add Ford_Fulkerson Algorithm using dp

Dynamic Programming/Ford_Fulkerson.java

@@ -0,0 +1,71 @@
+import java.util.LinkedList;
+import java.util.Queue;
+import java.util.Scanner;
+import java.util.Vector;
+
+public class Ford_Fulkerson {
+	Scanner scan = new Scanner(System.in);
+	final static int INF = 987654321;
+	static int V; // edges
+	static int[][] capacity, flow;
+
+	public static void main(String[] args) {
+		System.out.println("V : 6");
+		V = 6;
+		capacity = new int[V][V];
+
+		capacity[0][1] = 12;
+		capacity[0][3] = 13;
+		capacity[1][2] = 10;
+		capacity[2][3] = 13;
+		capacity[2][4] = 3;
+		capacity[2][5] = 15;
+		capacity[3][2] = 7;
+		capacity[3][4] = 15;
+		capacity[4][5] = 17;
+
+		System.out.println("Max capacity in networkFlow : " + networkFlow(0, 5));
+	}
+
+	private static int networkFlow(int source, int sink) {
+		flow = new int[V][V];
+		int totalFlow = 0;
+		while (true) {
+			Vector<Integer> parent = new Vector<>(V);
+			for (int i = 0; i < V; i++)
+				parent.add(-1);
+			Queue<Integer> q = new LinkedList<>();
+			parent.set(source, source);
+			q.add(source);
+			while (!q.isEmpty() && parent.get(sink) == -1) {
+				int here = q.peek();
+				q.poll();
+				for (int there = 0; there < V; ++there)
+					if (capacity[here][there] - flow[here][there] > 0 && parent.get(there) == -1) {
+						q.add(there);
+						parent.set(there, here);
+					}
+			}
+			if (parent.get(sink) == -1)
+				break;
+
+			int amount = INF;
+			String printer = "path : ";
+			StringBuilder sb = new StringBuilder();
+			for (int p = sink; p != source; p = parent.get(p)) {
+				amount = Math.min(capacity[parent.get(p)][p] - flow[parent.get(p)][p], amount);
+				sb.append(p + "-");
+			}
+			sb.append(source);
+			for (int p = sink; p != source; p = parent.get(p)) {
+				flow[parent.get(p)][p] += amount;
+				flow[p][parent.get(p)] -= amount;
+			}
+			totalFlow += amount;
+			printer += sb.reverse() + " / max flow : " + totalFlow;
+			System.out.println(printer);
+		}
+
+		return totalFlow;
+	}
+}