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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#121932#6187. Digit Sum ProblemUndertrainedOverpressure#AC ✓1841ms66736kbC++235.2kb2023-07-09 00:53:482023-07-09 00:53:51

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-07-09 00:53:51]
  • 评测
  • 测评结果:AC
  • 用时:1841ms
  • 内存:66736kb
  • [2023-07-09 00:53:48]
  • 提交

answer

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
#define TIME (clock() * 1.0 / CLOCKS_PER_SEC)

// если модуль подается на вход, убрать все <> и раскомментировать нужные строки
using uint = unsigned int;
using ull = unsigned long long;
template <uint MD> struct ModInt {
    using M = ModInt;
    // static int MD;
    uint v;
    ModInt(ll _v = 0) { set_v(uint(_v % MD + MD)); }
    M& set_v(uint _v) {
        v = (_v < MD) ? _v : _v - MD;
        return *this;
    }
    explicit operator bool() const { return v != 0; }
    M operator-() const { return M() - *this; }
    M operator+(const M& r) const { return M().set_v(v + r.v); }
    M operator-(const M& r) const { return M().set_v(v + MD - r.v); }
    M operator*(const M& r) const { return M().set_v(uint((ull)v * r.v % MD)); }
    M operator/(const M& r) const { return *this * r.inv(); }
    M& operator+=(const M& r) { return *this = *this + r; }
    M& operator-=(const M& r) { return *this = *this - r; }
    M& operator*=(const M& r) { return *this = *this * r; }
    M& operator/=(const M& r) { return *this = *this / r; }
    bool operator==(const M& r) const { return v == r.v; }
    bool operator!=(const M& r) const { return v != r.v; }
    M inv() const;
    friend istream& operator>>(istream& is, M& r) { ll x; is >> x; r = M(x); return is; }
    friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }
};

template<uint MD>
ModInt<MD> pow(ModInt<MD> x, ll n) {
    ModInt<MD> r = 1;
    while (n) {
        if (n & 1) r *= x;
        x *= x;
        n >>= 1;
    }
    return r;
}

template<uint MD>
ModInt<MD> ModInt<MD>::inv() const { return pow(*this, MD - 2); }
// or copy egcd and {return egcd(MD, v, 1).second;}

// if MD is from input
// this line is necessary, read later as you wish
// int ModInt::MD;

using Mint = ModInt<998244353>;
// using Mint = double;

#define V vector
void nft(bool type, V<Mint>& a) {
    Mint G = 3;
    int n = int(a.size()), s = 0;
    while ((1 << s) < n) s++;
    assert(1 << s == n);

    static V<Mint> ep, iep;
    while (int(ep.size()) <= s) {
        ep.push_back(pow(G, Mint(-1).v / (1 << ep.size())));
        iep.push_back(ep.back().inv());
    }
    V<Mint> b(n);
    for (int i = 1; i <= s; i++) {
        int w = 1 << (s - i);
        Mint base = type ? iep[i] : ep[i], now = 1;
        for (int y = 0; y < n / 2; y += w) {
            for (int x = 0; x < w; x++) {
                auto l = a[y << 1 | x];
                auto r = now * a[y << 1 | x | w];
                b[y | x] = l + r;
                b[y | x | n >> 1] = l - r;
            }
            now *= base;
        }
        swap(a, b);
    }
}

V<Mint> multiply_nft(const V<Mint>& a, const V<Mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (min(n, m) <= 50) {
        V<Mint> ans(n + m - 1);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
        return ans;
    }
    int lg = 0;
    while ((1 << lg) < n + m - 1) lg++;
    int z = 1 << lg;
    auto a2 = a, b2 = b;
    a2.resize(z);
    b2.resize(z);
    nft(false, a2);
    nft(false, b2);
    for (int i = 0; i < z; i++) a2[i] *= b2[i];
    nft(true, a2);
    a2.resize(n + m - 1);
    Mint iz = Mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a2[i] *= iz;
    return a2;
}

int f2(ll x) {
    int ans = 0;
    while (x) {
        ans += x % 2;
        x /= 2;
    }
    return ans;
}

int f3(ll x) {
    int ans = 0;
    while (x) {
        ans += x % 3;
        x /= 3;
    }
    return ans;
}

void solve() {
    ll n;
    Mint a, b, c;
    cin >> n >> a >> b >> c;
    n++;
    Mint ans = -1;

    const int K = 21;

    int k3 = 0;
    int pw3 = 1;
    while (3 * pw3 <= (1 << K)) {
        k3++;
        pw3 *= 3;
    }

    int cnt = n / (ll)(1 << K);

