Submission #1115795

#	Time	Username	Problem	Language	Result	Execution time	Memory
1115795		vjudge1	Toll (BOI17_toll)	C++17	100 / 100	240 ms	75084 KiB

toll

/*
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,fma,bmi,bmi2,sse4.2,popcnt,lzcnt")
*/

#include <bits/stdc++.h>
#define taskname ""
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define i64 long long
#define isz(x) (int)x.size()
using namespace std;

const int inf = 1e9;

template<class T>
struct matrix{
    int n, m;
    vector<vector<T>> data;
    vector<T> &operator[](int i){
        assert(0 <= i && i < n);
        return data[i];
    }
    const vector<T> &operator[](int i) const{
        assert(0 <= i && i < n);
        return data[i];
    }
    matrix &inplace_slice(int il, int ir, int jl, int jr){
        assert(0 <= il && il <= ir && ir <= n);
        assert(0 <= jl && jl <= jr && jr <= m);
        n = ir - il, m = jr - jl;
        if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
        data.resize(n);
        for(auto &row: data){
            row.erase(row.begin(), row.begin() + jl);
            row.resize(m);
        }
        return *this;
    }
    matrix slice(int il, int ir, int jl, int jr) const{
        return matrix(*this).inplace_slice(il, ir, jl, jr);
    }
    matrix &inplace_row_slice(int il, int ir){
        assert(0 <= il && il <= ir && ir <= n);
        n = ir - il;
        if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
        data.resize(n);
        return *this;
    }
    matrix row_slice(int il, int ir) const{
        return matrix(*this).inplace_row_slice(il, ir);
    }
    matrix &inplace_column_slice(int jl, int jr){
        assert(0 <= jl && jl <= jr && jr <= m);
        m = jr - jl;
        for(auto &row: data){
            row.erase(row.begin(), row.begin() + jl);
            row.resize(m);
        }
        return *this;
    }
    matrix column_slice(int jl, int jr) const{
        return matrix(*this).inplace_column_slice(jl, jr);
    }
    bool operator==(const matrix &a) const{
        assert(n == a.n && m == a.m);
        return data == a.data;
    }
    bool operator!=(const matrix &a) const{
        assert(n == a.n && m == a.m);
        return data != a.data;
    }
    matrix &operator+=(const matrix &a){
        assert(n == a.n && m == a.m);
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] += a[i][j];
        return *this;
    }
    matrix operator+(const matrix &a) const{
        return matrix(*this) += a;
    }
    matrix &operator-=(const matrix &a){
        assert(n == a.n && m == a.m);
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] -= a[i][j];
        return *this;
    }
    matrix operator-(const matrix &a) const{
        return matrix(*this) -= a;
    }
    matrix operator*=(const matrix &a){
        assert(m == a.n);
        int l = a.m;
        matrix res(n, l, inf, inf);
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) for(auto k = 0; k < l; ++ k) res[i][k] = min(res[i][k], data[i][j] + a[j][k]);
        return *this = res;
    }
    matrix operator*(const matrix &a) const{
        return matrix(*this) *= a;
    }
    matrix &operator*=(T c){
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] *= c;
        return *this;
    }
    matrix operator*(T c) const{
        return matrix(*this) *= c;
    }
    template<class U, typename enable_if<is_integral<U>::value>::type* = nullptr>
    matrix &inplace_power(U e){
        assert(n == m && e >= 0);
        matrix res(n, n, T{1});
        for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
        return *this = res;
    }
    template<class U>
    matrix power(U e) const{
        return matrix(*this).inplace_power(e);
    }
    matrix &inplace_transpose(){
        assert(n == m);
        for(auto i = 0; i < n; ++ i) for(auto j = i + 1; j < n; ++ j) swap(data[i][j], data[j][i]);
        return *this;
    }
    matrix transpose() const{
        if(n == m) return matrix(*this).inplace_transpose();
        matrix res(m, n);
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[j][i] = data[i][j];
        return res;
    }
    vector<T> operator*(const vector<T> &v) const{
        assert(m == (int)v.size());
        vector<T> res(n, T{0});
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[i] += data[i][j] * v[j];
        return res;
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
    // Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix &, T, int> inplace_REF(int up_to = -1){
        if(n == 0) return {*this, T{1}, 0};
        if(!~up_to) up_to = m;
        T det = 1;
        int rank = 0;
        for(auto j = 0; j < up_to; ++ j){
            if constexpr(is_floating_point_v<T>){
                static const T eps = 1e-9;
                int pivot = rank;
                for(auto i = rank + 1; i < n; ++ i) if(abs(data[pivot][j]) < abs(data[i][j])) pivot = i;
                if(rank != pivot){
                    swap(data[rank], data[pivot]);
                    det *= -1;
                }
                if(abs(data[rank][j]) <= eps) continue;
                det *= data[rank][j];
                T inv = 1 / data[rank][j];
                for(auto i = rank + 1; i < n; ++ i) if(abs(data[i][j]) > eps){
                    T coef = data[i][j] * inv;
                    for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
                }
                ++ rank;
            }
            else{
                for(auto i = rank + 1; i < n; ++ i) while(data[i][j]){
                    T q;
