From 5d0bf63c30e1d953c8a1bd3158f9c306f067cd81 Mon Sep 17 00:00:00 2001
From: Gourav Singh <49956754+GouravSingh2580@users.noreply.github.com>
Date: Thu, 15 Oct 2020 20:39:17 +0530
Subject: [PATCH] Added Bellman Ford Algorithm

---
 DP_problems/Bellman_Ford_Algorithm.cpp | 136 +++++++++++++++++++++++++
 1 file changed, 136 insertions(+)
 create mode 100644 DP_problems/Bellman_Ford_Algorithm.cpp

diff --git a/DP_problems/Bellman_Ford_Algorithm.cpp b/DP_problems/Bellman_Ford_Algorithm.cpp
new file mode 100644
index 0000000..e2a710d
--- /dev/null
+++ b/DP_problems/Bellman_Ford_Algorithm.cpp
@@ -0,0 +1,136 @@
+// A C++ program for Bellman-Ford's single source 
+// shortest path algorithm. 
+#include <bits/stdc++.h> 
+
+// a structure to represent a weighted edge in graph 
+struct Edge { 
+	int src, dest, weight; 
+}; 
+
+// a structure to represent a connected, directed and 
+// weighted graph 
+struct Graph { 
+	// V-> Number of vertices, E-> Number of edges 
+	int V, E; 
+
+	// graph is represented as an array of edges. 
+	struct Edge* edge; 
+}; 
+
+// Creates a graph with V vertices and E edges 
+struct Graph* createGraph(int V, int E) 
+{ 
+	struct Graph* graph = new Graph; 
+	graph->V = V; 
+	graph->E = E; 
+	graph->edge = new Edge[E]; 
+	return graph; 
+} 
+
+// A utility function used to print the solution 
+void printArr(int dist[], int n) 
+{ 
+	printf("Vertex Distance from Source\n"); 
+	for (int i = 0; i < n; ++i) 
+		printf("%d \t\t %d\n", i, dist[i]); 
+} 
+
+// The main function that finds shortest distances from src to 
+// all other vertices using Bellman-Ford algorithm. The function 
+// also detects negative weight cycle 
+void BellmanFord(struct Graph* graph, int src) 
+{ 
+	int V = graph->V; 
+	int E = graph->E; 
+	int dist[V]; 
+
+	// Step 1: Initialize distances from src to all other vertices 
+	// as INFINITE 
+	for (int i = 0; i < V; i++) 
+		dist[i] = INT_MAX; 
+	dist[src] = 0; 
+
+	// Step 2: Relax all edges |V| - 1 times. A simple shortest 
+	// path from src to any other vertex can have at-most |V| - 1 
+	// edges 
+	for (int i = 1; i <= V - 1; i++) { 
+		for (int j = 0; j < E; j++) { 
+			int u = graph->edge[j].src; 
+			int v = graph->edge[j].dest; 
+			int weight = graph->edge[j].weight; 
+			if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) 
+				dist[v] = dist[u] + weight; 
+		} 
+	} 
+
+	// Step 3: check for negative-weight cycles. The above step 
+	// guarantees shortest distances if graph doesn't contain 
+	// negative weight cycle. If we get a shorter path, then there 
+	// is a cycle. 
+	for (int i = 0; i < E; i++) { 
+		int u = graph->edge[i].src; 
+		int v = graph->edge[i].dest; 
+		int weight = graph->edge[i].weight; 
+		if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) { 
+			printf("Graph contains negative weight cycle"); 
+			return; // If negative cycle is detected, simply return 
+		} 
+	} 
+
+	printArr(dist, V); 
+
+	return; 
+} 
+
+// Driver program to test above functions 
+int main() 
+{ 
+	/* Let us create the graph given in above example */
+	int V = 5; // Number of vertices in graph 
+	int E = 8; // Number of edges in graph 
+	struct Graph* graph = createGraph(V, E); 
+
+	// add edge 0-1 (or A-B in above figure) 
+	graph->edge[0].src = 0; 
+	graph->edge[0].dest = 1; 
+	graph->edge[0].weight = -1; 
+
+	// add edge 0-2 (or A-C in above figure) 
+	graph->edge[1].src = 0; 
+	graph->edge[1].dest = 2; 
+	graph->edge[1].weight = 4; 
+
+	// add edge 1-2 (or B-C in above figure) 
+	graph->edge[2].src = 1; 
+	graph->edge[2].dest = 2; 
+	graph->edge[2].weight = 3; 
+
+	// add edge 1-3 (or B-D in above figure) 
+	graph->edge[3].src = 1; 
+	graph->edge[3].dest = 3; 
+	graph->edge[3].weight = 2; 
+
+	// add edge 1-4 (or A-E in above figure) 
+	graph->edge[4].src = 1; 
+	graph->edge[4].dest = 4; 
+	graph->edge[4].weight = 2; 
+
+	// add edge 3-2 (or D-C in above figure) 
+	graph->edge[5].src = 3; 
+	graph->edge[5].dest = 2; 
+	graph->edge[5].weight = 5; 
+
+	// add edge 3-1 (or D-B in above figure) 
+	graph->edge[6].src = 3; 
+	graph->edge[6].dest = 1; 
+	graph->edge[6].weight = 1; 
+
+	// add edge 4-3 (or E-D in above figure) 
+	graph->edge[7].src = 4; 
+	graph->edge[7].dest = 3; 
+	graph->edge[7].weight = -3; 
+
+	BellmanFord(graph, 0); 
+
+	return 0; 
+}