verify/unit_test/math/eratosthenes_sieve.test.cpp

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• Last update: 2025-04-27 00:17:33+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• divisor (src/math/divisor.hpp)
• EratosthenesSieve (src/math/eratosthenes_sieve.hpp)
• euler_phi (src/math/euler_phi.hpp)
• is_prime (src/math/is_prime.hpp)
• moebius (src/math/moebius.hpp)
• prime_factors (src/math/prime_factors.hpp)
• RandomNumberGenerator (src/random/random_number_generator.hpp)
• template (src/template/template.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "../../../src/template/template.hpp"
#include "../../../src/random/random_number_generator.hpp"
#include "../../../src/math/eratosthenes_sieve.hpp"
#include "../../../src/math/is_prime.hpp"
#include "../../../src/math/euler_phi.hpp"
#include "../../../src/math/moebius.hpp"
#include "../../../src/math/divisor.hpp"
#include "../../../src/math/prime_factors.hpp"
void test() {
    EratosthenesSieve sieve(10000000);
    rep(i, 0, 10000) {
        int n = rng(1, 10000000);
        if(is_prime(n)) {
            assert(sieve.min_factor[n] == n);
        } else {
            assert(sieve.min_factor[n] != n);
        }
        if(is_prime(i)) {
            assert(sieve.min_factor[i] == i);
        } else {
            assert(sieve.min_factor[i] != i);
        }
        assert(euler_phi(n) == sieve.euler[n]);
        assert(moebius(n) == sieve.moebius[n]);
    }
    rep(i, 1, 100) {
        if(is_prime(i)) {
            assert(sieve.min_factor[i] == i);
        } else {
            assert(sieve.min_factor[i] != i);
        }
        assert(euler_phi(i) == sieve.euler[i]);
        assert(moebius(i) == sieve.moebius[i]);
    }
    rep(i, 1, 10000) {
        int n = rng(1, 10000000);
        vector<pair<int, int>> pf1 = sieve.prime_factors(n);
        vector<pair<long long, int>> pf2 = prime_factors(n);
        assert(pf1.size() == pf2.size());
        for(int i = 0; i < (int)pf1.size(); ++i) {
            assert(pf1[i].first == pf2[i].first);
            assert(pf1[i].second == pf2[i].second);
        }
        vector<int> d1 = sieve.divisor(n);
        vector<ll> d2 = divisor(n);
        assert(d1.size() == d2.size());
        for(int i = 0; i < (int)d1.size(); ++i) {
            assert(d1[i] == d2[i]);
        }
    }
}
int main(void) {
    test();
    int a, b;
    cin >> a >> b;
    cout << a + b << '\n';
}

