Added few graph algorithms

Author: ssumukh

Graph/BellmanFordSSSP/BellmanFordSSSP.cpp

@@ -0,0 +1,139 @@
+// 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");
+    }
+ 
+    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
+    graph->edge[0].src = 0;
+    graph->edge[0].dest = 1;
+    graph->edge[0].weight = -1;
+ 
+    // add edge 0-2
+    graph->edge[1].src = 0;
+    graph->edge[1].dest = 2;
+    graph->edge[1].weight = 4;
+ 
+    // add edge 1-2
+    graph->edge[2].src = 1;
+    graph->edge[2].dest = 2;
+    graph->edge[2].weight = 3;
+ 
+    // add edge 1-3
+    graph->edge[3].src = 1;
+    graph->edge[3].dest = 3;
+    graph->edge[3].weight = 2;
+ 
+    // add edge 1-4
+    graph->edge[4].src = 1;
+    graph->edge[4].dest = 4;
+    graph->edge[4].weight = 2;
+ 
+    // add edge 3-2
+    graph->edge[5].src = 3;
+    graph->edge[5].dest = 2;
+    graph->edge[5].weight = 5;
+ 
+    // add edge 3-1
+    graph->edge[6].src = 3;
+    graph->edge[6].dest = 1;
+    graph->edge[6].weight = 1;
+ 
+    // add edge 4-3
+    graph->edge[7].src = 4;
+    graph->edge[7].dest = 3;
+    graph->edge[7].weight = -3;
+ 
+    BellmanFord(graph, 0);
+ 
+    return 0;
+}