Create bellman_ford.cpp

Algorithms/bellman_ford.cpp

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+// A C++ program for Bellman-Ford's single source
+// shortest path algorithm.
+#include <bits/stdc++.h>
+using namespace std;
+
+// 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's code
+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 B-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;
+
+      // Function call
+    BellmanFord(graph, 0);
+
+    return 0;
+}