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All Pair Shortest Paths Finder in C++ using Floyd-Warshall Algorithm

By Divyanshu Pandey

This project helps in finding the shortest paths using the Floyd-warshall algorithm. The project implementation is made in the C++ language.

In this project, our task is to find the shortest paths between all the pairs of vertices in a weighted graph using the Floyd-warshall algorithm as per the user's choice. The algorithm follows the approach of dynamic programming in which comparisons are made for all the possible paths between every pair of vertices in the graph.

Note:-

1.Ensure No negative cycles are formed.

How does this Project work?

Step 1: On execution of the project main menu is popped Having 2 functionalities

            1.All Possible Shortest Path.
            2.Quit Program.

Step 2: As Per User choice Entered For eg:- option 1 is chosen, then the user is asked to enter the number of vertices.

Step 3: After inputting the number of vertices, the user then will be required to enter the cost matrix i.e cost corresponding from each vertex to all other vertices.

Note:- While entering the cost matrix please note the user does not need to input the cost where the source vertex and destination vertex are the same. For Eg:- cost from vertex 0 to vertex 0. Cost is considered 0 in this case and other similar situations.

Step 4: After successful input of the cost matrix Press enter and Finally all pair shortest paths are generated and displayed.

Time Complexity of the program:- O(N^3).

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Submitted by Divyanshu Pandey (Divyanshu)

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