Binomial Coefficient (Prime Mod) (verify/combi/binom.test.cpp)

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• Last update: 2024-10-07 21:21:13+02:00
• Problem: https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod

Depends on

• cp-algo/math/combinatorics.hpp
• cp-algo/math/common.hpp
• cp-algo/number_theory/modint.hpp

Code

// @brief Binomial Coefficient (Prime Mod)
#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod"
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("tune=native")
#define CP_ALGO_MAXN 1e7
#include "cp-algo/number_theory/modint.hpp"
#include "cp-algo/math/combinatorics.hpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo;
using namespace math;
using base = dynamic_modint;

void solve() {
    int n, r;
    cin >> n >> r;
    cout << binom<base>(n, r) << "\n";
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    cin >> t;
    int m;
    cin >> m;
    base::switch_mod(m);
    while(t--) {
        solve();
    }
}

#line 1 "verify/combi/binom.test.cpp"
// @brief Binomial Coefficient (Prime Mod)
#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod"
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("tune=native")
#define CP_ALGO_MAXN 1e7
#line 1 "cp-algo/number_theory/modint.hpp"


#line 1 "cp-algo/math/common.hpp"


#include <functional>
#include <cstdint>
namespace cp_algo::math {
#ifdef CP_ALGO_MAXN
    const int maxn = CP_ALGO_MAXN;
#else
    const int maxn = 1 << 19;
#endif
    const int magic = 64; // threshold for sizes to run the naive algo

    auto bpow(auto const& x, int64_t n, auto const& one, auto op) {
        if(n == 0) {
            return one;
        } else {
            auto t = bpow(x, n / 2, one, op);
            t = op(t, t);
            if(n % 2) {
                t = op(t, x);
            }
            return t;
        }
    }
    auto bpow(auto x, int64_t n, auto ans) {
        return bpow(x, n, ans, std::multiplies{});
    }
    template<typename T>
    T bpow(T const& x, int64_t n) {
        return bpow(x, n, T(1));
    }
}

#line 4 "cp-algo/number_theory/modint.hpp"
#include <iostream>
#include <cassert>
namespace cp_algo::math {
    inline constexpr uint64_t inv64(uint64_t x) {
        assert(x % 2);
        uint64_t y = 1;
        while(y * x != 1) {
            y *= 2 - x * y;
        }
        return y;
    }

    template<typename modint>
    struct modint_base {
        static int64_t mod() {
            return modint::mod();
        }
        static uint64_t imod() {
            return modint::imod();
        }
        static __uint128_t pw128() {
            return modint::pw128();
        }
        static uint64_t m_reduce(__uint128_t ab) {
            if(mod() % 2 == 0) [[unlikely]] {
                return ab % mod();
            } else {
                uint64_t m = ab * imod();
                return (ab + __uint128_t(m) * mod()) >> 64;
            }
        }
        static uint64_t m_transform(uint64_t a) {
            if(mod() % 2 == 0) [[unlikely]] {
                return a;
            } else {
                return m_reduce(a * pw128());
            }
        }
        modint_base(): r(0) {}
        modint_base(int64_t rr): r(rr % mod()) {
            r = std::min(r, r + mod());
            r = m_transform(r);
        }
        modint inv() const {
            return bpow(to_modint(), mod() - 2);
        }
        modint operator - () const {
            modint neg;
            neg.r = std::min(-r, 2 * mod() - r);
            return neg;
        }
        modint& operator /= (const modint &t) {
            return to_modint() *= t.inv();
        }
        modint& operator *= (const modint &t) {
            r = m_reduce(__uint128_t(r) * t.r);
            return to_modint();
        }
        modint& operator += (const modint &t) {
            r += t.r; r = std::min(r, r - 2 * mod());
            return to_modint();
        }
        modint& operator -= (const modint &t) {
            r -= t.r; r = std::min(r, r + 2 * mod());
            return to_modint();
        }
        modint operator + (const modint &t) const {return modint(to_modint()) += t;}
        modint operator - (const modint &t) const {return modint(to_modint()) -= t;}
        modint operator * (const modint &t) const {return modint(to_modint()) *= t;}
        modint operator / (const modint &t) const {return modint(to_modint()) /= t;}
        // Why <=> doesn't work?..
        auto operator == (const modint_base &t) const {return getr() == t.getr();}
        auto operator != (const modint_base &t) const {return getr() != t.getr();}
        auto operator <= (const modint_base &t) const {return getr() <= t.getr();}
        auto operator >= (const modint_base &t) const {return getr() >= t.getr();}
        auto operator < (const modint_base &t) const {return getr() < t.getr();}
        auto operator > (const modint_base &t) const {return getr() > t.getr();}
        int64_t rem() const {
            uint64_t R = getr();
            return 2 * R > (uint64_t)mod() ? R - mod() : R;
        }