    Mint pwa = pow(a, ((ll)cnt << (ll)K));
    for (ll x = ((ll)cnt << (ll)K); x < n; x++) {
        ans += pwa * pow(b, f2(x)) * pow(c, f3(x));
        pwa *= a;
    }

    vector<Mint> p1((1 << K), 0);
    pwa = 1;
    for (int y = 0; y < (1 << K); y++) {
        p1[y] = pwa * pow(b, f2(y));
        pwa *= a;
    }

    vector<Mint> p2(pw3, 0);
    for (int y = 0; y < pw3; y++) {
        p2[y] = pow(c, f3(y));
    }

    reverse(p1.begin(), p1.end());
    auto sm = multiply_nft(p1, p2);

    Mint ml = pow(a, (1 << K));
    pwa = 1;
    for (int x = 0; x < cnt; x++) {
        ll L = (ll)x << (ll)K;
        ll R = L + (1 << K);

        Mint cur = 0;
        for (int i = (L / pw3); (ll)i * pw3 < R; i++) {
            ll Lc = (ll)i * pw3;
            int delta = L - Lc + (int)p1.size() - 1;
            cur += sm[delta] * pow(c, f3(i));
        }

        ans += cur * pwa * pow(b, f2(x));
        pwa *= ml;
    }

    cout << ans << "\n";
}

int main() {
#ifdef ONPC
    freopen("input", "r", stdin);
#endif
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    int t = 1;
    //cin >> t;
    while (t--) {
        solve();
    }

    cerr << TIME << "\n";

    return 0;
}

详细

Test #1:

score: 100
Accepted
time: 1142ms
memory: 66508kb

input:

123456 12345 234567 3456789

output:

664963464

result:

ok 1 number(s): "664963464"

Test #2:

score: 0
Accepted
time: 1841ms
memory: 66556kb

input:

9876543210987 12816 837595 128478

output:

7972694

result:

ok 1 number(s): "7972694"

Test #3:

score: 0
Accepted
time: 1613ms
memory: 66568kb

input:

9196665971964 727160879 966835565 746444639

output:

949890012

result:

ok 1 number(s): "949890012"

Test #4:

score: 0
Accepted
time: 1710ms
memory: 66532kb

input:

9361549073598 749653880 965489817 371100607

output:

949904373

result:

ok 1 number(s): "949904373"

Test #5:

score: 0
Accepted
time: 1649ms
memory: 66736kb

input:

9567572694963 193332930 544713669 390021151

output:

878781872

result:

ok 1 number(s): "878781872"

Test #6:

score: 0
Accepted
time: 1835ms
memory: 66560kb

input:

9769301349033 215825931 425927410 408941695

output:

351574791

result:

ok 1 number(s): "351574791"

Test #7:

score: 0
Accepted
time: 1790ms
memory: 66536kb

input:

9975324970399 657749333 5151262 729852127

output:

400022780

result:

ok 1 number(s): "400022780"

Test #8:

score: 0
Accepted
time: 1142ms
memory: 66512kb

input:

1 149762920 266126484 107367523

output:

910371791

result:

ok 1 number(s): "910371791"

Test #9:

score: 0
Accepted
time: 1319ms
memory: 66560kb

input:

903900971479 969144397 356713678 36786741

output:

414279957

result:

ok 1 number(s): "414279957"

Test #10:

score: 0
Accepted
time: 1300ms
memory: 66492kb

input:

1940757501452 72683414 106545701 263512239

output:

786323834

result:

ok 1 number(s): "786323834"

Test #11:

score: 0
Accepted
time: 1355ms
memory: 66512kb

input:

2914414844884 174466783 133201789 792227626

output:

187534312

result:

ok 1 number(s): "187534312"

Test #12:

score: 0
Accepted
time: 1353ms
memory: 66540kb

input:

3851250038782 553074217 881278164 297532837

output:

847958862

result:

ok 1 number(s): "847958862"

Test #13:

score: 0
Accepted
time: 1526ms
memory: 66580kb

input:

4692374803740 352867698 211679787 826248223

output:

426334178

result:

ok 1 number(s): "426334178"

Test #14:

score: 0
Accepted
time: 1506ms
memory: 66556kb

input:

5566041306806 454651067 959756163 633543322

output:

842296050

result:

ok 1 number(s): "842296050"

Test #15:

score: 0
Accepted
time: 1611ms
memory: 66576kb

input:

6902869060611 556434437 709588186 860268821

output:

897681255

result:

ok 1 number(s): "897681255"

Test #16:

score: 0
Accepted
time: 1683ms
memory: 66488kb

input:

7239695301792 356227918 736244273 667563920

output:

726280051

result:

ok 1 number(s): "726280051"

Test #17:

score: 0
Accepted
time: 1711ms
memory: 66512kb

input:

8217660029470 458011287 486076297 198034954

output:

967159922

result:

ok 1 number(s): "967159922"