public void Invalid()
{
var g = new MfGraphInt(2);
g.Invoking(g => g.Flow(0, 2)).Should().ThrowContractAssert();
g.Invoking(g => g.Flow(2, 0)).Should().ThrowContractAssert();
g.Invoking(g => g.Flow(2, 0, 0)).Should().ThrowContractAssert();
g.Invoking(g => g.Flow(0, 2, 0)).Should().ThrowContractAssert();
g.Invoking(g => g.Flow(0, 0)).Should().ThrowContractAssert();
g.Invoking(g => g.Flow(0, 0, 0)).Should().ThrowContractAssert();
g.Invoking(g => g.Flow(0, 1)).Should().NotThrow();
g.Invoking(g => g.Flow(1, 0, 1)).Should().NotThrow();
g.Invoking(g => g.AddEdge(0, 2, 0)).Should().ThrowContractAssert();
g.Invoking(g => g.AddEdge(2, 0, 0)).Should().ThrowContractAssert();
g.Invoking(g => g.AddEdge(0, 0, -1)).Should().ThrowContractAssert();
g.Invoking(g => g.AddEdge(0, 0, 0)).Should().NotThrow();
g.Invoking(g => g.AddEdge(1, 0, 10)).Should().NotThrow();
g.Invoking(g => g.GetEdge(-1)).Should().ThrowContractAssert();
g.Invoking(g => g.GetEdge(2)).Should().ThrowContractAssert();
g.Invoking(g => g.GetEdge(0)).Should().NotThrow();
g.Invoking(g => g.GetEdge(1)).Should().NotThrow();
g.Invoking(g => g.ChangeEdge(-1, 2, 2)).Should().ThrowContractAssert();
g.Invoking(g => g.ChangeEdge(2, 2, 2)).Should().ThrowContractAssert();
g.Invoking(g => g.ChangeEdge(0, 2, 2)).Should().NotThrow();
g.Invoking(g => g.ChangeEdge(1, 2, 2)).Should().NotThrow();
g.Invoking(g => g.ChangeEdge(0, 1, 2)).Should().ThrowContractAssert();
g.Invoking(g => g.ChangeEdge(1, 1, 2)).Should().ThrowContractAssert();
g.Invoking(g => g.ChangeEdge(0, 0, -1)).Should().ThrowContractAssert();
}
public void Simple()
{
var g = new MfGraphInt(4);
g.AddEdge(0, 1, 1).Should().Be(0);
g.AddEdge(0, 2, 1).Should().Be(1);
g.AddEdge(1, 3, 1).Should().Be(2);
g.AddEdge(2, 3, 1).Should().Be(3);
g.AddEdge(1, 2, 1).Should().Be(4);
g.Flow(0, 3).Should().Be(2);
MfGraphInt.Edge e;
e = new MfGraphInt.Edge(0, 1, 1, 1);
g.GetEdge(0).Should().Be(e);
e = new MfGraphInt.Edge(0, 2, 1, 1);
g.GetEdge(1).Should().Be(e);
e = new MfGraphInt.Edge(1, 3, 1, 1);
g.GetEdge(2).Should().Be(e);
e = new MfGraphInt.Edge(2, 3, 1, 1);
g.GetEdge(3).Should().Be(e);
e = new MfGraphInt.Edge(1, 2, 1, 0);
g.GetEdge(4).Should().Be(e);
g.MinCut(0).Should().Equal(new[] { true, false, false, false });
}
public void Cut()
{
var g = new MfGraphInt(3);
g.AddEdge(0, 1, 2).Should().Be(0);
g.AddEdge(1, 2, 1).Should().Be(1);
g.Flow(0, 2).Should().Be(1);
MfGraphInt.Edge e;
e = new MfGraphInt.Edge(0, 1, 2, 1);
g.GetEdge(0).Should().Be(e);
e = new MfGraphInt.Edge(1, 2, 1, 1);
g.GetEdge(1).Should().Be(e);
g.MinCut(0).Should().Equal(new[] { true, true, false });
}
public void NotSimple()
{
var g = new MfGraphInt(2);
g.AddEdge(0, 1, 1).Should().Be(0);
g.AddEdge(0, 1, 2).Should().Be(1);
g.AddEdge(0, 1, 3).Should().Be(2);
g.AddEdge(0, 1, 4).Should().Be(3);
g.AddEdge(0, 1, 5).Should().Be(4);
g.AddEdge(0, 0, 6).Should().Be(5);
g.AddEdge(1, 1, 7).Should().Be(6);
g.Flow(0, 1).Should().Be(15);
MfGraphInt.Edge e;
e = new MfGraphInt.Edge(0, 1, 1, 1);
g.GetEdge(0).Should().Be(e);
e = new MfGraphInt.Edge(0, 1, 2, 2);
g.GetEdge(1).Should().Be(e);
e = new MfGraphInt.Edge(0, 1, 3, 3);
g.GetEdge(2).Should().Be(e);
e = new MfGraphInt.Edge(0, 1, 4, 4);
g.GetEdge(3).Should().Be(e);
e = new MfGraphInt.Edge(0, 1, 5, 5);
g.GetEdge(4).Should().Be(e);
g.MinCut(0).Should().Equal(new[] { true, false });
}
public void SelfLoop()
{
var g = new MfGraphInt(3);
g.AddEdge(0, 0, 100).Should().Be(0);
MfGraphInt.Edge e = new MfGraphInt.Edge(0, 0, 100, 0);
g.GetEdge(0).Should().Be(e);
}
public void Twice()
{
var g = new MfGraphInt(3);
g.AddEdge(0, 1, 1).Should().Be(0);
g.AddEdge(0, 2, 1).Should().Be(1);
g.AddEdge(1, 2, 1).Should().Be(2);
