Bellman_Ford.cpp

/**
 * Descrption: BellmanFord (Finds the shortest path from source s to all vertices v. Detects a negative weight cycle if present.)
 * Usage: See below O(V.E) = O(n^2)
 */

 #include <iostream>
 #include <vector>
 #define INT_MAX 10000
 using namespace std;
 int V,E;
 struct edge{

 int src,dst,wt;
 };

 void bellmanFord(vector<edge>& Edges){

    int parent[V];  //To store parent node
    //int cost_parent[V]; //Cost of node to parent

    vector<int> distance(V,INT_MAX);

    parent[0]=-1;
    distance[0]=0;

    bool update;
    for(int i=0;i<V-1;i++){

        update=false;

        for(int j=0;j<E;j++){

            int U=Edges[j].src;
            int V=Edges[j].dst;
            int wt=Edges[j].wt;
            if(distance[U]!=INT_MAX && distance[U]+wt<distance[V]){

                distance[V]=distance[U]+wt;
                parent[V]=U;
                //cost_parent[V]=distance[V];
                update=true;

            }
        }
        if(update==false)
            break;

    }

    //Now let's check it has negative edge cycle or not by relaxing one more time

    for(int j=0;j<E && update==true;j++){
         int U=Edges[j].src;
            int V=Edges[j].dst;
            int wt=Edges[j].wt;
            if(distance[U]!=INT_MAX && distance[U]+wt<distance[V]){


                cout<<"Graph has negative Edge Cycle :( "<<endl;
                return;

            }


    }

    //Print Shortest path

    for(int i=1;i<V;i++){

        cout<<"U->V: 0->"<<i<<" Cost to reach "<<i<<" from source 0 = "<<distance[i]<<endl;




 }



 }




 int main(){

 cin>>V>>E; //no of vertices and edges

 vector<edge> Edges(E);

 int src,dst,wt;

 for(int i=0;i<E;i++){
    cin>>src>>dst>>wt;
    Edges[i].src=src;
    Edges[i].dst=dst;
    Edges[i].wt=wt;

 }

 bellmanFord(Edges);

 return 0;
 }