Counting Paths of Length K in Directed Graphs Using Matrix Exponentiation
By
jxmorris12
Crisp on the outside, thoughtful on the inside. A keeper.
Summary
This article presents a programming problem about counting paths of length K between two nodes in a directed unweighted graph, where paths can revisit nodes and edges. The solution involves using matrix exponentiation techniques to compute the result modulo a large prime number to handle potentially very large numbers.
Key quotes
· 3 pulledGiven a directed unweighted graph with V vertices and E edges, how many paths of length K are there from node A to node B?
Paths may visit the same node or edge multiple times
To avoid dealing with very large numbers, assume that we're computing our answer modulo a large prime
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