#line 1 "verify/unit_test/math/eratosthenes_sieve.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/random/random_number_generator.hpp"
struct RandomNumberGenerator {
    RandomNumberGenerator()
        : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
    template <typename T>
    inline T operator()(const T lower, const T upper) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(lower <= upper);
        if constexpr(is_integral_v<T>) {
            uniform_int_distribution<T> dist(lower, upper);
            return dist(mt);
        } else if constexpr(is_floating_point_v<T>) {
            uniform_real_distribution<T> dist(lower, upper);
            return dist(mt);
        }
    }
    template <typename T>
    inline vector<T> vec(const int n, const T lower, const T upper, const bool dup = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(lower <= upper);
        if(n == 0) return {};
        vector<T> res(n);
        if(dup or is_floating_point_v<T>) {
            for(int i = 0; i < n; ++i) res[i] = this->operator()(lower, upper);
        } else {
            assert(upper - lower + 1 >= n);
            if(upper - lower + 1 >= 2 * n) {
                set<T> used;
                while((int)used.size() < n) {
                    const T a = this->operator()(lower, upper);
                    used.insert(a);
                }
                int i = 0;
                for(const T a : used) {
                    res[i] = a;
                    ++i;
                }
            } else {
                const vector<int> p = perm(upper - lower + 1, false);
                for(int i = 0; i < n; ++i) {
                    res[i] = p[i] + lower;
                }
            }
        }
        return res;
    }
    inline vector<int> perm(const int n, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        vector<int> res(n);
        for(int i = 0; i < n; ++i) res[i] = i + one;
        for(int i = n - 1; i > 0; --i) {
            swap(res[i], res[this->operator()(0, i)]);
        }
        return res;
    }
    inline pair<vector<int>, vector<int>> tree(const int n, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        if(n <= 1) return {{}, {}};
        if(n == 2) return {{0 + one}, {1 + one}};
        vector<int> u(n - 1), v(n - 1);
        const vector<int> pruefer = vec(n - 2, 0, n - 1);
        set<int> st;
        vector<int> cnt(n);
        for(int i = 0; i < n; ++i) st.insert(i);
        auto add = [&](const int x) -> void {
            if(x > n) return;
            if(cnt[x] == 0) st.erase(x);
            ++cnt[x];
        };
        auto del = [&](const int x) -> void {
            if(x > n) return;
            --cnt[x];
            if(cnt[x] == 0) st.insert(x);
        };
        for(int i = 0; i < n - 2; ++i) add(pruefer[i]);
        for(int i = 0; i < n - 2; ++i) {
            const int a = *st.begin();
            const int b = pruefer[i];
            u[i] = a + one;
            v[i] = b + one;
            del(b);
            add(a);
        }
        const int a = *st.begin();
        add(a);
        const int b = *st.begin();
        u[n - 2] = a + one;
        v[n - 2] = b + one;
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_tree(const int n, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(lower <= upper);
        if(n == 0) return {{}, {}, {}};
        const auto [u, v] = tree(n, one);
        const vector<T> w = vec(n - 1, lower, upper, true);
        return {u, v, w};
    }
    inline pair<vector<int>, vector<int>> graph(const int n, const int m, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        assert(0 <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        vector<int> u, v;
        u.reserve(m);
        v.reserve(m);
        if(1ll * n * (n - 1) / 2 >= 2e6) {
            set<pair<int, int>> edge;
            while((int)edge.size() < m) {
                const int a = this->operator()(0, n - 1);
                const int b = this->operator()(0, n - 1);
                if(a >= b) continue;
                edge.insert({a, b});
            }
            for(const auto& [a, b] : edge) {
                u.push_back(a + one);
                v.push_back(b + one);
            }
        } else {
            vector<pair<int, int>> edge;
            edge.reserve(n * (n - 1) / 2);
            for(int i = 0; i < n; ++i) {
                for(int j = i + 1; j < n; ++j) {
                    edge.push_back({i, j});
                }
            }
            const vector<int> p = perm(n * (n - 1) / 2, false);
            for(int i = 0; i < m; ++i) {
                u.push_back(edge[p[i]].first + one);
                v.push_back(edge[p[i]].second + one);
            }
        }
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_graph(const int n, const int m, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(0 <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        assert(lower <= upper);
        const auto [u, v] = graph(n, m, one);
        const vector<T> w = vec(m, lower, upper, true);
        return {u, v, w};
    }
    inline pair<vector<int>, vector<int>> connected_graph(const int n, const int m, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        assert(max(n - 1, 0) <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        if(n <= 1) return {{}, {}};
        vector<int> u, v;
        u.reserve(m);
        v.reserve(m);
        auto [ut, vt] = tree(n, false);
        if(1ll * n * (n - 1) / 2 >= 2e6) {
            set<pair<int, int>> edge;
            for(int i = 0; i < n - 1; ++i) {
                edge.insert({min(ut[i], vt[i]), max(ut[i], vt[i])});
            }
            while((int)edge.size() < m) {
                const int a = this->operator()(0, n - 1);
                const int b = this->operator()(0, n - 1);
                if(a >= b) continue;
                edge.insert({a, b});
            }
            for(const auto& [a, b] : edge) {
                u.push_back(a + one);
                v.push_back(b + one);
            }
        } else {
            set<pair<int, int>> used;
            for(int i = 0; i < n - 1; ++i) {
                u.push_back(ut[i] + one);
                v.push_back(vt[i] + one);
                used.insert({min(ut[i], vt[i]), max(ut[i], vt[i])});
            }
            vector<pair<int, int>> edge;
            edge.reserve(n * (n - 1) / 2 - (n - 1));
            for(int i = 0; i < n; ++i) {
                for(int j = i + 1; j < n; ++j) {
                    if(used.find({i, j}) == used.end()) edge.push_back({i, j});
                }
            }
            const vector<int> p = perm(n * (n - 1) / 2 - (n - 1), false);
            for(int i = 0; i < m - (n - 1); ++i) {
                u.push_back(edge[p[i]].first + one);
                v.push_back(edge[p[i]].second + one);
            }
        }
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_connected_graph(const int n, const int m, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(max(n - 1, 0) <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        assert(lower <= upper);
        const auto [u, v] = connected_graph(n, m, one);
        const vector<T> w = vec(m, lower, upper, true);
        return {u, v, w};
    }
    inline string parenthesis(const int n) {
        assert(0 <= n and n <= 1e8);
        string res = "";
        int N = n, M = n;
        for(int i = 0; i < 2 * n; ++i) {
            if(this->operator()(0.0l, 1.0l) > 1.0l * (N - M) * (N + 1) / ((N - M + 1) * (N + M))) {
                res += "(";
                --M;
            } else {
                res += ")";
                --N;
            }
        }
        return res;
    }

