Binomial (二項係数) (math/binomial.hpp)

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• Last update: 2025-11-15 20:52:05+09:00
• Include: #include "math/binomial.hpp"
• Link: https://blog.hamayanhamayan.com/entry/2018/06/06/210256

概要

二項係数を前計算する

コンストラクタ

Binomial<T>(unsigned n)

• サイズnのテーブルを作成する

計算量

逆元の計算を$O(\log{M})$，その他の演算を$O(1)$として

• $O(n+\log{M})$

p

T p(int a, int b)

順列の総数${}_a P_b$を返す

計算量

• $O(1)$

c

T c(int a, int b)

組み合わせの総数${}_a C_b$を返す

計算量

• $O(1)$

h

T h(int a, int b)

重複組み合わせの総数${}_a H_b$を返す

計算量

• $O(1)$

Depends on

• template/constant.hpp
• template/include.hpp
• template/macro.hpp
• 提出用テンプレート (template/template.hpp)
• template/type_alias.hpp
• Choose Minimum / Maximum (utility/choose_min_max.hpp)
• utility/set_io.hpp

Required by

• test/utility/next_combination.test.cpp

Verified with

• test/math/binomial.test.cpp

Code

#pragma once

#include "../template/template.hpp"

/**
 * @brief Binomial (二項係数)
 * @note 参考: https://blog.hamayanhamayan.com/entry/2018/06/06/210256
 */
template <class T>
class Binomial {
  private:
    int n;
    vector<T> fact, ifact;

  public:
    Binomial() : Binomial(0) {}
    Binomial(int _n) : n(_n), fact(_n + 1), ifact(_n + 1) {
        assert(0 <= _n);

        fact[0] = T(1);
        rep (i, 0, n) {
            fact[i + 1] = fact[i] * T(i + 1);
        }

        ifact[n] = T(1) / fact[n];
        rrep (i, n, 1) {
            ifact[i - 1] = ifact[i] * T(i);
        }
    }

    //! 順列
    T p(int a, int b) const {
        if (b < 0 || a < b) {
            return T(0);
        }

        assert(0 <= a && a <= n);
        assert(0 <= a - b && a - b <= n);

        return fact[a] * ifact[a - b];
    }

    //! 組合せ
    T c(int a, int b) const {
        if (b < 0 || a < b) {
            return T(0);
        }

        assert(0 <= b && b <= n);

        return p(a, b) * ifact[b];
    }

    //! 重複組合せ
    T h(int a, int b) const {
        if (a == 0 && b == 0) {
            return T(1);
        }

        if (a <= 0 || b < 0) {
            return T(0);
        }

        return c(a + b - 1, b);
    }
};

#line 2 "math/binomial.hpp"

#line 2 "template/template.hpp"

/**
 * @author ku_senjan
 * @title 提出用テンプレート
 * @see https://github.com/kogetsu0728/ku-library
 */

#line 2 "template/constant.hpp"

#line 2 "template/include.hpp"

#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>
using namespace std;
#line 2 "template/type_alias.hpp"

#line 4 "template/type_alias.hpp"

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;

using ld = long double;

template <class T, bool REVERSE = false>
using heap = priority_queue<T, vector<T>, conditional_t<REVERSE, greater<T>, less<T>>>;
#line 5 "template/constant.hpp"

template <class T>
inline constexpr T INF = numeric_limits<T>::max() / 2;

inline constexpr array<int, 4> DY4 = {0, -1, 0, 1};
inline constexpr array<int, 4> DX4 = {1, 0, -1, 0};
inline constexpr array<int, 8> DY8 = {0, -1, -1, -1, 0, 1, 1, 1};
inline constexpr array<int, 8> DX8 = {1, 1, 0, -1, -1, -1, 0, 1};

inline constexpr char LF = '\n';
#line 2 "template/macro.hpp"

#line 5 "template/macro.hpp"

/**
 * @see https://trap.jp/post/1224/
 */

#ifdef LOCAL
inline constexpr bool IS_LOCAL = true;
#else
inline constexpr bool IS_LOCAL = false;
#endif

#define IF_LOCAL if constexpr (IS_LOCAL)

#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)

#define overload4(a, b, c, d, e, ...) e

#define rep1(i, a) for (ll i = 0; (i) < (ll)(a); ++(i))
#define rep2(i, a, b) for (ll i = (ll)(a); (i) < (ll)(b); ++(i))
#define rep3(i, a, b, c) for (ll i = (ll)(a); (i) < (ll)(b); (i) += (ll)(c))
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep1(i, a) for (ll i = (ll)(a); (i) >= 0; --(i))
#define rrep2(i, a, b) for (ll i = (ll)(a); (i) >= (ll)(b); --(i))
#define rrep3(i, a, b, c) for (ll i = (ll)(a); (i) >= (ll)(b); (i) -= (ll)(c))
#define rrep(...) overload4(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__)
#line 13 "template/template.hpp"

#line 2 "utility/choose_min_max.hpp"

/**
 * @title Choose Minimum / Maximum
 */

template <class T>
bool chmin(T& a, const T& b) {
    if (a > b) {
        a = b;
        return true;
    }

    return false;
}

template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return true;
    }

    return false;
}
#line 2 "utility/set_io.hpp"

#line 4 "utility/set_io.hpp"

void set_io(int d = 16) {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(d);

    return;
}
#line 4 "math/binomial.hpp"

/**
 * @brief Binomial (二項係数)
 * @note 参考: https://blog.hamayanhamayan.com/entry/2018/06/06/210256
 */
template <class T>
class Binomial {
  private:
    int n;
    vector<T> fact, ifact;

  public:
    Binomial() : Binomial(0) {}
    Binomial(int _n) : n(_n), fact(_n + 1), ifact(_n + 1) {
        assert(0 <= _n);

        fact[0] = T(1);
        rep (i, 0, n) {
            fact[i + 1] = fact[i] * T(i + 1);
        }

        ifact[n] = T(1) / fact[n];
        rrep (i, n, 1) {
            ifact[i - 1] = ifact[i] * T(i);
        }
    }

    //! 順列
    T p(int a, int b) const {
        if (b < 0 || a < b) {
            return T(0);
        }

        assert(0 <= a && a <= n);
        assert(0 <= a - b && a - b <= n);

        return fact[a] * ifact[a - b];
    }

    //! 組合せ
    T c(int a, int b) const {
        if (b < 0 || a < b) {
            return T(0);
        }

        assert(0 <= b && b <= n);

        return p(a, b) * ifact[b];
    }

    //! 重複組合せ
    T h(int a, int b) const {
        if (a == 0 && b == 0) {
            return T(1);
        }

        if (a <= 0 || b < 0) {
            return T(0);
        }

        return c(a + b - 1, b);
    }
};

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