lib/math/bell.hpp

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• Last update: 2026-02-15 06:34:51+09:00
• Include: #include "lib/math/bell.hpp"

Depends on

• lib/fft/formal_power_series.hpp
• 畳み込み (lib/fft/ntt.hpp)
• lib/internal/internal_fft.hpp
• Montgomery modular multiplication (lib/internal/internal_math.hpp)
• lib/internal/internal_type_traits.hpp
• 二項係数 (lib/math/combination.hpp)
• lib/math/modint.hpp
• lib/template/template.hpp

Verified with

• test/yosupo/enumerative_conbinatorics/bell_number.test.cpp

Code

#pragma once
#include <vector>
#include "fft/formal_power_series.hpp"

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> bell(int n) {
    if (n == 0) return std::vector<mint>(1, mint(1));
    std::vector<mint> res(n + 1);
    res[1] = 1;
    res = fps::exp(res);
    res[0] -= 1;
    res = fps::exp(res);
    mint mul = 1;
    for (int i = 0; i <= n; ++i) {
        res[i] *= mul;
        mul *= i + 1;
    }
    return res;
}

Traceback (most recent call last):
  File "/home/runner/.local/lib/python3.12/site-packages/competitive_verifier/oj/resolver.py", line 291, in resolve
    bundled_code = language.bundle(path, basedir=basedir)
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/runner/.local/lib/python3.12/site-packages/competitive_verifier/oj/verify/languages/cplusplus.py", line 242, in bundle
    bundler.update(path)
  File "/home/runner/.local/lib/python3.12/site-packages/competitive_verifier/oj/verify/languages/cplusplus_bundle.py", line 479, in update
    self._resolve(pathlib.Path(included), included_from=path)
  File "/home/runner/.local/lib/python3.12/site-packages/competitive_verifier/oj/verify/languages/cplusplus_bundle.py", line 286, in _resolve
    raise BundleErrorAt(path, -1, "no such header")
competitive_verifier.oj.verify.languages.cplusplus_bundle.BundleErrorAt: fft/formal_power_series.hpp: line -1: no such header

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