndist < dist[edge.To])
{
update = true;
dist[edge.To] = ndist;
}
}
if (edge.Flow == 0)
{
continue;
}
{
var ndist = dist[edge.To] - edge.Cost;
if (ndist < dist[edge.From])
{
update = true;
dist[edge.From] = ndist;
}
}
}
if (!update)
{
break;
}
}
});
}
}
public void GetResidualGraph_must_work()
{
// Quelle und Senke erstellen.
Vertex <string> source = new Vertex <string>("s");
Vertex <string> target = new Vertex <string>("t");
// alle weiteren Knoten des Graphens erstellen.
Vertex <string> vA = new Vertex <string>("a");
Vertex <string> vB = new Vertex <string>("b");
Vertex <string> vC = new Vertex <string>("c");
Vertex <string> vD = new Vertex <string>("d");
// Den Graphen erstellen.
FlowGraph <string> flowGraph = new FlowGraph <string>(source, target, new List <Vertex <string> >()
{
source, vA, vB, vC, vD, target
});
// Die Kanten des Graphens erstellen.
flowGraph.AddEdge("s", "a", capacity: 5, flow: 5);
flowGraph.AddEdge("s", "b", capacity: 7, flow: 3);
flowGraph.AddEdge("a", "b", capacity: 7, flow: 3);
flowGraph.AddEdge("a", "c", capacity: 4, flow: 2);
flowGraph.AddEdge("b", "c", capacity: 3, flow: 3);
flowGraph.AddEdge("b", "d", capacity: 3, flow: 3);
flowGraph.AddEdge("c", "d", capacity: 4, flow: 0);
flowGraph.AddEdge("c", "t", capacity: 5, flow: 5);
flowGraph.AddEdge("d", "t", capacity: 6, flow: 3);
FlowGraph <string> residualGraph = flowGraph.GetResidualGraph();
// Die Kanten überprüfen
Assert.AreEqual(13, residualGraph.Edges.Count);
// a --> s
Assert.AreEqual(vA, residualGraph.Edges[0].From);
Assert.AreEqual(source, residualGraph.Edges[0].To);
Assert.AreEqual(5, residualGraph.Edges[0].Capacity);
Assert.AreEqual(-5, residualGraph.Edges[0].Flow);
// s --> b
Assert.AreEqual(source, residualGraph.Edges[1].From);
Assert.AreEqual(vB, residualGraph.Edges[1].To);
Assert.AreEqual(7, residualGraph.Edges[1].Capacity);
Assert.AreEqual(4, residualGraph.Edges[1].Flow);
// b --> s
Assert.AreEqual(vB, residualGraph.Edges[2].From);
Assert.AreEqual(source, residualGraph.Edges[2].To);
Assert.AreEqual(7, residualGraph.Edges[2].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[2].Flow);
// a --> b
Assert.AreEqual(vA, residualGraph.Edges[3].From);
Assert.AreEqual(vB, residualGraph.Edges[3].To);
Assert.AreEqual(7, residualGraph.Edges[3].Capacity);
Assert.AreEqual(4, residualGraph.Edges[3].Flow);
// b --> a
Assert.AreEqual(vB, residualGraph.Edges[4].From);
Assert.AreEqual(vA, residualGraph.Edges[4].To);
Assert.AreEqual(7, residualGraph.Edges[4].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[4].Flow);
// a --> c
Assert.AreEqual(vA, residualGraph.Edges[5].From);
Assert.AreEqual(vC, residualGraph.Edges[5].To);
Assert.AreEqual(4, residualGraph.Edges[5].Capacity);
Assert.AreEqual(2, residualGraph.Edges[5].Flow);
// c --> a
Assert.AreEqual(vC, residualGraph.Edges[6].From);
Assert.AreEqual(vA, residualGraph.Edges[6].To);
Assert.AreEqual(4, residualGraph.Edges[6].Capacity);
Assert.AreEqual(-2, residualGraph.Edges[6].Flow);
// c --> b
Assert.AreEqual(vC, residualGraph.Edges[7].From);
Assert.AreEqual(vB, residualGraph.Edges[7].To);
Assert.AreEqual(3, residualGraph.Edges[7].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[7].Flow);
// d --> b
Assert.AreEqual(vD, residualGraph.Edges[8].From);
Assert.AreEqual(vB, residualGraph.Edges[8].To);
Assert.AreEqual(3, residualGraph.Edges[8].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[8].Flow);
// c --> d
Assert.AreEqual(vC, residualGraph.Edges[9].From);
Assert.AreEqual(vD, residualGraph.Edges[9].To);
Assert.AreEqual(4, residualGraph.Edges[9].Capacity);
Assert.AreEqual(4, residualGraph.Edges[9].Flow);
// t --> c
Assert.AreEqual(target, residualGraph.Edges[10].From);
Assert.AreEqual(vC, residualGraph.Edges[10].To);
Assert.AreEqual(5, residualGraph.Edges[10].Capacity);
Assert.AreEqual(-5, residualGraph.Edges[10].Flow);
// d --> t
Assert.AreEqual(vD, residualGraph.Edges[11].From);
Assert.AreEqual(target, residualGraph.Edges[11].To);
Assert.AreEqual(6, residualGraph.Edges[11].Capacity);
Assert.AreEqual(3, residualGraph.Edges[11].Flow);
// t --> d
Assert.AreEqual(target, residualGraph.Edges[12].From);
Assert.AreEqual(vD, residualGraph.Edges[12].To);
Assert.AreEqual(6, residualGraph.Edges[12].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[12].Flow);
}
public static void Solve()
{
var NM = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();
var(N, M) = (NM[0], NM[1]);
var G = new char[N][].Select(x => Console.ReadLine().ToCharArray()).ToArray();
var fg = new FlowGraph(N * M + 2);
var s = N * M;
var t = N * M + 1;
for (var i = 0; i < N; i++)
{
for (var j = 0; j < M; j++)
{
if (G[i][j] == '#')
{
continue;
}
var v = i * M + j;
if ((i + j) % 2 == 0)
{
fg.AddEdge(s, v, 1);
}
else
{
fg.AddEdge(v, t, 1);
}
}
}
var di = new[] { -1, 0, 1, 0 };
var dj = new[] { 0, -1, 0, 1 };
for (var i = 0; i < N; i++)
{
for (var j = 0; j < M; j++)
{
if ((i + j) % 2 == 1 || G[i][j] == '#')
{
continue;
}
var v0 = i * M + j;
for (var k = 0; k < 4; k++)
{
var ci = i + di[k];
var cj = j + dj[k];
if (ci < 0 || N <= ci)
{
continue;
}
if (cj < 0 || M <= cj)
{
continue;
}
if (G[ci][cj] != '.')
{
continue;
}
var v1 = ci * M + cj;
fg.AddEdge(v0, v1, 1);
}
}
}
Console.WriteLine(fg.MaxFlow(s, t));
foreach (var edge in fg.GetEdges().Where(x => x.From != s && x.To != t && x.Flow != 0))
{
var(i0, j0) = (edge.From / M, edge.From % M);
var(i1, j1) = (edge.To / M, edge.To % M);
if (i0 == i1 + 1)
{
G[i1][j1] = 'v';
G[i0][j0] = '^';
}
else if (j0 == j1 + 1)
{
G[i1][j1] = '>';
G[i0][j0] = '<';
}
else if (i0 == i1 - 1)
{
G[i0][j0] = 'v';
G[i1][j1] = '^';
}
else
{
G[i0][j0] = '>';
G[i1][j1] = '<';
}
}
Console.WriteLine(string.Join("\n", G.Select(x => new string(x))));
}