使用ISAP算法进行二分图匹配（附UOJ - 78 二分图最大匹配代码）

Author: Dev-XYS

Bigraph-Matching(Improved-Shortest-Augmenting-Path).cpp

@@ -0,0 +1,121 @@
+#include <cstdio>
+
+#define INF 1000000000
+
+using namespace std;
+
+struct vertex
+{
+	int first, dis;
+}V[1010];
+
+struct edge
+{
+	int endp, next, flow;
+}E[502010];
+
+int nl, nr, iec, ec = 2, src = 1005, sink = 1006, gap[1010];
+
+inline int min(int x, int y)
+{
+	return x < y ? x : y;
+}
+
+void init()
+{
+	gap[0] = nl + nr + 2;
+}
+
+void add_edge(int u, int v, int f)
+{
+	E[ec].next = V[u].first;
+	V[u].first = ec;
+	E[ec].endp = v;
+	E[ec].flow = f;
+	ec++;
+}
+
+int isap(int u, int curf)
+{
+	if (u == sink)
+	{
+		return curf;
+	}
+	int totalf = 0, mindis = nl + nr + 2;
+	for (int cur = V[u].first; cur != 0 && totalf < curf; cur = E[cur].next)
+	{
+		if (E[cur].flow > 0)
+		{
+			if (V[u].dis == V[E[cur].endp].dis + 1)
+			{
+				int f = isap(E[cur].endp, min(curf - totalf, E[cur].flow));
+				E[cur].flow -= f;
+				E[cur ^ 1].flow += f;
+				totalf += f;
+			}
+			if (V[E[cur].endp].dis < mindis)
+			{
+				mindis = V[E[cur].endp].dis;
+			}
+		}
+	}
+	if (totalf == 0)
+	{
+		if (--gap[V[u].dis] == 0) V[src].dis = nl + nr + 2;
+		V[u].dis = mindis + 1;
+		gap[V[u].dis]++;
+	}
+	return totalf;
+}
+
+int max_flow()
+{
+	int res = 0;
+	while (V[src].dis < nl + nr + 2)
+	{
+		res += isap(src, INF);
+	}
+	return res;
+}
+
+int main()
+{
+	int u, v;
+	scanf("%d%d%d", &nl, &nr, &iec);
+	for (int i = 0; i < iec; i++)
+	{
+		scanf("%d%d", &u, &v);
+		add_edge(u, v + nl, 1);
+		add_edge(v + nl, u, 0);
+	}
+	for (int i = 1; i <= nl; i++)
+	{
+		add_edge(src, i, 1);
+		add_edge(i, src, 0);
+	}
+	for (int i = 1; i <= nr; i++)
+	{
+		add_edge(i + nl, sink, 1);
+		add_edge(sink, i + nl, 0);
+	}
+	init();
+	printf("%d\n", max_flow());
+	for (int i = 1; i <= nl; i++)
+	{
+		bool has = false;
+		for (int cur = V[i].first; cur != 0; cur = E[cur].next)
+		{
+			if (E[cur].endp != src && E[cur].flow == 0)
+			{
+				printf("%d ", E[cur].endp - nl);
+				has = true;
+				break;
+			}
+		}
+		if (has == false)
+		{
+			printf("0 ");
+		}
+	}
+	return 0;
+}