        // Only use if you really know what you're doing!
        uint64_t modmod() const {return 8ULL * mod() * mod();};
        void add_unsafe(uint64_t t) {r += t;}
        void pseudonormalize() {r = std::min(r, r - modmod());}
        modint const& normalize() {
            if(r >= (uint64_t)mod()) {
                r %= mod();
            }
            return to_modint();
        }
        void setr(uint64_t rr) {r = m_transform(rr);}
        uint64_t getr() const {
            uint64_t res = m_reduce(r);
            return std::min(res, res - mod());
        }
        void setr_direct(uint64_t rr) {r = rr;}
        uint64_t getr_direct() const {return std::min(r, r - mod());}
    private:
        uint64_t r;
        modint& to_modint() {return static_cast<modint&>(*this);}
        modint const& to_modint() const {return static_cast<modint const&>(*this);}
    };
    template<typename modint>
    std::istream& operator >> (std::istream &in, modint_base<modint> &x) {
        uint64_t r;
        auto &res = in >> r;
        x.setr(r);
        return res;
    }
    template<typename modint>
    std::ostream& operator << (std::ostream &out, modint_base<modint> const& x) {
        return out << x.getr();
    }

    template<typename modint>
    concept modint_type = std::is_base_of_v<modint_base<modint>, modint>;

    template<int64_t m>
    struct modint: modint_base<modint<m>> {
        static constexpr uint64_t im = m % 2 ? inv64(-m) : 0;
        static constexpr uint64_t r2 = __uint128_t(-1) % m + 1;
        static constexpr int64_t mod() {return m;}
        static constexpr uint64_t imod() {return im;}
        static constexpr __uint128_t pw128() {return r2;}
        using Base = modint_base<modint<m>>;
        using Base::Base;
    };

    struct dynamic_modint: modint_base<dynamic_modint> {
        static int64_t mod() {return m;}
        static uint64_t imod() {return im;}
        static __uint128_t pw128() {return r2;}
        static void switch_mod(int64_t nm) {
            m = nm;
            im = m % 2 ? inv64(-m) : 0;
            r2 = __uint128_t(-1) % m + 1;
        }
        using Base = modint_base<dynamic_modint>;
        using Base::Base;

        // Wrapper for temp switching
        auto static with_mod(int64_t tmp, auto callback) {
            struct scoped {
                int64_t prev = mod();
                ~scoped() {switch_mod(prev);}
            } _;
            switch_mod(tmp);
            return callback();
        }
    private:
        static int64_t m;
        static uint64_t im, r1, r2;
    };
    int64_t dynamic_modint::m = 1;
    uint64_t dynamic_modint::im = -1;
    uint64_t dynamic_modint::r2 = 0;
}

#line 1 "cp-algo/math/combinatorics.hpp"


#line 5 "cp-algo/math/combinatorics.hpp"
namespace cp_algo::math {
    // fact/rfact/small_inv are caching
    // Beware of usage with dynamic mod
    template<typename T>
    T fact(int n) {
        static std::vector<T> F(maxn);
        static bool init = false;
        if(!init) {
            F[0] = T(1);
            for(int i = 1; i < maxn; i++) {
                F[i] = F[i - 1] * T(i);
            }
            init = true;
        }
        return F[n];
    }
    // Only works for modint types
    template<typename T>
    T rfact(int n) {
        static std::vector<T> F(maxn);
        static bool init = false;
        if(!init) {
            int t = std::min<int64_t>(T::mod(), maxn) - 1;
            F[t] = T(1) / fact<T>(t);
            for(int i = t - 1; i >= 0; i--) {
                F[i] = F[i + 1] * T(i + 1);
            }
            init = true;
        }
        return F[n];
    }
    template<typename T>
    T small_inv(int n) {
        static std::vector<T> F(maxn);
        static bool init = false;
        if(!init) {
            for(int i = 1; i < maxn; i++) {
                F[i] = rfact<T>(i) * fact<T>(i - 1);
            }
            init = true;
        }
        return F[n];
    }
    template<typename T>
    T binom_large(T n, int r) {
        assert(r < maxn);
        T ans = 1;
        for(int i = 0; i < r; i++) {
            ans = ans * T(n - i) * small_inv<T>(i + 1);
        }
        return ans;
    }
    template<typename T>
    T binom(int n, int r) {
        if(r < 0 || r > n) {
            return T(0);
        } else if(n >= maxn) {
            return binom_large(T(n), r);
        } else {
            return fact<T>(n) * rfact<T>(r) * rfact<T>(n - r);
        }
    }
}

#line 8 "verify/combi/binom.test.cpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo;
using namespace math;
using base = dynamic_modint;

void solve() {
    int n, r;
    cin >> n >> r;
    cout << binom<base>(n, r) << "\n";
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    cin >> t;
    int m;
    cin >> m;
    base::switch_mod(m);
    while(t--) {
        solve();
    }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	112 ms	160 MB
g++	example_01	AC	117 ms	160 MB
g++	large_random_00	AC	384 ms	160 MB
g++	large_random_01	AC	380 ms	160 MB
g++	large_random_02	AC	386 ms	160 MB
g++	med_random_00	AC	272 ms	160 MB
g++	med_random_01	AC	271 ms	160 MB
g++	med_random_02	AC	288 ms	160 MB
g++	mod1000000007_00	AC	387 ms	160 MB
g++	mod1000000007_01	AC	379 ms	160 MB
g++	mod2_00	AC	249 ms	160 MB
g++	mod2_01	AC	251 ms	160 MB
g++	mod3_00	AC	237 ms	160 MB
g++	mod3_01	AC	236 ms	160 MB
g++	mod998244353_00	AC	385 ms	160 MB
g++	mod998244353_01	AC	387 ms	160 MB
g++	mod998244353_maxi_00	AC	446 ms	160 MB
g++	small_random_00	AC	240 ms	160 MB
g++	small_random_01	AC	237 ms	160 MB
g++	small_random_02	AC	252 ms	160 MB

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