Floyd Warshall Algorithm follows a dynamic programming approach. Here are the steps:

1. Initialization: Create a matrix of size n*n where n is the number of vertices. The value of i and j in the matrix represents the weight of the edge between the vertices i and j. If there is no direct edge between i and j, the value is infinity.

2. Iteration: The algorithm iterates over all pairs of vertices (i, j). For each pair, it checks if there is a vertex k such that the path from i to j through k is shorter than the current shortest path from i to j. If such a vertex is found, the value in the matrix for the pair (i, j) is updated to the shorter path.

3. Path Reconstruction: After the iteration step, the matrix contains the shortest paths between all pairs of vertices. The path between any two vertices can be reconstructed by backtracking from the destination vertex to the source vertex.

4. Return the matrix: The final matrix represents the shortest path between every pair of vertices in the graph.

Question

Floyd Warshall Algorithm follows a dynamic programming approach. Here are the steps:

1. Initialization: Create a matrix of size n*n where n is the number of vertices. The value of i and j in the matrix represents the weight of the edge between the vertices i and j. If there is no direct edge between i and j, the value is infinity.

2. Iteration: The algorithm iterates over all pairs of vertices (i, j). For each pair, it checks if there is a vertex k such that the path from i to j through k is shorter than the current shortest path from i to j. If such a vertex is found, the value in the matrix for the pair (i, j) is updated to the shorter path.

3. Path Reconstruction: After the iteration step, the matrix contains the shortest paths between all pairs of vertices. The path between any two vertices can be reconstructed by backtracking from the destination vertex to the source vertex.

4. Return the matrix: The final matrix represents the shortest path between every pair of vertices in the graph.

Knowee AI · Accepted Answer

Floyd Warshall Algorithm follows a dynamic programming approach. Here are the steps:

1. Initialization: Create a matrix of size n*n where n is the number of vertices. The value of i and j in the matrix represents the weight of the edge between the vertices i and j. If there is no direct edge between i and j, the value is infinity.

2. Iteration: The algorithm iterates over all pairs of vertices (i, j). For each pair, it checks if there is a vertex k such that the path from i to j through k is shorter than the current shortest path from i to j. If such a vertex is found, the value in the matrix for the pair (i, j) is updated to the shorter path.

3. Path Reconstruction: After the iteration step, the matrix contains the shortest paths between all pairs of vertices. The path between any two vertices can be reconstructed by backtracking from the destination vertex to the source vertex.

4. Return the matrix: The final matrix represents the shortest path between every pair of vertices in the graph.

What approach is being followed in Floyd Warshall Algorithm?

Question

Solution

Similar Questions

Upgrade your grade with Knowee