Page 81 - Data Structures Interactive Book

8.4.3 Floyd-Warshall Algorithm

The Floyd-Warshall algorithm is an all-pairs shortest path algorithm, meaning it

computes the shortest paths between every pair of vertices. It is particularly useful for dense

graphs and small to medium-sized networks. The algorithm uses dynamic programming,

gradually improving path estimates by considering intermediate vertices.

Step-by-step process:
1. Initialize a distance matrix with direct edge weights.
,
2. For each vertex , update all pairs ( )by checking if going through provides a shorter

path.
3. After considering all vertices, the matrix contains shortest paths between all pairs.

Example in C++:

This program computes shortest paths between all pairs of vertices, producing a

matrix that can be used for routing or network analysis.

8.5 Minimum Spanning Tree (MST)

A Minimum Spanning Tree (MST) is a subset of the edges of a connected, weighted,

undirected graph that connects all the vertices together without any cycles and with the

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