Bellman–Ford Algorithm.cpp

// A C++ program for Bellman-Ford's single source 
// shortest path algorithm. 
#include <bits/stdc++.h> 

// a 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 = new Graph; 
	graph->V = V; 
	graph->E = E; 
	graph->edge = new Edge[E]; 
	return graph; 
} 

// A utility function used to print the solution 
void printArr(int dist[], int n) 
{ 
	printf("Vertex Distance from Source\n"); 
	for (int i = 0; i < n; ++i) 
		printf("%d \t\t %d\n", 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"); 
			return; // If negative cycle is detected, simply return 
		} 
	} 

	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; 
}