poly/integrate.hpp

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• Last update: 2023-06-13 03:24:50+09:00
• Include: #include "poly/integrate.hpp"

Required by

• graph/count/count_labeled_biconnected.hpp
• graph/count/count_labeled_bipartite.hpp
• graph/count/count_labeled_bridgeless.hpp
• graph/count/count_labeled_forest.hpp
• poly/composed_product.hpp
• poly/composed_sum.hpp
• poly/composition_f_a_plus_bx_div_c_plus_dx.hpp
• poly/composition_f_log_1_minus_x.hpp
• poly/compositional_inverse.hpp
• poly/fps_exp.hpp
• poly/fps_pow.hpp
• poly/fps_sqrt.hpp
• poly/product_of_f_rk_x.hpp
• poly/product_of_one_minus_xn.hpp
• poly/product_of_one_plus_xn.hpp
• poly/product_of_pow_of_linear.hpp
• seq/famous/bell_number.hpp
• seq/famous/stirling_number_1.hpp
• seq/famous/stirling_number_2.hpp
• seq/famous/surjection.hpp

Verified with

• test/library_checker/math/sharp_p_subset_sum.test.cpp
• test/library_checker/math/stirling_number_of_the_first_kind.test.cpp
• test/library_checker/math/stirling_number_of_the_first_kind_fixed_k.test.cpp
• test/library_checker/math/stirling_number_of_the_second_kind.test.cpp
• test/library_checker/polynomial/compositional_inverse.test.cpp
• test/library_checker/polynomial/exp_of_fps.test.cpp
• test/library_checker/polynomial/exp_of_fps_dmint.test.cpp
• test/library_checker/polynomial/exp_of_fps_sparse.test.cpp
• test/library_checker/polynomial/exp_of_fps_sparse_dmint.test.cpp
• test/library_checker/polynomial/pow_of_fps.test.cpp
• test/library_checker/polynomial/pow_of_fps_dmint.test.cpp
• test/library_checker/polynomial/pow_of_fps_sparse.test.cpp
• test/library_checker/polynomial/pow_of_fps_sparse_dmint.test.cpp
• test/library_checker/polynomial/sqrt_of_fps.test.cpp
• test/library_checker/polynomial/sqrt_of_fps_sparse.test.cpp
• test/mytest/bell.test.cpp
• test/mytest/bell_number.test.cpp
• test/mytest/composition_log_1_minus_x.test.cpp
• test/mytest/compositional_inverset.test.cpp
• test/mytest/count_bipartite.test.cpp
• test/mytest/count_labeled_biconnected.test.cpp
• test/mytest/count_labeled_bridgeless.test.cpp
• test/mytest/count_labeled_forest.test.cpp
• test/mytest/graph_count.test.cpp
• test/mytest/online_exp.test.cpp
• test/mytest/online_pow.test.cpp
• test/mytest/online_square.test.cpp
• test/mytest/power_projection.test.cpp
• test/mytest/product_of_one_pm_xn.test.cpp
• test/mytest/sparse_pow_2d.test.cpp
• test/yukicoder/1080.test.cpp
• test/yukicoder/1321.test.cpp
• test/yukicoder/1392.test.cpp
• test/yukicoder/1533.test.cpp
• test/yukicoder/1549.test.cpp
• test/yukicoder/1875.test.cpp
• test/yukicoder/1939.test.cpp
• test/yukicoder/2062.test.cpp
• test/yukicoder/2097.test.cpp
• test/yukicoder/2583.test.cpp
• test_atcoder/abc222h.test.cpp
• test_atcoder/abc267h.test.cpp
• test_atcoder/abc285h.test.cpp
• test_atcoder/abc288ex.test.cpp
• test_atcoder/abc318h.test.cpp
• test_atcoder/abc331g.test.cpp
• test_atcoder/arc133f.test.cpp
• test_atcoder/arc153f.test.cpp
• test_atcoder/arc160d.test.cpp

Code

#pragma once

// 不定積分：integrate(f)
// 定積分：integrate(f, L, R)
template <typename mint>
vc<mint> integrate(const vc<mint>& f) {
  vc<mint> g(len(f) + 1);
  FOR3(i, 1, len(g)) g[i] = f[i - 1] * inv<mint>(i);
  return g;
}

// 不定積分：integrate(f)
// 定積分：integrate(f, L, R)
template <typename mint>
mint integrate(const vc<mint>& f, mint L, mint R) {
  mint I = 0;
  mint pow_L = 1, pow_R = 1;
  FOR(i, len(f)) {
    pow_L *= L, pow_R *= R;
    I += inv<mint>(i + 1) * f[i] * (pow_R - pow_L);
  }
  return I;
}

#line 2 "poly/integrate.hpp"

// 不定積分：integrate(f)
// 定積分：integrate(f, L, R)
template <typename mint>
vc<mint> integrate(const vc<mint>& f) {
  vc<mint> g(len(f) + 1);
  FOR3(i, 1, len(g)) g[i] = f[i - 1] * inv<mint>(i);
  return g;
}

// 不定積分：integrate(f)
// 定積分：integrate(f, L, R)
template <typename mint>
mint integrate(const vc<mint>& f, mint L, mint R) {
  mint I = 0;
  mint pow_L = 1, pow_R = 1;
  FOR(i, len(f)) {
    pow_L *= L, pow_R *= R;
    I += inv<mint>(i + 1) * f[i] * (pow_R - pow_L);
  }
  return I;
}

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