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Problem solution · Python

ABC215 E — Chain Contestant

ABC215 E — Chain Contestant: a Python solution using dynamic programming. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Dynamic programming
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

Dynamic programming

For ABC215 E — Chain Contestant, the implementation records answers for smaller states and reuses them to build the requested result without repeating work.

  1. Define precisely what one DP state represents.
  2. Establish the base cases before transitions are evaluated.
  3. Process states in dependency order and combine only already-known values.

Code notes

  • 61 lines of Python from the credited upstream file abc215_e.py.
  • The implementation visibly relies on cached states.
  • No explicit loop blocks detected.

Complexity

Multiply the number of reachable states by the work performed for each transition, then include the stored state table in memory usage.

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 codeABC215 E — Chain Contestant · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  def get_offset(alphabet: str, base_alphabet: str = 'A') -> int:    '''Get offset between the base_alphabet and alphabet.    Args:        alphabet: The alphabet to use.         base_alphabet: The base alphabet to use.    Returns:        difference between the base_alphabet and alphabet.        See:    https://docs.python.org/3.11/library/functions.html?highlight=chr#ord    '''        return ord(alphabet) - ord(base_alphabet)  def main():    import sys     input = sys.stdin.readline     n = int(input())    s = input().rstrip()    types = 10    patterns = 1 << types    dp = [[0] * types for _ in range(patterns)]    mod = 998244353     for i in range(n):        cur = get_offset(s[i])         for pattern in reversed(range(patterns)):            for prev in range(types):                if pattern >> prev & 1:                    if cur == prev:                        dp[pattern][prev] += dp[pattern][prev]                        dp[pattern][prev] %= mod                                              if ~pattern >> cur & 1:                        dp[pattern | 1 << cur][cur] += dp[pattern][prev]                        dp[pattern | 1 << cur][cur] %= mod                            dp[1 << cur][cur] += 1        dp[1 << cur][cur] %= mod                dp = dp        ans = 0        for d in dp:        ans += sum(d)        ans %= mod     print(ans)     if __name__ == "__main__":    main()

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