floyd warshall algorithm for finding all pair shortest path in a conn…

…ected graph

floyd_warshall_algorithm/CPP/floyd-warshall algorithm.cpp

@@ -0,0 +1,73 @@
+//Floyd-Warshall Algorithm: all pair shortest path
+#include <iostream>
+#include <climits>
+using namespace std;
+
+#define INF 999999999
+
+int main()
+{
+	int graph[1001][1001],i,j,k,n,m;
+	cin>>n>>m;	//number of vertices and edges respectively
+
+	for(i=1;i<=n;i++)
+	{
+		for(j=1;j<=n;j++)
+			if(i==j)	graph[i][j]=0;	//Shortest distance between (i,i) is 0
+			else
+				graph[i][j] = INF;		//Initializing other distances as infinite
+	}
+
+	for(i=1;i<=m;i++)
+	{
+		int u,v,w;
+		cin>>u>>v>>w;
+		graph[u][v] = w;				//input graph
+		graph[v][u] = w;				//Shortest distance between (i,j) using atmost one edge
+	}
+
+
+	for(k=1;k<=n;k++)					
+	{
+		for(int u=1;u<=n;u++)
+		{
+			for(int v=1;v<=n;v++)
+			{
+				//Shortest distance between (i,j) using atmost k edges
+				graph[u][v] = min(graph[u][v],graph[u][k]+graph[k][v]);	
+			}
+		}
+	}
+
+	//Resulting all pair shortest path in given graph
+	for(int u=1;u<=n;u++)
+	{
+		for(int v=1;v<=n;v++)
+		{
+			cout<<graph[u][v]<<" ";
+		}
+		cout<<endl;
+	}
+	cout<<endl;
+	return 0;
+}
+
+/*
+Input:-
+First line contain two space separated integer n and m 
+where n is the number of vertices and m is the number 
+of edges.Next m lines contains three space seprated integers
+u, v and w which represents that there is an edge between u and v
+and weight of the edge is w
+Sample Input:-
+6 9
+1 2 1
+1 3 2
+1 4 5
+2 4 5
+2 5 2
+3 4 3
+4 5 1
+4 6 1
+5 6 4
+*/