From 9cd56c01ad87cc282ddc815ff3bf2a9ec79801e9 Mon Sep 17 00:00:00 2001
From: arpanjain97 <arpanjain97@gmail.com>
Date: Thu, 12 Oct 2017 17:23:14 +0530
Subject: [PATCH] Add Floyd-Warshall Algorithm

---
 Dynamic Programming/Floyd-Warshall.cpp | 106 +++++++++++++++++++++++++
 1 file changed, 106 insertions(+)
 create mode 100644 Dynamic Programming/Floyd-Warshall.cpp

diff --git a/Dynamic Programming/Floyd-Warshall.cpp b/Dynamic Programming/Floyd-Warshall.cpp
new file mode 100644
index 000000000..9f037a64d
--- /dev/null
+++ b/Dynamic Programming/Floyd-Warshall.cpp	
@@ -0,0 +1,106 @@
+#include<iostream>
+#include<limits.h>
+#include<string.h>
+
+using namespace std;
+
+//Wrapper class for storing a graph
+class Graph{
+	public:
+	int vertexNum;
+	int** edges;
+
+	//Constructs a graph with V vertices and E edges
+	Graph(int V){
+		this->vertexNum = V;
+		this->edges =(int**) malloc(V * sizeof(int*));
+		for(int i=0; i<V; i++){
+			this->edges[i] = (int*) malloc(V * sizeof(int));
+			for(int j=0; j<V; j++)
+				this->edges[i][j] = INT_MAX;
+			this->edges[i][i] = 0;
+		}		
+	}
+
+	//Adds the given edge to the graph 
+	void addEdge(int src, int dst, int weight){
+		this->edges[src][dst] = weight;
+	}
+	
+
+};
+
+
+//Utility function to print distances
+void print(int dist[], int V){
+	cout<<"\nThe Distance matrix for Floyd - Warshall"<<endl;
+	for(int i = 0; i < V; i++){
+		for(int j=0; j<V; j++){
+
+		if(dist[i*V+j] != INT_MAX)	
+			cout<<dist[i*V+j]<<"\t";
+		else
+			cout<<"INF"<<"\t";
+		}
+		cout<<endl;
+	}
+}
+
+//The main function that finds the shortest path from a vertex
+//to all other vertices using Floyd-Warshall Algorithm.
+void FloydWarshall(Graph graph){
+	int V = graph.vertexNum;
+	int dist[V][V];
+	
+	//Initialise distance array
+	for(int i=0; i<V; i++)
+		for(int j=0; j<V; j++)
+			dist[i][j] = graph.edges[i][j];	
+			
+	
+	//Calculate distances
+	for(int k=0; k<V; k++)
+	//Choose an intermediate vertex
+
+		for(int i=0; i<V; i++)	
+		//Choose a source vertex for given intermediate
+
+			for(int j=0; j<V; j++)
+			//Choose a destination vertex for above source vertex
+
+				if(dist[i][k] != INT_MAX && dist[k][j] != INT_MAX && dist[i][k] + dist[k][j] < dist[i][j])
+				//If the distance through intermediate vertex is less than direct edge then update value in distance array
+					dist[i][j] = dist[i][k] + dist[k][j];
+
+	
+	//Convert 2d array to 1d array for print
+	int dist1d[V*V];	
+	for(int i=0; i<V; i++)
+		for(int j=0; j<V; j++)
+			dist1d[i*V+j] = dist[i][j];
+	
+	print(dist1d,V);	
+	}
+
+//Driver Function
+int main(){
+	int V,E;
+	int src,dst,weight;
+	cout<<"Enter number of vertices: ";
+	cin>>V;
+	cout<<"Enter number of edges: ";
+	cin>>E;
+	Graph G(V);
+	for(int i=0; i<E; i++){
+		cout<<"\nEdge "<<i+1<<"\nEnter source: ";
+		cin>>src;
+		cout<<"Enter destination: ";
+		cin>>dst;
+		cout<<"Enter weight: ";
+		cin>>weight;
+		G.addEdge(src, dst, weight);
+	}
+	FloydWarshall(G);
+
+	return 0;
+}