static int[] FindMatching(bool[][] bipartiteGraph)
{
int numLeft = bipartiteGraph.Length;
int numRight = bipartiteGraph[0].Length;
int[] matching = new int[numLeft];
FlowGraph graph = ReadGraph(bipartiteGraph);
MaxFlow(graph, 0, graph.Size() - 1);
for (int i = 0; i < numLeft; i++)
{
foreach (int id in graph.GetIds(i + 1))
{
Edge edge = graph.GetEdge(id);
if (edge.flow == 1)
{
matching[i] = edge.to - numLeft;
break;
}
matching[i] = -1;
}
}
return(matching);
}
static void MaxFlow(FlowGraph graph, int from, int to)
{
while (true)
{
bool foundPath = false;
var queue = new Queue <int>();
var parentIds = new int[graph.Size()];
for (int i = 0; i < parentIds.Length; i++)
{
parentIds[i] = -1; //unvisited nodes are -1
}
queue.Enqueue(0);
//Breadth-first search, finding shortest path
while (queue.Count != 0 && !foundPath)
{
int node = queue.Dequeue();
var ids = graph.GetIds(node); // all the edges from current node
foreach (int id in ids)
{
var edge = graph.GetEdge(id);
if (edge.flow < edge.capacity && parentIds[edge.to] == -1) // if there's capacity left and "edge pointing" vertice isn't visited
{
if (edge.to == edge.from)
{
continue;
}
parentIds[edge.to] = id;
if (edge.to == graph.Size() - 1) // we found path
{
foundPath = true;
break;
}
queue.Enqueue(edge.to);
}
}
}
if (!foundPath)
{
break;
}
//find the value of the flow
to = graph.Size() - 1;
var minCap = -1;
//calculate min capacity
while (to != 0)
{
var id = parentIds[to];
var edge = graph.GetEdge(id);
if (minCap == -1 || (edge.capacity - edge.flow) < minCap)
{
minCap = edge.capacity - edge.flow;
}
to = edge.from;
}
to = graph.Size() - 1;
//adding flow to edges
while (to != 0)
{
var id = parentIds[to];
var edge = graph.GetEdge(id);
graph.AddFlow(id, minCap);
to = edge.from;
}
}
}
static int MaxFlow(FlowGraph graph, int from, int to)
{
int flow = 0;
while (true)
{
bool foundPath = false;
var queue = new Queue <int>();
var parentIds = new int[graph.Size()];
for (int i = 0; i < parentIds.Length; i++)
{
parentIds[i] = -1; //unvisited nodes are -1
}
queue.Enqueue(0);
//bfs
while (queue.Count != 0 && !foundPath)
{
int node = queue.Dequeue();
var ids = graph.GetIds(node); // all the edges from current node
foreach (int id in ids)
{
var edge = graph.GetEdge(id);
if (edge.flow < edge.capacity && parentIds[edge.to] == -1)
{
if (edge.to == edge.from)
{
continue;
}
parentIds[edge.to] = id;
if (edge.to == graph.Size() - 1) // we found path
{
foundPath = true;
break;
}
queue.Enqueue(edge.to);
}
}
}
if (!foundPath)
{
break;
}
//find the value of the flow
to = graph.Size() - 1;
var minCap = -1;
//calculate min capacity
while (to != 0)
{
var id = parentIds[to];
var edge = graph.GetEdge(id);
if (minCap == -1 || (edge.capacity - edge.flow) < minCap)
{
minCap = edge.capacity - edge.flow;
}
to = edge.from;
}
to = graph.Size() - 1;
//adding flow to edges
while (to != 0)
{
var id = parentIds[to];
var edge = graph.GetEdge(id);
graph.AddFlow(id, minCap);
to = edge.from;
}
}
//calculate the flow
// to do that we only sum the flows of the start node
foreach (int id in graph.GetIds(0))
{
var edge = graph.GetEdge(id);
flow += edge.flow;
}
return(flow);
}