   private:
    mt19937_64 mt;
} rng;
#line 3 "src/math/eratosthenes_sieve.hpp"
struct EratosthenesSieve {
    vector<int> primes, min_factor, moebius, euler;
    EratosthenesSieve(const int N)
        : primes(), min_factor(N + 1), moebius(N + 1, 1), euler(N + 1), N(N) {
        assert(N >= 1);
        iota(min_factor.begin(), min_factor.end(), 0);
        min_factor[0] = min_factor[1] = -1;
        iota(euler.begin(), euler.end(), 0);
        for(int i = 2; i <= N; ++i) {
            if(min_factor[i] < i) continue;
            primes.emplace_back(i);
            moebius[i] = -1;
            euler[i] = euler[i] / i * (i - 1);
            for(int j = i * 2; j <= N; j += i) {
                if(min_factor[j] == j) min_factor[j] = i;
                if((j / i) % i == 0) moebius[j] = 0;
                else moebius[j] = -moebius[j];
                euler[j] = euler[j] / i * (i - 1);
            }
        }
    }
    vector<pair<int, int>> prime_factors(int n) const {
        assert(1 <= n and n <= N);
        vector<pair<int, int>> res;
        while(n > 1) {
            const int p = min_factor[n];
            int exp = 0;
            while(min_factor[n] == p) {
                n /= p;
                ++exp;
            }
            res.emplace_back(p, exp);
        }
        return res;
    }
    vector<int> divisor(const int n) const {
        assert(1 <= n and n <= n);
        vector<int> res({1});
        const auto pf = prime_factors(n);
        for(const auto& p : pf) {
            const int s = (int)res.size();
            for(int i = 0; i < s; ++i) {
                int v = 1;
                for(int j = 0; j < p.second; ++j) {
                    v *= p.first;
                    res.push_back(res[i] * v);
                }
            }
        }
        sort(res.begin(), res.end());
        return res;
    }

   private:
    int N;
};
#line 3 "src/math/is_prime.hpp"
constexpr bool is_prime(const long long n) {
    if(n <= 1) return false;
    for(long long i = 2; i * i <= n; ++i) {
        if(n % i == 0) return false;
    }
    return true;
}
#line 3 "src/math/euler_phi.hpp"
constexpr long long euler_phi(long long n) {
    long long res = max(n, 0ll);
    for(long long i = 2; i * i <= n; ++i) {
        if(n % i == 0) {
            res -= res / i;
            while(n % i == 0) n /= i;
        }
    }
    if(n > 1) res -= res / n;
    return res;
}
#line 3 "src/math/prime_factors.hpp"
vector<pair<long long, int>> prime_factors(long long n) {
    assert(n >= 1);
    vector<pair<long long, int>> res;
    for(long long i = 2; i * i <= n; ++i) {
        if(n % i == 0) {
            res.emplace_back(i, 0);
            while(n % i == 0) {
                n /= i;
                ++res.back().second;
            }
        }
    }
    if(n >= 2) res.emplace_back(n, 1);
    return res;
}
#line 4 "src/math/moebius.hpp"
int moebius(const long long n) {
    assert(n >= 1);
    if(n == 1) return 1;
    const vector<pair<long long, int>> p = prime_factors(n);
    int res = 1;
    for(const auto& it : p) {
        if(it.second >= 2) return 0;
        res = -res;
    }
    return res;
}
#line 3 "src/math/divisor.hpp"
vector<long long> divisor(const long long n) {
    assert(n >= 1);
    vector<long long> res;
    for(long long i = 1; i * i <= n; ++i) {
        if(n % i == 0) {
            res.push_back(i);
            if(i * i != n) res.emplace_back(n / i);
        }
    }
    sort(res.begin(), res.end());
    return res;
}
#line 10 "verify/unit_test/math/eratosthenes_sieve.test.cpp"
void test() {
    EratosthenesSieve sieve(10000000);
    rep(i, 0, 10000) {
        int n = rng(1, 10000000);
        if(is_prime(n)) {
            assert(sieve.min_factor[n] == n);
        } else {
            assert(sieve.min_factor[n] != n);
        }
        if(is_prime(i)) {
            assert(sieve.min_factor[i] == i);
        } else {
            assert(sieve.min_factor[i] != i);
        }
        assert(euler_phi(n) == sieve.euler[n]);
        assert(moebius(n) == sieve.moebius[n]);
    }
    rep(i, 1, 100) {
        if(is_prime(i)) {
            assert(sieve.min_factor[i] == i);
        } else {
            assert(sieve.min_factor[i] != i);
        }
        assert(euler_phi(i) == sieve.euler[i]);
        assert(moebius(i) == sieve.moebius[i]);
    }
    rep(i, 1, 10000) {
        int n = rng(1, 10000000);
        vector<pair<int, int>> pf1 = sieve.prime_factors(n);
        vector<pair<long long, int>> pf2 = prime_factors(n);
        assert(pf1.size() == pf2.size());
        for(int i = 0; i < (int)pf1.size(); ++i) {
            assert(pf1[i].first == pf2[i].first);
            assert(pf1[i].second == pf2[i].second);
        }
        vector<int> d1 = sieve.divisor(n);
        vector<ll> d2 = divisor(n);
        assert(d1.size() == d2.size());
        for(int i = 0; i < (int)d1.size(); ++i) {
            assert(d1[i] == d2[i]);
        }
    }
}
int main(void) {
    test();
    int a, b;
    cin >> a >> b;
    cout << a + b << '\n';
}

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