Bellman_Ford.cpp

#include <iostream>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
 
using namespace std;
 
struct Edge
{
    // This structure is equal to an edge. Edge contains two end points. These edges are directed edges so they
	//contain source and destination and some weight. These 3 are elements in this structure
    int source, destination, weight;
};
 
// a structure to represent a connected, directed and weighted graph
struct Graph
{
    int V, E;
	// V is number of vertices and E is number of edges
 
    struct Edge* edge;
	// This structure contain another structure which we already created edge.
};
 
struct Graph* createGraph(int V, int E)
{
    struct Graph* graph = (struct Graph*) malloc( sizeof(struct Graph));
	//Allocating space to structure graph
 
    graph->V = V;   //assigning values to structure elements that taken form user.
 
    graph->E = E;
 
    graph->edge = (struct Edge*) malloc( graph->E * sizeof( struct Edge ) );
	//Creating "Edge" type structures inside "Graph" structure, the number of edge type structures are equal to number of edges
 
    return graph;
}
 
void FinalSolution(int dist[], int n)
{
	// This function prints the final solution
    cout<<"\nVertex\tDistance from Source Vertex\n";
    int i;
 
    for (i = 0; i < n; ++i){
		cout<<i<<"\t\t"<<dist[i]<<"\n";
	}
}
 
void BellmanFord(struct Graph* graph, int source)
{
    int V = graph->V;
 
    int E = graph->E;
 
    int StoreDistance[V];
 
    int i,j;
 
    // This is initial step that we know , we initialize all distance to infinity except source.
	// We assign source distance as 0(zero)
 
    for (i = 0; i < V; i++)
        StoreDistance[i] = INT_MAX;
 
    StoreDistance[source] = 0;
 
    //The shortest path of graph that contain V vertices, never contain "V-1" edges. So we do here "V-1" relaxations
    for (i = 1; i <= V-1; i++)
    {
        for (j = 0; j < E; j++)
        {
            int u = graph->edge[j].source;
 
            int v = graph->edge[j].destination;
 
            int weight = graph->edge[j].weight;
 
            if (StoreDistance[u] + weight < StoreDistance[v])
                StoreDistance[v] = StoreDistance[u] + weight;
        }
    }
 
    // Actually upto now shortest path found. But BellmanFord checks for negative edge cycle. In this step we check for that
    // shortest distances if graph doesn't contain negative weight cycle.
 
    // If we get a shorter path, then there is a negative edge cycle.
    for (i = 0; i < E; i++)
    {
        int u = graph->edge[i].source;
 
        int v = graph->edge[i].destination;
 
        int weight = graph->edge[i].weight;
 
        if (StoreDistance[u] + weight < StoreDistance[v])
            cout<<"\nThis graph contains negative edge cycle\n";
    }
 
    FinalSolution(StoreDistance, V);
 
    return;
}
 
int main()
{
    int V,E,S;  //V = no.of Vertices, E = no.of Edges, S is source vertex
 
	cout<<"Enter number of vertices in graph\n";
    cin>>V;
 
	cout<<"Enter number of edges in graph\n";
    cin>>E;
 
	cout<<"Enter your source vertex number\n";
	cin>>S;
 
    struct Graph* graph = createGraph(V, E);    //calling the function to allocate space to these many vertices and edges
 
    int i;
    for(i=0;i<E;i++){
        cout<<"\nEnter edge "<<i+1<<" properties Source, destination, weight respectively\n";
        cin>>graph->edge[i].source;
        cin>>graph->edge[i].destination;
        cin>>graph->edge[i].weight;
    }
 
    BellmanFord(graph, S);
	//passing created graph and source vertex to BellmanFord Algorithm function
 
    return 0;
}