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Problem solution · Python

ARC161 B — Exactly Three Bits

ARC161 B — Exactly Three Bits: 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
57 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 ARC161 B — Exactly Three Bits, 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

  • 57 lines of Python from the credited upstream file arc161_b.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 codeARC161 B — Exactly Three Bits · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*- from bisect import bisect_rightfrom typing import List  def bisect_le(sorted_array: List[int], value: int):    """Find the largest element <= x and its index, or None if it doesn't exist."""     if sorted_array[0] <= value:        index: int = bisect_right(sorted_array, value) - 1         return index, sorted_array[index]     return None, None  def solve(candidates):    n = int(input())     _, value = bisect_le(candidates, n)     if value is None:        print(-1)    else:        print(value)  def main():    import sys     input = sys.stdin.readline     t = int(input())     from itertools import combinations     candidates = []     m = 60     for i, j, k in combinations(range(m), 3):        if i == j or j == k or i == k:            continue         candidate = 2**i + 2**j + 2**k        candidates.append(candidate)     candidates.sort()     for _ in range(t):        solve(candidates)  if __name__ == "__main__":    main()

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