setfunc/ranked_zeta.hpp

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• Last update: 2023-09-23 23:33:32+09:00
• Include: #include "setfunc/ranked_zeta.hpp"
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Required by

• linalg/hafnian.hpp
• setfunc/sps_composition.hpp
• setfunc/sps_exp.hpp
• setfunc/sps_inv.hpp
• setfunc/sps_log.hpp
• setfunc/subset_convolution.hpp
• setfunc/transposed_sps_composition.hpp

Verified with

• test/library_checker/convolution/subset_convolution.test.cpp
• test/library_checker/math/composition_sps.test.cpp
• test/library_checker/math/powproj_sps.test.cpp
• test/library_checker/math/sps_exp.test.cpp
• test/library_checker/matrix/hafnian_of_matrix.test.cpp
• test/yukicoder/2507.test.cpp
• test_atcoder/abc213g.test.cpp
• test_atcoder/abc236h.test.cpp
• test_atcoder/abc253h.test.cpp
• test_atcoder/abc306h.test.cpp
• test_atcoder/abc321g.test.cpp
• test_atcoder/arc105.test.cpp

Code

#pragma once

template <typename T, int LIM>
vc<array<T, LIM + 1>> ranked_zeta(const vc<T>& f) {
  int n = topbit(len(f));
  assert(n <= LIM);
  assert(len(f) == 1 << n);
  vc<array<T, LIM + 1>> Rf(1 << n);
  for (int s = 0; s < (1 << n); ++s) Rf[s][popcnt(s)] = f[s];
  for (int i = 0; i < n; ++i) {
    int w = 1 << i;
    for (int p = 0; p < (1 << n); p += 2 * w) {
      for (int s = p; s < p + w; ++s) {
        int t = s | 1 << i;
        for (int d = 0; d <= n; ++d) Rf[t][d] += Rf[s][d];
      }
    }
  }
  return Rf;
}

template <typename T, int LIM>
vc<T> ranked_mobius(vc<array<T, LIM + 1>>& Rf) {
  int n = topbit(len(Rf));
  assert(len(Rf) == 1 << n);
  for (int i = 0; i < n; ++i) {
    int w = 1 << i;
    for (int p = 0; p < (1 << n); p += 2 * w) {
      for (int s = p; s < p + w; ++s) {
        int t = s | 1 << i;
        for (int d = 0; d <= n; ++d) Rf[t][d] -= Rf[s][d];
      }
    }
  }
  vc<T> f(1 << n);
  for (int s = 0; s < (1 << n); ++s) f[s] = Rf[s][popcnt(s)];
  return f;
}

#line 2 "setfunc/ranked_zeta.hpp"

template <typename T, int LIM>
vc<array<T, LIM + 1>> ranked_zeta(const vc<T>& f) {
  int n = topbit(len(f));
  assert(n <= LIM);
  assert(len(f) == 1 << n);
  vc<array<T, LIM + 1>> Rf(1 << n);
  for (int s = 0; s < (1 << n); ++s) Rf[s][popcnt(s)] = f[s];
  for (int i = 0; i < n; ++i) {
    int w = 1 << i;
    for (int p = 0; p < (1 << n); p += 2 * w) {
      for (int s = p; s < p + w; ++s) {
        int t = s | 1 << i;
        for (int d = 0; d <= n; ++d) Rf[t][d] += Rf[s][d];
      }
    }
  }
  return Rf;
}

template <typename T, int LIM>
vc<T> ranked_mobius(vc<array<T, LIM + 1>>& Rf) {
  int n = topbit(len(Rf));
  assert(len(Rf) == 1 << n);
  for (int i = 0; i < n; ++i) {
    int w = 1 << i;
    for (int p = 0; p < (1 << n); p += 2 * w) {
      for (int s = p; s < p + w; ++s) {
        int t = s | 1 << i;
        for (int d = 0; d <= n; ++d) Rf[t][d] -= Rf[s][d];
      }
    }
  }
  vc<T> f(1 << n);
  for (int s = 0; s < (1 << n); ++s) f[s] = Rf[s][popcnt(s)];
  return f;
}

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