Detect_negative_weight_cycle_in_Graph.cpp

#include <bits/stdc++.h>
using namespace std;

struct Edge
{
    int source, destination, weight;
};

struct Graph
{
    int V, E;
    struct Edge *edge;
};

struct Graph *createGraph(int V, int E)
{
    struct Graph *graph = new Graph;
    graph->V = V;
    graph->E = E;
    graph->edge = new Edge[graph->E];
    return graph;
}

bool isNegCycleBellmanFord(struct Graph *graph, int source)
{
    int V = graph->V;
    int E = graph->E;
    int distance[V];

    for (int i = 0; i < V; i++)
        distance[i] = INT_MAX;
    distance[source] = 0;

    for (int i = 1; i <= V - 1; i++)
    {
        for (int j = 0; j < E; j++)
        {
            int u = graph->edge[j].source;
            int v = graph->edge[j].destination;
            int weight = graph->edge[j].weight;
            if (distance[u] != INT_MAX && distance[u] + weight < distance[v])
                distance[v] = distance[u] + weight;
        }
    }

    // Iterating one more time if distance changes then
    // there is a negative edge weight cycle.
    for (int i = 0; i < E; i++)
    {
        int u = graph->edge[i].source;
        int v = graph->edge[i].destination;
        int weight = graph->edge[i].weight;
        if (distance[u] != INT_MAX && distance[u] + weight < distance[v])
            return true;
    }

    return false;
}

int main()
{
    int V = 5;
    int E = 8;
    struct Graph *graph = createGraph(V, E);

    graph->edge[0].source = 0;
    graph->edge[0].destination = 1;
    graph->edge[0].weight = -1;

    graph->edge[1].source = 0;
    graph->edge[1].destination = 2;
    graph->edge[1].weight = 4;

    graph->edge[2].source = 1;
    graph->edge[2].destination = 2;
    graph->edge[2].weight = 3;

    graph->edge[3].source = 1;
    graph->edge[3].destination = 3;
    graph->edge[3].weight = 2;

    graph->edge[4].source = 1;
    graph->edge[4].destination = 4;
    graph->edge[4].weight = 2;

    graph->edge[5].source = 3;
    graph->edge[5].destination = 2;
    graph->edge[5].weight = 5;

    graph->edge[6].source = 3;
    graph->edge[6].destination = 1;
    graph->edge[6].weight = 1;

    graph->edge[7].source = 4;
    graph->edge[7].destination = 3;
    graph->edge[7].weight = -3;

    if (isNegCycleBellmanFord(graph, 0))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}