結果

問題 No.888 約数の総和
コンテスト
ユーザー SnowBeenDiding
提出日時 2025-03-16 02:48:57
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 3,748 bytes
コンパイル時間 5,967 ms
コンパイル使用メモリ 334,276 KB
実行使用メモリ 7,324 KB
最終ジャッジ日時 2025-03-16 02:49:05
合計ジャッジ時間 7,473 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <atcoder/all>
#include <bits/stdc++.h>
#define rep(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
using namespace atcoder;
using namespace std;

typedef long long ll;

vector<ll> getDivisors(ll n) {
    auto mod_mul = [](ll a, ll b, ll mod) -> ll {
        return (__int128)a * b % mod;
    };

    auto mod_pow = [&](ll base, ll exp, ll mod) -> ll {
        ll result = 1;
        base %= mod;
        while (exp) {
            if (exp & 1)
                result = mod_mul(result, base, mod);
            base = mod_mul(base, base, mod);
            exp >>= 1;
        }
        return result;
    };

    auto is_prime = [&](ll num) -> bool {
        if (num < 2)
            return false;
        int smallPrimes[12] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};
        for (int p : smallPrimes) {
            if (num == p)
                return true;
            if (num % p == 0)
                return false;
        }
        ll d = num - 1;
        int s = 0;
        while ((d & 1) == 0) {
            d /= 2;
            s++;
        }
        ll testPrimes[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
        for (ll a : testPrimes) {
            if (a % num == 0)
                continue;
            ll x = mod_pow(a, d, num);
            if (x == 1 || x == num - 1)
                continue;
            bool composite = true;
            for (int i = 0; i < s - 1; i++) {
                x = mod_mul(x, x, num);
                if (x == num - 1) {
                    composite = false;
                    break;
                }
            }
            if (composite)
                return false;
        }
        return true;
    };

    function<ll(ll)> pollard_rho;
    pollard_rho = [&](ll num) -> ll {
        if (num % 2 == 0)
            return 2;
        mt19937_64 rng(random_device{}());
        uniform_int_distribution<ll> dist(2, num - 2);
        ll x = dist(rng), y = x, c = dist(rng), d = 1;
        auto f = [&](ll x, ll c, ll mod) -> ll {
            return (mod_mul(x, x, mod) + c) % mod;
        };
        while (d == 1) {
            x = f(x, c, num);
            y = f(y, c, num);
            y = f(y, c, num);
            d = gcd(abs(x - y), num);
            if (d == num)
                return pollard_rho(num);
        }
        return d;
    };

    function<void(ll, vector<ll> &)> factorize;
    factorize = [&](ll num, vector<ll> &factors) {
        if (num == 1)
            return;
        if (is_prime(num)) {
            factors.push_back(num);
            return;
        }
        ll factor = pollard_rho(num);
        factorize(factor, factors);
        factorize(num / factor, factors);
    };

    vector<ll> factors;
    factorize(n, factors);
    sort(factors.begin(), factors.end());
    vector<pair<ll, int>> factorCounts;
    for (ll f : factors) {
        if (factorCounts.empty() || factorCounts.back().first != f)
            factorCounts.push_back({f, 1});
        else
            factorCounts.back().second++;
    }
    vector<ll> divisors;
    function<void(int, ll)> dfs = [&](int idx, ll current) {
        if (idx == factorCounts.size()) {
            divisors.push_back(current);
            return;
        }
        ll prime = factorCounts[idx].first;
        int exp = factorCounts[idx].second;
        for (int i = 0; i <= exp; i++) {
            dfs(idx + 1, current);
            current *= prime;
        }
    };
    dfs(0, 1);
    sort(divisors.begin(), divisors.end());
    return divisors;
}

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);
    ll n;
    cin >> n;
    vector<ll> divisors = getDivisors(n);
    ll ans = 0;
    for (ll d : divisors) {
        ans += d;
    }
    cout << ans << endl;
}
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