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Problem solution · Python

ABC346 E — Paint

ABC346 E — Paint: 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
61 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 ABC346 E — Paint, 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

  • 61 lines of Python from the credited upstream file abc346_e.py.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup.
  • 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 codeABC346 E — Paint · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  def main():    import sys    from collections import defaultdict     input = sys.stdin.readline     h, w, m = map(int, input().split())    tax = list()     for i in range(m):        tax.append(list(map(int, input().split())))     colors = defaultdict(int)    remain_h, remain_w = h, w    used_h, used_w = [False] * h, [False] * w     # 後の操作が優先される場合は、逆順にみる    # 行単位 / 列単位で更新する場合は、行列を入れ替えても結果が変わらないことを利用    for i in range(m - 1, -1, -1):        ti, ai, xi = tax[i]        ai -= 1         if ti == 1:            if used_h[ai]:                continue             used_h[ai] = True             colors[xi] += remain_w            remain_h -= 1        else:            if used_w[ai]:                continue             used_w[ai] = True             colors[xi] += remain_h            remain_w -= 1     # 左上の領域の0の個数を追加    colors[0] += remain_h * remain_w    ans = list()     for key in sorted(colors.keys()):        count = colors[key]         if count > 0:            ans.append((key, count))     print(len(ans))     for key, count in ans:        print(key, count)  if __name__ == "__main__":    main()

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