private static bool BreadthFirstSearch(GridFlowGraph graph, Vector3i[,] parent, out Vector3i sink)
{
int width = graph.Width;
int height = graph.Height;
Queue <Vector2i> queue = new Queue <Vector2i>();
bool[,] isVisited = new bool[width, height];
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
if (graph.Label[x, y] != GridFlowGraph.SOURCE)
{
continue;
}
queue.Enqueue(new Vector2i(x, y));
parent[x, y] = new Vector3i(x, y, -1);
isVisited[x, y] = true;
}
}
while (queue.Count != 0)
{
Vector2i u = queue.Dequeue();
for (int i = 0; i < 8; i++)
{
float residual = graph.Capacity[u.x, u.y, i] - graph.Flow[u.x, u.y, i];
if (residual <= 0)
{
continue;
}
int xi = u.x + D8.OFFSETS[i, 0];
int yi = u.y + D8.OFFSETS[i, 1];
if (xi < 0 || xi >= width)
{
continue;
}
if (yi < 0 || yi >= height)
{
continue;
}
if (isVisited[xi, yi])
{
continue;
}
queue.Enqueue(new Vector2i(xi, yi));
parent[xi, yi] = new Vector3i(u.x, u.y, i);
isVisited[xi, yi] = true;
if (graph.Label[xi, yi] == GridFlowGraph.SINK)
{
sink = new Vector3i(xi, yi, -1);
return(true);
}
}
}
sink = new Vector3i(-1, -1, -1);
return(false);
}
public void FoldFulkersonMaxFlow()
{
int width = 4;
int height = 2;
GridFlowGraph graph = new GridFlowGraph(width, height);
graph.Label[0, 0] = GridFlowGraph.SOURCE;
graph.Label[3, 0] = GridFlowGraph.SINK;
graph.Capacity[0, 0, D8.RIGHT] = 16;
graph.Capacity[0, 0, D8.RIGHT_TOP] = 13;
graph.Capacity[1, 0, D8.TOP] = 10;
graph.Capacity[1, 0, D8.RIGHT] = 12;
graph.Capacity[1, 1, D8.BOTTOM] = 4;
graph.Capacity[1, 1, D8.RIGHT] = 14;
graph.Capacity[2, 0, D8.RIGHT] = 20;
graph.Capacity[2, 0, D8.LEFT_TOP] = 9;
graph.Capacity[2, 1, D8.BOTTOM] = 7;
graph.Capacity[2, 1, D8.RIGHT_BOTTOM] = 4;
graph.FordFulkersonMaxFlow();
Assert.AreEqual(23, graph.MaxFlow);
Assert.AreEqual(GridFlowGraph.SOURCE, graph.Label[0, 0]);
Assert.AreEqual(GridFlowGraph.SOURCE, graph.Label[1, 0]);
Assert.AreEqual(GridFlowGraph.SOURCE, graph.Label[1, 1]);
Assert.AreEqual(GridFlowGraph.SOURCE, graph.Label[2, 1]);
Assert.AreEqual(GridFlowGraph.SINK, graph.Label[2, 0]);
Assert.AreEqual(GridFlowGraph.SINK, graph.Label[3, 0]);
float minCut = 0;
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
if (graph.Label[x, y] != GridFlowGraph.SOURCE)
{
continue;
}
for (int i = 0; i < 8; i++)
{
int xi = x + D8.OFFSETS[i, 0];
int yi = y + D8.OFFSETS[i, 1];
if (xi < 0 || xi > width - 1)
{
continue;
}
if (yi < 0 || yi > height - 1)
{
continue;
}
if (graph.Label[xi, yi] == GridFlowGraph.SINK)
{
minCut += graph.Flow[x, y, i];
}
}
}
}
Assert.AreEqual(23, minCut);
}
internal static float MaxFlow(GridFlowGraph graph)
{
int width = graph.Width;
int height = graph.Height;
Vector3i[,] parent = new Vector3i[width, height];
float maxFlow = 0;
Vector3i sink, v;
while (BreadthFirstSearch(graph, parent, out sink))
{
float flow = float.PositiveInfinity;
v = sink;
while (true)
{
Vector3i u = parent[v.x, v.y];
if (u.x == v.x && u.y == v.y)
{
throw new InvalidOperationException("Did not stop at source.");
}
float residual = graph.Capacity[u.x, u.y, u.z] - graph.Flow[u.x, u.y, u.z];
flow = Math.Min(flow, residual);
if (graph.Label[u.x, u.y] == GridFlowGraph.SOURCE)
{
break;
}
else
{
v = u;
}
}
if (flow == float.PositiveInfinity)
{
throw new InvalidOperationException("Could not find path flow.");
}
maxFlow += flow;
v = sink;
while (true)
{
Vector3i u = parent[v.x, v.y];
graph.Flow[u.x, u.y, u.z] += flow;
graph.Flow[v.x, v.y, D8.OPPOSITES[u.z]] -= flow;
if (graph.Label[u.x, u.y] == GridFlowGraph.SOURCE)
{
break;
}
else
{
v = u;
}
}
}
return(maxFlow);
}
