#### C++ Program to Use the Bellman Ford Algorithm to Find the Shortest Path Between Two Vertices. Assuming that Negative Size Edges Exist in the Graph

Here is source code of the C++ Program to Use the Bellman Ford Algorithm to Find the Shortest Path Between Two Vertices Assuming that Negative Size Edges existing the Graph.

#include <stdio.h> #include <stdlib.h> #include <string.h> #include <limits.h> // 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 = (struct Graph*) malloc(sizeof(struct Graph)); graph->V = V; graph->E = E; graph->edge = (struct Edge*) malloc(graph->E * sizeof(struct Edge)); return graph; } // A utility function used to print the solution void printArr(int dist[], int n) { printf("Vertex Distance from Sourcen"); for (int i = 0; i < n; ++i) printf("%d tt %dn", 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"); } 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; }

## OUTPUT:

Vertex Distance from Source 0 0 1 -1 2 2 3 -2 4 1