From 6b952a061028a1a7c2a037a6cc92cc9cdeffbc3b Mon Sep 17 00:00:00 2001
From: Abhishek-kumar82078
 <63895917+Abhishek-kumar82078@users.noreply.github.com>
Date: Sun, 17 Oct 2021 21:33:49 +0530
Subject: [PATCH] Added Floyd Warshall Algorithm in c++

Added an algorithm to find shortest distance
---
 Graph_Algorithms/src/Floyd_Warshall.cpp | 63 +++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 Graph_Algorithms/src/Floyd_Warshall.cpp

diff --git a/Graph_Algorithms/src/Floyd_Warshall.cpp b/Graph_Algorithms/src/Floyd_Warshall.cpp
new file mode 100644
index 0000000..25251e5
--- /dev/null
+++ b/Graph_Algorithms/src/Floyd_Warshall.cpp
@@ -0,0 +1,63 @@
+// Floyd Warshall Algorithm
+// A space efficient algorithm to find shortest distance in space complexity of (O(1))
+// Time complexity - O(v^3)
+
+#include<bits/stdc++.h>
+using namespace std;
+
+// Function which finds the shortest distance
+void shortest_distance(vector<vector<int>>&matrix)
+{
+       // Making first loop as intermediate between two vertices
+	    for(int k=0;k<matrix.size();k++)
+	    {
+	        // Value of i is treated as starting vertex of edge
+	        for(int i=0;i<matrix.size();i++)
+	        {
+	            // Value of j is treated as starting vertex of edge
+	              for(int j=0;j<matrix.size();j++)
+	              {
+                    // Avoiding self edge as well as intermediate vertex which is same as either of the two vertices of edge
+	                if(k!=i && k!=j  && i!=j)
+	                {
+	                    // Not trying to put unavailable edge as intermediate edge And also adding edge if not available
+	                    if(matrix[i][k]!=-1 && matrix[k][j]!=-1 && ((matrix[i][j] > (matrix[i][k]+matrix[k][j])) || matrix[i][j]==-1))
+	                     matrix[i][j]=matrix[i][k]+matrix[k][j];
+	                }
+	              }
+
+	        }
+	    }
+}
+
+int main()
+{
+ int v;
+ cin>>v;
+ vector<vector<int>>matrix(v,vector<int>(v,-1));
+ for(int i=0;i<v;i++)
+ {
+  for(int j=0;j<v;j++)
+  {
+   cin>>matrix[i][j];
+  }
+ }
+ shortest_distance(matrix);
+
+ // Printing the updated matrix
+ for(int i=0;i<v;i++)
+ {
+  for(int j=0;j<v;j++)
+  {
+   cout<<matrix[i][j]<<" ";
+  }
+  cout<<endl;
+ }
+ return 0;
+}
+
+// Description
+// This algorithm helps in finding shortest distance between
+// every pair of vertices in a given edge weighted directed Graph in in-place.
+// Core idea:- add any other vertex in between two edge and check if the previous distance
+// is greater than adding two edge connected with the intermediate edge, if yes update it.