Util
(library/math/util.hpp)

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• Last update: 2024-01-30 20:57:42+09:00
• Include: #include "library/math/util.hpp"

Util

Depends on

• 階乗テーブル (library/math/factorial.hpp)

Verified with

• test/src/math/util/abc240_g.test.cpp

Code

#ifndef SUISEN_MATH_UTIL
#define SUISEN_MATH_UTIL

#include "library/math/factorial.hpp"

namespace suisen {
    template <typename mint>
    mint random_walk_1d(int n, int x) {
        if (x < 0) x = -x;
        factorial<mint> fac(n);
        int m = n + x;
        return m & 1 ? 0 : fac.binom(n, m / 2);
    }
    template <typename mint>
    mint random_walk_2d(int n, int x, int y) {
        return random_walk_1d<mint>(n, x + y) * random_walk_1d<mint>(n, x - y);
    }

    template <typename mint, typename BinomialCoefficient>
    mint random_walk_1d(int n, int x, const BinomialCoefficient &binom_n) {
        if (x < 0) x = -x;
        int m = n + x;
        return m & 1 ? 0 : binom_n(m / 2);
    }
    template <typename mint, typename BinomialCoefficient>
    mint random_walk_2d(int n, int x, int y, const BinomialCoefficient &binom_n) {
        return random_walk_1d<mint>(n, x + y, binom_n) * random_walk_1d<mint>(n, x - y, binom_n);
    }
} // namespace suisen


#endif // SUISEN_MATH_UTIL

#line 1 "library/math/util.hpp"



#line 1 "library/math/factorial.hpp"



#include <cassert>
#include <vector>

namespace suisen {
    template <typename T, typename U = T>
    struct factorial {
        factorial() = default;
        factorial(int n) { ensure(n); }

        static void ensure(const int n) {
            int sz = _fac.size();
            if (n + 1 <= sz) return;
            int new_size = std::max(n + 1, sz * 2);
            _fac.resize(new_size), _fac_inv.resize(new_size);
            for (int i = sz; i < new_size; ++i) _fac[i] = _fac[i - 1] * i;
            _fac_inv[new_size - 1] = U(1) / _fac[new_size - 1];
            for (int i = new_size - 1; i > sz; --i) _fac_inv[i - 1] = _fac_inv[i] * i;
        }

        T fac(const int i) {
            ensure(i);
            return _fac[i];
        }
        T operator()(int i) {
            return fac(i);
        }
        U fac_inv(const int i) {
            ensure(i);
            return _fac_inv[i];
        }
        U binom(const int n, const int r) {
            if (n < 0 or r < 0 or n < r) return 0;
            ensure(n);
            return _fac[n] * _fac_inv[r] * _fac_inv[n - r];
        }
        template <typename ...Ds, std::enable_if_t<std::conjunction_v<std::is_integral<Ds>...>, std::nullptr_t> = nullptr>
        U polynom(const int n, const Ds& ...ds) {
            if (n < 0) return 0;
            ensure(n);
            int sumd = 0;
            U res = _fac[n];
            for (int d : { ds... }) {
                if (d < 0 or d > n) return 0;
                sumd += d;
                res *= _fac_inv[d];
            }
            if (sumd > n) return 0;
            res *= _fac_inv[n - sumd];
            return res;
        }
        U perm(const int n, const int r) {
            if (n < 0 or r < 0 or n < r) return 0;
            ensure(n);
            return _fac[n] * _fac_inv[n - r];
        }
    private:
        static std::vector<T> _fac;
        static std::vector<U> _fac_inv;
    };
    template <typename T, typename U>
    std::vector<T> factorial<T, U>::_fac{ 1 };
    template <typename T, typename U>
    std::vector<U> factorial<T, U>::_fac_inv{ 1 };
} // namespace suisen


#line 5 "library/math/util.hpp"

namespace suisen {
    template <typename mint>
    mint random_walk_1d(int n, int x) {
        if (x < 0) x = -x;
        factorial<mint> fac(n);
        int m = n + x;
        return m & 1 ? 0 : fac.binom(n, m / 2);
    }
    template <typename mint>
    mint random_walk_2d(int n, int x, int y) {
        return random_walk_1d<mint>(n, x + y) * random_walk_1d<mint>(n, x - y);
    }

    template <typename mint, typename BinomialCoefficient>
    mint random_walk_1d(int n, int x, const BinomialCoefficient &binom_n) {
        if (x < 0) x = -x;
        int m = n + x;
        return m & 1 ? 0 : binom_n(m / 2);
    }
    template <typename mint, typename BinomialCoefficient>
    mint random_walk_2d(int n, int x, int y, const BinomialCoefficient &binom_n) {
        return random_walk_1d<mint>(n, x + y, binom_n) * random_walk_1d<mint>(n, x - y, binom_n);
    }
} // namespace suisen

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