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Problem solution · Python

ABC425 E — Count Sequences 2

ABC425 E — Count Sequences 2: a Python solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Direct simulation
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

Direct simulation

For ABC425 E — Count Sequences 2, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 61 lines of Python from the credited upstream file abc425_e.py.
  • The implementation visibly relies on sequence storage, ordered lookup.
  • No explicit loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

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 codeABC425 E — Count Sequences 2 · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  def calc_pascals_triangle(n_max, mod):    """Calc binomial coefficients (nCk).     Args:        n_max: A max number (greater than or equal to 0).     Returns:        List of binomial coefficients.     Examples:        7C3: c[7][3]     Landau notation: O(n_max ** 2).    """     assert n_max >= 0     c = [[0 for _ in range(n_max + 1)] for _ in range(n_max + 1)]    c[0][0] = 1     for i in range(n_max):        for j in range(i + 1):            c[i + 1][j] += c[i][j] % mod            c[i + 1][j + 1] += c[i][j] % mod     return c  def solve(pascals_triangle, mod):    n = int(input())    c = list(map(int, input().split()))    summed_c = 0    ans = 1     for ci in c:        summed_c += ci        ans *= pascals_triangle[summed_c][ci]        ans %= mod     print(ans)  def main():    import sys     input = sys.stdin.readline     t, mod = map(int, input().split())    c_max = 5000    pascals_triangle = calc_pascals_triangle(c_max, mod)     for _ in range(t):        solve(pascals_triangle, mod)  if __name__ == "__main__":    main()

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