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Floyd Warshall Algorithm in DAA with example in Hindi

In this video I have explained Floyd Warshall Algorithm for finding Shortest Paths in a weighted graph. It is All Pair Shortest Path Graph Algorithm. It uses Dynamic Programming Approach.

Floyd-Warshall algorithm to find all pairs of shortest paths between all nodes in a graph using dynamic programming.

Step by step instructions showing how to run the Floyd–Warshall algorithm on a graph.

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The Floyd-Warshall algorithm, named after its creators Robert Floyd and Stephen Warshall, is a fundamental algorithm in computer science and graph theory. It is used to find the shortest paths between all pairs of nodes in a weighted graph. This algorithm is highly efficient and can handle graphs with both positive and negative edge weights, making it a versatile tool for solving a wide range of network and connectivity problems.

Idea Behind Floyd Warshall Algorithm:
Suppose we have a graph G[][] with V vertices from 1 to N. Now we have to evaluate a shortestPathMatrix[][] where shortestPathMatrix[i][j] represents the shortest path between vertex i to j.
Obviously the shortest path between i to j will have some k number of intermediate nodes. The idea behind floyd warshall algorithm is to treat each and every vertex from 1 to N as an intermediate node one by one.

The Floyd-Warshall algorithm is a graph algorithm that is deployed to find the shortest path between all the vertices present in a weighted graph. This algorithm is different from other shortest path algorithms; to describe it simply, this algorithm uses each vertex in the graph as a pivot to check if it provides the shortest way to travel from one point to another.

Floyd-Warshall algorithm works on both directed and undirected weighted graphs unless these graphs do not contain any negative cycles in them. By negative cycles, it is meant that the sum of all the edges in the graph must not lead to a negative number.

Since, the algorithm deals with overlapping sub-problems – the path found by the vertices acting as pivot are stored for solving the next steps – it uses the dynamic programming approach.

Floyd-Warshall algorithm is one of the methods in All-pairs shortest path algorithms and it is solved using the Adjacency Matrix representation of graphs.

The algorithm works with the aid of computing the shortest direction between every pair of vertices within the graph, the usage of a matrix of intermediate vertices to keep music of the exceptional-recognized route thus far.