結果

問題 No.732 3PrimeCounting
ユーザー gyouzasushi
提出日時 2020-03-30 01:01:00
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 5,047 bytes
コンパイル時間 1,641 ms
コンパイル使用メモリ 170,564 KB
実行使用メモリ 30,968 KB
最終ジャッジ日時 2025-01-02 16:11:38
合計ジャッジ時間 69,980 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
other AC * 88 WA * 1
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 <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) int(x.size())
#define get_unique(x) x.erase(unique(all(x)), x.end());
typedef long long ll;
typedef complex<double> Complex;
const int INF = 1e9;
const ll LINF = 1e18;
const ll MOD = LINF;
template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
vector<T> make_vec(size_t a) {
    return vector<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
struct NumberTheoreticTransform {
    ll ext_gxd(ll a, ll b, ll& x, ll& y) {
        if (b == 0) {
            x = 1;
            y = 0;
            return a;
        }
        ll q = a / b;
        ll g = ext_gxd(b, a - q * b, x, y);
        ll z = x - q * y;
        x = y;
        y = z;
        return g;
    }

    ll modinv(ll a, ll m) {
        ll x, y;
        ext_gxd(a, m, x, y);
        x %= m;
        if (x < 0) x += m;
        return x;
    }

    ll modpow(ll a, ll n, ll m) {
        ll ret = 1;
        ll now = a;
        while (n > 0) {
            if (n % 2 == 1) ret = ret * now % m;
            now = now * now % m;
            n /= 2;
        }
        return ret;
    }

    void ntt(vector<ll>& a, ll mod, bool inv = 0) {
        const int n = sz(a);
        assert((n & (n - 1)) == 0);

        const ll g = 3;
        ll h = modpow(g, (mod - 1) / n, mod);
        if (inv) h = modinv(h, mod);

        int i = 0;
        for (int j = 1; j < n - 1; j++) {
            for (int k = n >> 1; k > (i ^= k); k >>= 1) {
            };
            if (j < i) swap(a[i], a[j]);
        }

        for (int m = 1; m < n; m *= 2) {
            const int m2 = m * 2;
            const ll base = modpow(h, n / m2, mod);
            ll w = 1;
            for (int x = 0; x < m; x++) {
                for (int s = x; s < n; s += m2) {
                    ll u = a[s];
                    ll d = a[s + m] * w % mod;
                    a[s] = u + d;
                    if (a[s] >= mod) a[s] -= mod;
                    a[s + m] = u - d;
                    if (a[s + m] < 0) a[s + m] += mod;
                }
                w = w * base % mod;
            }
        }

        for (auto& x : a) {
            if (x < 0) x += mod;
        }

        if (inv) {
            const int n_inv = modinv(n, mod);
            for (auto& x : a) x = x * n_inv % mod;
        }
    }

    vector<ll> convolution(const vector<ll>& a, vector<ll>& b, ll mod) {
        int ntt_size = 1;
        while (ntt_size < sz(a) + sz(b)) ntt_size <<= 1;

        vector<ll> _a = a, _b = b;
        _a.resize(ntt_size);
        _b.resize(ntt_size);

        ntt(_a, mod);
        ntt(_b, mod);

        for (int i = 0; i < ntt_size; i++) {
            _a[i] *= _b[i];
            _a[i] %= mod;
        }

        ntt(_a, mod, 1);
        return _a;
    }

    vector<ll> modconv(vector<ll> a, vector<ll> b, ll mod = MOD) {
        for (auto& x : a) x %= mod;
        for (auto& x : b) x %= mod;

        auto x = convolution(a, b, 167772161);
        auto y = convolution(a, b, 469762049);
        auto z = convolution(a, b, 1224736769);

        const ll mod1 = 167772161, mod2 = 469762049, mod3 = 1224736769;
        const ll mod1_inv_mod2 = modinv(mod1, mod2);
        const ll mod1mod2_inv_mod3 = modinv(mod1 * mod2, mod3);
        const ll mod1mod2_mod = mod1 * mod2 % mod;
        vector<ll> ret(sz(x));
        for (int i = 0; i < sz(x); i++) {
            ll v1 = (y[i] - x[i]) * mod1_inv_mod2 % mod2;
            if (v1 < 0) v1 += mod2;
            ll v2 =
                (z[i] - (x[i] + mod1 * v1) % mod3) * mod1mod2_inv_mod3 % mod3;
            if (v2 < 0) v2 += mod3;
            ll constants3 = (x[i] + mod1 * v1 + mod1mod2_mod * v2) % mod;
            if (constants3 < 0) constants3 += mod;
            ret[i] = constants3;
        }
        return ret;
    }
};
int main() {
    vector<int> prime;
    for (int p = 2; p <= 300000; p++) {
        bool isprime = 1;
        for (int d = 2; d * d <= p; d++) {
            isprime &= (p % d > 0);
        }
        if (isprime) {
            prime.push_back(p);
        }
    }

    NumberTheoreticTransform ntt;
    int n;
    cin >> n;
    vector<ll> v(n + 1);
    for (int i = 0; prime[i] <= n; i++) {
        v[prime[i]]++;
    }

    auto c = ntt.modconv(ntt.modconv(v, v), v);
    ll ans = 0;
    for (int i = 0; prime[i] <= 3 * n; i++) {
        ans += c[prime[i]]++;
    }

    vector<ll> w(2 * n + 1);
    for (int i = 0; prime[i] <= n; i++) {
        w[2 * prime[i]]++;
    }
    auto d = ntt.modconv(v, w);
    for (int i = 0; prime[i] <= 3 * n; i++) {
        ans -= 3 * d[prime[i]];
    }
    cout << ans / 6 << endl;
}
0