oj.uz

Submission #508539

# Submission time Handle Problem Language Result Execution time Memory
508539 2022-01-13T11:54:44 Z KoD Set (COCI21_set) C++17
110 / 110
 399 ms 20876 KB 
#include <bits/stdc++.h>

using std::vector;
using std::array;
using std::pair;
using std::tuple;

template <int mod> struct Fp {
    int x;
    Fp(int x = 0) : x(x) {}
    
    Fp& operator+=(const Fp& other) {
        if ((x += other.x) >= mod) x -= mod;
        return *this;
    }
    Fp& operator-=(const Fp& other) {
        if ((x -= other.x) < 0) x += mod;
        return *this;
    }
    Fp& operator*=(const Fp& other) {
        x = (long long)x * other.x % mod;
        return *this;
    }
    Fp& operator/=(const Fp& other) {
        return *this *= other.inv();
    }

    Fp operator+(const Fp& other) const {
        return Fp(*this) += other;
    }
    Fp operator-(const Fp& other) const {
        return Fp(*this) -= other;
    }
    Fp operator*(const Fp& other) const {
        return Fp(*this) *= other;
    }
    Fp operator/(const Fp& other) const {
        return Fp(*this) /= other;
    }

    Fp pow(int exp) const {
        Fp ret(1), mul(*this);
        while (exp > 0) {
            if (exp & 1) ret *= mul;
            mul *= mul;
            exp >>= 1;
        }
        return ret;
    }
    Fp inv() const {
        return pow(mod - 2);
    }
};

template <int m> void transform(vector<Fp<m>>& f, const Fp<m> omega) {
    const int n = f.size();
    for (int i = 1; i < n; i *= 3) {
        for (int j = 0; j < n; ++j) {
            if ((j / i) % 3 == 0) {
                const auto a = f[j], b = f[j + i], c = f[j + i * 2];
                f[j] = a + b + c;
                f[j + i] = a + b * omega + c * omega * omega;
                f[j + i * 2] = a + b * omega * omega + c * omega;
            }
        }
    }
}

template <int m, int r> vector<int> square(const vector<int>& a) {
    const int n = a.size();
    vector<Fp<m>> f(n);
    for (int i = 0; i < n; ++i) {
        f[i] = a[i];
    }
    const auto omega = Fp<m>(r).pow((m - 1) / 3);
    transform<m>(f, omega);
    for (int i = 0; i < n; ++i) {
        f[i] *= f[i];
    }
    transform<m>(f, omega * omega);
    const auto inv = Fp<m>(n).inv();
    vector<int> b(n);
    for (int i = 0; i < n; ++i) {
        b[i] = (f[i] * inv).x;
    }
    return b;
}

constexpr int mod1 = 99999931;
constexpr int root1 = 2;

constexpr int mod2 = 99999043;
constexpr int root2 = 2;

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int N, K;
    std::cin >> N >> K;
    vector<int> pow(K + 1);
    pow[0] = 1;
    for (int i = 0; i < K; ++i) {
        pow[i + 1] = pow[i] * 3;
    }
    const int L = pow[K];
    vector<int> inv(N);
    vector<int> freq(L);
    for (int i = 0; i < N; ++i) {
        int x = 0;
        for (int j = 0; j < K; ++j) {
            char c;
            std::cin >> c;
            x += (c - '1') * pow[j];
            inv[i] += (('4' - c) % 3) * pow[j];
        }
        freq[x] += 1;
    }
    const auto a = square<mod1, root1>(freq);
    const auto b = square<mod2, root2>(freq);
    vector<long long> c(L);
    for (int i = 0; i < L; ++i) {
        // x = a[i] mod M1
        // x = b[i] mod M2
        const int k = ((Fp<mod2>(b[i]) - Fp<mod2>(a[i])) / Fp<mod2>(mod1)).x;
        c[i] = (long long)mod1 * k + a[i];
    }
    long long ans = 0;
    for (int i = 0; i < N; ++i) {
        ans += c[inv[i]];
    }
    std::cout << (ans - N) / 6 << '\n';
    return 0;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 312 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 312 KB Output is correct
6 Correct 1 ms 312 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 312 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 0 ms 204 KB Output is correct
14 Correct 0 ms 324 KB Output is correct
15 Correct 0 ms 316 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 312 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 312 KB Output is correct
6 Correct 1 ms 312 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 312 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 0 ms 204 KB Output is correct
14 Correct 0 ms 324 KB Output is correct
15 Correct 0 ms 316 KB Output is correct
16 Correct 2 ms 332 KB Output is correct
17 Correct 1 ms 316 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 320 KB Output is correct
20 Correct 0 ms 204 KB Output is correct
21 Correct 1 ms 308 KB Output is correct
22 Correct 0 ms 208 KB Output is correct
23 Correct 2 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 2 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 0 ms 312 KB Output is correct
29 Correct 0 ms 204 KB Output is correct
30 Correct 1 ms 312 KB Output is correct

Subtask #3
70.0 / 70.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 312 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 312 KB Output is correct
6 Correct 1 ms 312 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 312 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 0 ms 204 KB Output is correct
14 Correct 0 ms 324 KB Output is correct
15 Correct 0 ms 316 KB Output is correct
16 Correct 2 ms 332 KB Output is correct
17 Correct 1 ms 316 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 320 KB Output is correct
20 Correct 0 ms 204 KB Output is correct
21 Correct 1 ms 308 KB Output is correct
22 Correct 0 ms 208 KB Output is correct
23 Correct 2 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 2 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 0 ms 312 KB Output is correct
29 Correct 0 ms 204 KB Output is correct
30 Correct 1 ms 312 KB Output is correct
31 Correct 282 ms 12752 KB Output is correct
32 Correct 271 ms 12792 KB Output is correct
33 Correct 281 ms 12772 KB Output is correct
34 Correct 377 ms 20876 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 1 ms 204 KB Output is correct
37 Correct 1 ms 332 KB Output is correct
38 Correct 383 ms 20160 KB Output is correct
39 Correct 311 ms 14604 KB Output is correct
40 Correct 394 ms 20124 KB Output is correct
41 Correct 282 ms 13440 KB Output is correct
42 Correct 399 ms 20048 KB Output is correct
43 Correct 1 ms 204 KB Output is correct
44 Correct 1 ms 204 KB Output is correct
45 Correct 0 ms 204 KB Output is correct