g.Flow(0, 2).Should().Be(2);
MfGraphInt.Edge e;
e = new MfGraphInt.Edge(0, 1, 1, 1);
g.GetEdge(0).Should().Be(e);
e = new MfGraphInt.Edge(0, 2, 1, 1);
g.GetEdge(1).Should().Be(e);
e = new MfGraphInt.Edge(1, 2, 1, 1);
g.GetEdge(2).Should().Be(e);
g.ChangeEdge(0, 100, 10);
e = new MfGraphInt.Edge(0, 1, 100, 10);
g.GetEdge(0).Should().Be(e);
g.Flow(0, 2).Should().Be(0);
g.Flow(0, 1).Should().Be(90);
e = new MfGraphInt.Edge(0, 1, 100, 100);
g.GetEdge(0).Should().Be(e);
e = new MfGraphInt.Edge(0, 2, 1, 1);
g.GetEdge(1).Should().Be(e);
e = new MfGraphInt.Edge(1, 2, 1, 1);
g.GetEdge(2).Should().Be(e);
g.Flow(2, 0).Should().Be(2);
e = new MfGraphInt.Edge(0, 1, 100, 99);
g.GetEdge(0).Should().Be(e);
e = new MfGraphInt.Edge(0, 2, 1, 0);
g.GetEdge(1).Should().Be(e);
e = new MfGraphInt.Edge(1, 2, 1, 0);
g.GetEdge(2).Should().Be(e);
}
public void Bound()
{
MfGraphInt.Edge e;
const int INF = int.MaxValue;
var g = new MfGraphInt(3);
g.AddEdge(0, 1, INF).Should().Be(0);
g.AddEdge(1, 0, INF).Should().Be(1);
g.AddEdge(0, 2, INF).Should().Be(2);
g.Flow(0, 2).Should().Be(INF);
e = new MfGraphInt.Edge(0, 1, INF, 0);
g.GetEdge(0).Should().Be(e);
e = new MfGraphInt.Edge(1, 0, INF, 0);
g.GetEdge(1).Should().Be(e);
e = new MfGraphInt.Edge(0, 2, INF, INF);
g.GetEdge(2).Should().Be(e);
}
public void Stress()
{
var mt = MTRandom.Create();
for (int phase = 0; phase < 10000; phase++)
{
int n = mt.Next(2, 21);
int m = mt.Next(1, 101);
var(s, t) = mt.NextPair(0, n);
if (mt.NextBool())
{
(s, t) = (t, s);
}
var g = new MfGraphInt(n);
for (int i = 0; i < m; i++)
{
int u = mt.Next(0, n);
int v = mt.Next(0, n);
int c = mt.Next(0, 10001);
g.AddEdge(u, v, c);
}
int flow = g.Flow(s, t);
int dual = 0;
var cut = g.MinCut(s);
var vFlow = new int[n];
foreach (var e in g.Edges())
{
vFlow[e.From] -= e.Flow;
vFlow[e.To] += e.Flow;
if (cut[e.From] && !cut[e.To])
{
dual += e.Cap;
}
}
dual.Should().Be(flow);
vFlow[s].Should().Be(-flow);
vFlow[t].Should().Be(flow);
for (int i = 0; i < n; i++)
{
if (i == s || i == t)
{
continue;
}
vFlow[i].Should().Be(0);
}
}
}
static void Solver(TextReader reader, TextWriter writer)
{
int[] nm = reader.ReadLine().Split().Select(int.Parse).ToArray();
(int n, int m) = (nm[0], nm[1]);
char[][] grid = new char[n][];
for (int i = 0; i < n; i++)
{
grid[i] = reader.ReadLine().ToCharArray();
}
var g = new MfGraphInt(n * m + 2);
int s = n * m, t = n * m + 1;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
if (grid[i][j] == '#')
{
continue;
}
int v = i * m + j;
if ((i + j) % 2 == 0)
{
g.AddEdge(s, v, 1);
}
else
{
g.AddEdge(v, t, 1);
}
}
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
if ((i + j) % 2 != 0 || grid[i][j] == '#')
{
continue;
}
int v0 = i * m + j;
if (i != 0 && grid[i - 1][j] == '.')
{
int v1 = (i - 1) * m + j;
g.AddEdge(v0, v1, 1);
}
if (j != 0 && grid[i][j - 1] == '.')
{
int v1 = i * m + (j - 1);
g.AddEdge(v0, v1, 1);
}
if (i + 1 < n && grid[i + 1][j] == '.')
{
int v1 = (i + 1) * m + j;
g.AddEdge(v0, v1, 1);
}
if (j + 1 < m && grid[i][j + 1] == '.')
{
int v1 = i * m + (j + 1);
g.AddEdge(v0, v1, 1);
}
}
}
writer.WriteLine(g.Flow(s, t));
MfGraph <int, IntOperator> .Edge[] edges = g.Edges();
foreach (MfGraph <int, IntOperator> .Edge e in edges)
{
if (e.From == s || e.To == t || e.Flow == 0)
{
continue;
}
int i0 = e.From / m, j0 = e.From % m;
int i1 = e.To / m, j1 = e.To % m;
if (i0 == i1 + 1)
{
grid[i1][j1] = 'v';
grid[i0][j0] = '^';
}
else if (j0 == j1 + 1)
{
grid[i1][j1] = '>'; grid[i0][j0] = '<';
}
else if (i0 == i1 - 1)
{
grid[i0][j0] = 'v';
grid[i1][j1] = '^';
}
else
{
grid[i0][j0] = '>'; grid[i1][j1] = '<';
}
}
for (int i = 0; i < n; i++)
{
writer.WriteLine(grid[i]);
}
}
