From dbeacd4e176bdc3b930f554640ac07aea6b30604 Mon Sep 17 00:00:00 2001
From: arpanjain97 <arpanjain97@gmail.com>
Date: Thu, 12 Oct 2017 17:20:34 +0530
Subject: [PATCH] Add Bellman-Ford Algorithm

---
 Dynamic Programming/Bellman-Ford.cpp | 112 +++++++++++++++++++++++++++
 1 file changed, 112 insertions(+)
 create mode 100644 Dynamic Programming/Bellman-Ford.cpp

diff --git a/Dynamic Programming/Bellman-Ford.cpp b/Dynamic Programming/Bellman-Ford.cpp
new file mode 100644
index 000000000..83d2aead0
--- /dev/null
+++ b/Dynamic Programming/Bellman-Ford.cpp	
@@ -0,0 +1,112 @@
+#include<iostream>
+#include<limits.h>
+
+using namespace std;
+
+//Wrapper class for storing an edge
+class Edge{
+	public: int src,dst,weight;
+};
+
+//Wrapper class for storing a graph
+class Graph{
+	public:
+	int vertexNum,edgeNum;
+	Edge* edges;
+
+	//Constructs a graph with V vertices and E edges
+	Graph(int V,int E){
+		this->vertexNum = V;
+		this->edgeNum = E;
+		this->edges =(Edge*) malloc(E * sizeof(Edge));
+	}
+
+	//Adds the given edge to the graph 
+	void addEdge(int src, int dst, int weight){
+		static int edgeInd = 0;
+		if(edgeInd < this->edgeNum){
+			Edge newEdge;
+			newEdge.src = src;
+			newEdge.dst = dst;
+			newEdge.weight = weight;
+			this->edges[edgeInd++] = newEdge;
+		}
+
+	}
+	
+};
+
+//Utility function to print distances
+void print(int dist[], int V){
+	cout<<"\nVertex  Distance"<<endl;
+	for(int i = 0; i < V; i++)
+		cout<<i<<"\t"<<dist[i]<<endl;
+}
+
+//The main function that finds the shortest path from given source
+//to all other vertices using Bellman-Ford.It also detects negative
+//weight cycle
+void BellmanFord(Graph graph, int src){
+	int V = graph.vertexNum;
+	int E = graph.edgeNum;
+	int dist[V];
+
+	//Initialize distances array as INF for all except source
+	//Intialize source as zero
+	for(int i=0; i<V; i++)
+		dist[i] = INT_MAX;
+	dist[src] = 0;
+
+	//Calculate shortest path distance from source to all edges
+	//A path can contain maximum (|V|-1) edges
+	for(int i=0; i<=V-1; i++)
+		for(int j = 0; j<E; j++){
+			int u = graph.edges[j].src;
+			int v = graph.edges[j].dst;
+			int w = graph.edges[j].weight;
+			
+			if(dist[u]!=INT_MAX && dist[u] + w < dist[v])
+				dist[v] = dist[u] + w;
+		}
+	
+	//Iterate inner loop once more to check for negative cycle
+	for(int j = 0; j<E; j++){
+		int u = graph.edges[j].src;
+		int v = graph.edges[j].dst;
+		int w = graph.edges[j].weight;
+		
+		if(dist[u]!=INT_MAX && dist[u] + w < dist[v]){
+			cout<<"Graph contains negative weight cycle. Hence, shortest distance not guaranteed."<<endl;
+			return;
+		}
+	}
+
+	print(dist, V);
+	
+	return;
+}
+
+//Driver Function
+int main(){
+	int V,E,gsrc;
+	int src,dst,weight;
+	cout<<"Enter number of vertices: ";
+	cin>>V;
+	cout<<"Enter number of edges: ";
+	cin>>E;
+	Graph G(V,E);
+	for(int i=0; i<E; i++){
+		cout<<"\nEdge "<<i+1<<"\nEnter source: ";
+		cin>>src;
+		cout<<"Enter destination: ";
+		cin>>dst;
+		cout<<"Enter weight: ";
+		cin>>weight;
+		G.addEdge(src, dst, weight);
+	}
+	cout<<"\nEnter source: ";
+	cin>>gsrc;
+	BellmanFord(G,gsrc);
+
+	return 0;
+}