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Problem solution · Python

ABC272 D — Root M Leaper

ABC272 D — Root M Leaper: a Python solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Breadth-first search
Source
KATO-Hiro AtCoder Solutions
Length
46 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Breadth-first search

For ABC272 D — Root M Leaper, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 46 lines of Python from the credited upstream file abc272_d.py.
  • The implementation visibly relies on sequence storage, ordered lookup, work queue.
  • No explicit loop blocks detected.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from KATO-Hiro AtCoder Solutions by KATO-Hiro and is used under the CC0-1.0 licence.

Open problem ↗Original source ↗
Full codeABC272 D — Root M Leaper · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  def main():    from collections import deque    import sys     input = sys.stdin.readline     n, m = map(int, input().split())    dxy = list()     # 前計算: 到達可能なマスを列挙    for dx in range(-n, n):        for dy in range(-n, n):            if (dx ** 2 + dy ** 2) == m:                dxy.append((dx, dy))        # BFS    not_visited = -1    dist = [[not_visited] * n for _ in range(n)]    dist[0][0] = 0    d = deque()    d.append((0, 0, 0))  # cur_dist, x, y     while d:        di, x, y = d.popleft()         for dx, dy in dxy:            nx = x + dx            ny = y + dy             if nx < 0 or nx >= n or ny < 0 or ny >= n:                continue             if dist[ny][nx] == -1:                dist[ny][nx] = di + 1                d.append((di + 1, nx, ny))     for di in dist:        print(*di)  if __name__ == "__main__":    main()

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