Complexity Analysis of Floyd Warshall Algorithm
- Time Complexity: O(V3), where V is the number of vertices in the graph and we run three nested loops each of size V
- Auxiliary Space: O(V2), to create a 2-D matrix in order to store the shortest distance for each pair of nodes.
Note: The above program only prints the shortest distances. We can modify the solution to print the shortest paths also by storing the predecessor information in a separate 2D matrix.
Floyd Warshall Algorithm
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.
Table of Content
- Floyd Warshall Algorithm
- Idea Behind Floyd Warshall Algorithm
- Floyd Warshall Algorithm Algorithm
- Pseudo-Code of Floyd Warshall Algorithm
- Illustration of Floyd Warshall Algorithm
- Complexity Analysis of Floyd Warshall Algorithm
- Why Floyd-Warshall Algorithm better for Dense Graphs and not for Sparse Graphs?
- Important Interview questions related to Floyd-Warshall
- Real World Applications of Floyd-Warshall Algorithm
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