Question
You are given an n x n adjacency matrix `adj` of a directed graph (adj[i][j] == 1 means an edge i->j, else 0), a start node `src`, a destination node `dst`, and an integer `k`. Return the number of distinct walks of EXACTLY k edges from `src` to `dst`, modulo 1_000_000_007. n is up to 50 and k can be as large as 10^9, so you must use fast matrix exponentiation rather than DP over k.
count_walks(adj: list[list[int]], src: int, dst: int, k: int) → int[[[0,1,0],[0,0,1],[1,0,0]],0,0,3]out1State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.