seq/hook_length_formula.hpp

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• Last update: 2022-12-07 02:54:40+09:00
• Include: #include "seq/hook_length_formula.hpp"

Required by

• seq/domino_standard_tableaux.hpp

Verified with

• test/yukicoder/2149.test.cpp

Code

#pragma once

template <typename mint>
mint hook_length_formula(vc<int> A) {
  if (len(A) == 0) return 1;
  int H = len(A), W = A[0];
  FOR(i, H - 1) assert(A[i] >= A[i + 1]);
  vc<int> B(W);
  reverse(all(A));
  mint ANS = fact<mint>(SUM<int>(A));
  for (auto&& a: A) {
    FOR(j, a) { ANS *= inv<mint>(B[j] + a - j), ++B[j]; }
  }
  return ANS;
}

#line 2 "seq/hook_length_formula.hpp"

template <typename mint>
mint hook_length_formula(vc<int> A) {
  if (len(A) == 0) return 1;
  int H = len(A), W = A[0];
  FOR(i, H - 1) assert(A[i] >= A[i + 1]);
  vc<int> B(W);
  reverse(all(A));
  mint ANS = fact<mint>(SUM<int>(A));
  for (auto&& a: A) {
    FOR(j, a) { ANS *= inv<mint>(B[j] + a - j), ++B[j]; }
  }
  return ANS;
}

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