library

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Combination
(Math/comb.hpp)

• View this file on GitHub
• Last update: 2024-10-22 03:59:04+09:00
• Include: #include "Math/comb.hpp"

Required by

• Relaxed Convolution (Convolution/relax.hpp)
• Subset Convolution (Convolution/subset.hpp)
• $f(\exp(x))$ (FPS/compexp.hpp)
• Compositional Inverse (FPS/compinv.hpp)
• Factorial (Large) (FPS/factlarge.hpp)
• Famous Sequence (FPS/famous.hpp)
• Number of Increasing Sequences Between Two Sequences (FPS/incseqcount.hpp)
• interpolate (one point) (FPS/interpolate.hpp)
• Mobius Transform (FPS/mobius.hpp)
• P-recursive (FPS/p-recursive.hpp)
• Prefix Sum of Polynomial (FPS/prefixsumofpoly.hpp)
• Enumerate $\sum_{k=0}^{N-1} k^i$ (FPS/prefixsumofpowers.hpp)
• Shift of Sampling Points of Polynomial (FPS/samplepointshift.hpp)
• $\sum_{k} r^k\cdot poly(k)$ (FPS/sumofpolyexp.hpp)
• Chromatic Number (Graph/chromaticpoly.hpp)
• Hafnian of matrix (Math/hafnian.hpp)

Verified with

• Verify/LC_bernoulli_number.test.cpp
• Verify/LC_convolution_mod_2.test.cpp
• Verify/LC_hafnian_of_matrix.test.cpp
• Verify/LC_many_factorials.test.cpp
• Verify/LC_partition_function.test.cpp
• Verify/LC_shift_of_sampling_points_of_polynomial.test.cpp
• Verify/LC_stirling_number_of_the_first_kind.test.cpp
• Verify/LC_stirling_number_of_the_second_kind.test.cpp
• Verify/LC_subset_convolution.test.cpp
• Verify/LC_sum_of_exponential_times_polynomial.test.cpp
• Verify/LC_sum_of_exponential_times_polynomial_limit.test.cpp
• Verify/YUKI_1080.test.cpp
• Verify/YUKI_2097.test.cpp
• Verify/YUKI_310.test.cpp

Code

#pragma once

template <typename T> T Inv(ll n) {
    static int md;
    static vector<T> buf({0, 1});
    if (md != T::get_mod()) {
        md = T::get_mod();
        buf = vector<T>({0, 1});
    }
    assert(n > 0);
    n %= md;
    while (SZ(buf) <= n) {
        int k = SZ(buf), q = (md + k - 1) / k;
        buf.push_back(buf[k * q - md] * q);
    }
    return buf[n];
}

template <typename T> T Fact(ll n, bool inv = 0) {
    static int md;
    static vector<T> buf({1, 1}), ibuf({1, 1});
    if (md != T::get_mod()) {
        md = T::get_mod();
        buf = ibuf = vector<T>({1, 1});
    }
    assert(n >= 0 and n < md);
    while (SZ(buf) <= n) {
        buf.push_back(buf.back() * SZ(buf));
        ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
    }
    return inv ? ibuf[n] : buf[n];
}

template <typename T> T nPr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
// sum = n, r tuples
template <typename T> T nHr(int n, int r, bool inv = 0) {
    return nCr<T>(n + r - 1, r - 1, inv);
}
// sum = n, a nonzero tuples and b tuples
template <typename T> T choose(int n, int a, int b) {
    if (n == 0)
        return !a;
    return nCr<T>(n + b - 1, a + b - 1);
}

/**
 * @brief Combination
 */

#line 2 "Math/comb.hpp"

template <typename T> T Inv(ll n) {
    static int md;
    static vector<T> buf({0, 1});
    if (md != T::get_mod()) {
        md = T::get_mod();
        buf = vector<T>({0, 1});
    }
    assert(n > 0);
    n %= md;
    while (SZ(buf) <= n) {
        int k = SZ(buf), q = (md + k - 1) / k;
        buf.push_back(buf[k * q - md] * q);
    }
    return buf[n];
}

template <typename T> T Fact(ll n, bool inv = 0) {
    static int md;
    static vector<T> buf({1, 1}), ibuf({1, 1});
    if (md != T::get_mod()) {
        md = T::get_mod();
        buf = ibuf = vector<T>({1, 1});
    }
    assert(n >= 0 and n < md);
    while (SZ(buf) <= n) {
        buf.push_back(buf.back() * SZ(buf));
        ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
    }
    return inv ? ibuf[n] : buf[n];
}

template <typename T> T nPr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
// sum = n, r tuples
template <typename T> T nHr(int n, int r, bool inv = 0) {
    return nCr<T>(n + r - 1, r - 1, inv);
}
// sum = n, a nonzero tuples and b tuples
template <typename T> T choose(int n, int a, int b) {
    if (n == 0)
        return !a;
    return nCr<T>(n + b - 1, a + b - 1);
}

/**
 * @brief Combination
 */

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