From 46e513dcbb7799b601c9c5e307b7aaad196646d5 Mon Sep 17 00:00:00 2001
From: Sunny Singh <singhsunny0712@gmail.com>
Date: Thu, 1 Oct 2020 18:03:11 +0530
Subject: [PATCH] Create MaxFlow Ford Fulkerson

---
 src/algo/graph/MaxFlow Ford Fulkerson | 33 +++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 src/algo/graph/MaxFlow Ford Fulkerson

diff --git a/src/algo/graph/MaxFlow Ford Fulkerson b/src/algo/graph/MaxFlow Ford Fulkerson
new file mode 100644
index 0000000..23d9fbf
--- /dev/null
+++ b/src/algo/graph/MaxFlow Ford Fulkerson	
@@ -0,0 +1,33 @@
+// https://en.wikipedia.org/wiki/Ford–Fulkerson_algorithm in O(V^2 * flow)
+public class MaxFlowFordFulkerson {
+    public static int maxFlow(int[][] cap, int s, int t) {
+        for (int flow = 0;;) {
+            int df = findPath(cap, new boolean[cap.length], s, t, Integer.MAX_VALUE);
+            if (df == 0)
+                return flow;
+            flow += df;
+        }
+    }
+
+    static int findPath(int[][] cap, boolean[] vis, int u, int t, int f) {
+        if (u == t)
+            return f;
+        vis[u] = true;
+        for (int v = 0; v < vis.length; v++)
+            if (!vis[v] && cap[u][v] > 0) {
+                int df = findPath(cap, vis, v, t, Math.min(f, cap[u][v]));
+                if (df > 0) {
+                    cap[u][v] -= df;
+                    cap[v][u] += df;
+                    return df;
+                }
+            }
+        return 0;
+    }
+
+    // Usage example
+    public static void main(String[] args) {
+        int[][] capacity = {{0, 3, 2}, {0, 0, 2}, {0, 0, 0}};
+        System.out.println(4 == maxFlow(capacity, 0, 2));
+    }
+}