Merge pull request matthewsamuel95#900 from 3agwa/add-Hopkraft-Karp-to-NetworkFlow

Update NetworkFlow/Hopkraft Karp/Hopkraft Karp.cpp

Author: matthewsamuel95

NetworkFlow/Hopkraft Karp/Hopkraft Karp.cpp

@@ -0,0 +1,84 @@
+const int MAXN1 = 50000;
+const int MAXN2 = 50000;
+const int MAXM = 150000;
+
+int n1, n2, edges, last[MAXN1], _prev[MAXM], head[MAXM];
+int matching[MAXN2], dist[MAXN1], Q[MAXN1];
+bool used[MAXN1], vis[MAXN1];
+
+void init(int _n1, int _n2)
+{
+	n1 = _n1;
+	n2 = _n2;
+	edges = 0;
+	fill(last, last + n1, -1);
+}
+
+void addEdge(int u, int v)
+{
+	head[edges] = v;
+	_prev[edges] = last[u];
+	last[u] = edges++;
+}
+
+void bfs()
+{
+	fill(dist, dist + n1, -1);
+	int sizeQ = 0;
+	for (int u = 0; u < n1; ++u)
+	{
+		if (!used[u])
+		{
+			Q[sizeQ++] = u;
+			dist[u] = 0;
+		}
+	}
+	for (int i = 0; i < sizeQ; i++)
+	{
+		int u1 = Q[i];
+		for (int e = last[u1]; e >= 0; e = _prev[e])
+		{
+			int u2 = matching[head[e]];
+			if (u2 >= 0 && dist[u2] < 0)
+			{
+				dist[u2] = dist[u1] + 1;
+				Q[sizeQ++] = u2;
+			}
+		}
+	}
+}
+
+bool dfs(int u1)
+{
+	vis[u1] = true;
+	for (int e = last[u1]; e >= 0; e = _prev[e])
+	{
+		int v = head[e];
+		int u2 = matching[v];
+		if (u2 < 0 || !vis[u2] && dist[u2] == dist[u1] + 1 && dfs(u2))
+		{
+			matching[v] = u1;
+			used[u1] = true;
+			return true;
+		}
+	}
+	return false;
+}
+
+int maxMatching()
+{
+	fill(used, used + n1, false);
+	fill(matching, matching + n2, -1);
+	for (int res = 0;;)
+	{
+		bfs();
+		fill(vis, vis + n1, false);
+		int f = 0;
+		for (int u = 0; u < n1; ++u)
+			if (!used[u] && dfs(u))
+				++f;
+		if (!f)
+			return res;
+		res += f;
+	}
+}