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Problem solution · Python

ABC275 C — Counting Squares

ABC275 C — Counting Squares: a Python solution using sorting and greedy selection. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Sorting and greedy selection
Source
KATO-Hiro AtCoder Solutions
Length
60 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

Sorting and greedy selection

For ABC275 C — Counting Squares, the implementation first exposes a useful order, then scans that order while making locally justified choices.

  1. Choose the key that reveals the greedy or grouping structure.
  2. Sort the relevant records by that key.
  3. Scan in order, maintaining the invariant that makes each local choice safe.

Code notes

  • 60 lines of Python from the credited upstream file abc275_c.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Sorting is typically the dominant term unless the subsequent scan uses a more expensive nested operation.

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 codeABC275 C — Counting Squares · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  def main():    from itertools import combinations    import sys     input = sys.stdin.readline     s = [input().rstrip() for _ in range(9)]    xy = list()    count = 0     for x in range(9):        for y in range(9):            if s[y][x] == "#":                xy.append((x, y))                count += 1                ans = 0        # points: [(x1, y1), (x2, y2), (x3, y3), (x4, y4)]    def is_square(points):        # See:        # https://sugim48.hatenadiary.org/entry/20141007/1412679470         dist = list()          for i in range(4):            x1, y1 = points[i]             for j in range(i + 1, 4):                x2, y2 = points[j]                 dx = (x2 - x1) ** 2                dy = (y2 - y1) ** 2                 dist.append(dx + dy)         dist = sorted(dist)        base = dist[0]         if base == 0:            return False # duplicated                if dist.count(base) == 4 and dist.count(base * 2) == 2:            return True        else:            return False     for a, b, c, d in combinations(range(count), 4):        if is_square((xy[a], xy[b], xy[c], xy[d])):            ans += 1     print(ans)     if __name__ == "__main__":    main()

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