Ford-Fulkerson Algorithm for Maximum Flow

Author: amitbansal7

10.Graphs/Flow Networks/FordFulkerson.cpp

@@ -0,0 +1,92 @@
+/* Amit Bansal - @amitbansal7 */
+//References GeeksForGeeks
+#include <bits/stdc++.h>
+#include <string>
+#define lli long long int
+#define llu unsigned long long int
+#define S(x) scanf("%d",&x)
+#define Sl(x) scanf("%lld",&x)
+#define Mset(p,i) memset(p,i,sizeof(p))
+#define mlc(t,n) (t *)malloc(sizeof(t)*n)
+#define NIL -1
+#define INF INT_MAX
+#define TC int testcase; S(testcase); while(testcase--)
+#define Pi 3.14159
+using namespace std;
+
+const int V = 6;
+
+bool BFS(int graph[V][V],int s,int t,int parent[])
+{
+	queue <int>Q;
+	int visited[V];
+	Mset(visited,0);
+	visited[s] = 1;
+	Q.push(s);
+	parent[s] = NIL;
+
+	while(!Q.empty())
+	{
+		int u = Q.front();
+		Q.pop();
+
+		for(int v=0;v<V;v++)
+		{
+			if(!visited[v] && graph[u][v] > 0)
+			{
+				Q.push(v);
+				parent[v] = u;
+				visited[v] = 1;
+			}
+		}
+	}
+	return(visited[t]);
+}
+
+int FordFulkerson(int graph[V][V],int s,int t)
+{
+	//residual graph
+	int rGraph[V][V];
+	memcpy(rGraph,graph,sizeof(int)*V*V);
+
+	int maxflow = 0;
+	int parent[V];
+
+	while(BFS(rGraph,s,t,parent))
+	{
+		int u,v;
+		int path_flow = INT_MAX;
+		//finding minimum residual capacity along the augmented path.
+		for(int v = t;v!=s;v = parent[v])
+		{
+			u = parent[v];
+			path_flow = min(path_flow,rGraph[u][v]);
+		}
+
+		for(v = t;v!=s;v=parent[v])
+		{
+			u = parent[v];
+			rGraph[u][v] -= path_flow;
+			rGraph[v][u] += path_flow;
+		}
+
+		maxflow += path_flow;
+	}
+
+	return maxflow;
+}
+
+int main()
+{
+	//CLRS fig 26.1(a)
+	int graph[V][V] = {{0,16,12,0,0,0},
+					{0,0,0,12,0,0},
+					{0,4,0,0,14,0},
+					{0,0,9,0,0,20},
+					{0,0,0,7,0,4},
+					{0,0,0,0,0,0}};
+
+	printf("Max flow is %d\n",FordFulkerson(graph,0,5));
+
+	return 0;
+}