                    if constexpr(is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) q = data[rank][j] / data[i][j];
                    else q = data[rank][j].data / data[i][j].data;
                    if(q) for(auto k = j; k < m; ++ k) data[rank][k] -= q * data[i][k];
                    swap(data[rank], data[i]);
                    det *= -1;
                }
                if(rank == j) det *= data[rank][j];
                else det = T{0};
                if(data[rank][j]) ++ rank;
            }
            if(rank == n) break;
        }
        return {*this, det, rank};
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
    // Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix, T, int> REF(int up_to = -1) const{
        return matrix(*this).inplace_REF(up_to);
    }
    // Assumes T is a field.
    // O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix &, T, int> inplace_REF_field(int up_to = -1){
        if(n == 0) return {*this, T{1}, 0};
        if(!~up_to) up_to = m;
        T det = T{1};
        int rank = 0;
        for(auto j = 0; j < up_to; ++ j){
            int pivot = -1;
            for(auto i = rank; i < n; ++ i) if(data[i][j] != T{0}){
                pivot = i;
                break;
            }
            if(!~pivot){
                det = T{0};
                continue;
            }
            if(rank != pivot){
                swap(data[rank], data[pivot]);
                det *= -1;
            }
            det *= data[rank][j];
            T inv = 1 / data[rank][j];
            for(auto i = rank + 1; i < n; ++ i) if(data[i][j] != T{0}){
                T coef = data[i][j] * inv;
                for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
            }
            ++ rank;
            if(rank == n) break;
        }
        return {*this, det, rank};
    }
    // Assumes T is a field.
    // O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
    // Returns {REF matrix, determinant, rank}
    tuple<matrix, T, int> REF_field(int up_to = -1) const{
        return matrix(*this).inplace_REF_field(up_to);
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    optional<matrix> inverse() const{
        assert(n == m);
        if(n == 0) return *this;
        auto a = data;
        auto res = multiplicative_identity();
        for(auto j = 0; j < n; ++ j){
            int rank = j, pivot = -1;
            if constexpr(is_floating_point_v<T>){
                static const T eps = 1e-9;
                pivot = rank;
                for(auto i = rank + 1; i < n; ++ i) if(abs(a[pivot][j]) < abs(a[i][j])) pivot = i;
                if(abs(a[pivot][j]) <= eps) return {};
            }
            else{
                for(auto i = rank; i < n; ++ i) if(a[i][j] != T{0}){
                    pivot = i;
                    break;
                }
                if(!~pivot) return {};
            }
            swap(a[rank], a[pivot]), swap(res[rank], res[pivot]);
            T inv = 1 / a[rank][j];
            for(auto k = 0; k < n; ++ k) a[rank][k] *= inv, res[rank][k] *= inv;
            for(auto i = 0; i < n; ++ i){
                if constexpr(is_floating_point_v<T>){
                    static const T eps = 1e-9;
                    if(i != rank && abs(a[i][j]) > eps){
                        T d = a[i][j];
                        for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
                    }
                }
                else if(i != rank && a[i][j] != T{0}){
                    T d = a[i][j];
                    for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
                }
            }
        }
        return res;
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
    T determinant() const{
        assert(n == m);
        return get<1>(REF());
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    T determinant_field() const{
        assert(n == m);
        return get<1>(REF_field());
    }
    // Assumes T is either a floating, integral, or a modular type.
    // If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    // Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
    int rank() const{
        return get<2>(REF());
    }
    // Assumes T is a field.
    // O(n) divisions with O(n^3) additions, subtractions, and multiplications.
    int rank_field() const{
        return get<2>(REF_field());
    }
    // Regarding the matrix as a system of linear equations by separating first m-1 columns, find a solution of the linear equation.
    // Assumes T is a field
    // O(n * m^2)
    optional<vector<T>> find_a_solution() const{
        assert(m >= 1);
        auto [ref, _, rank] = REF_field(m - 1);
        for(auto i = rank; i < n; ++ i) if(ref[i][m - 1] != T{0}) return {};
        vector<T> res(m - 1);
        for(auto i = rank - 1; i >= 0; -- i){
            int pivot = 0;
            while(pivot < m - 1 && ref[i][pivot] == T{0}) ++ pivot;
            assert(pivot < m - 1);
            res[pivot] = ref[i][m - 1];
            for(auto j = pivot + 1; j < m - 1; ++ j) res[pivot] -= ref[i][j] * res[j];
            res[pivot] /= ref[i][pivot];
        }
        return res;
    }
    // O(n * 2^n)
    T permanent() const{
        assert(n <= 30 && n == m);
        T perm = n ? 0 : 1;
        vector<T> sum(n);
        for(auto order = 1; order < 1 << n; ++ order){
            int j = __lg(order ^ order >> 1 ^ order - 1 ^ order - 1 >> 1), sign = (order ^ order >> 1) & 1 << j ? 1 : -1;
            T prod = order & 1 ? -1 : 1;
            if((order ^ order >> 1) & 1 << j) for(auto i = 0; i < n; ++ i) prod *= sum[i] += data[i][j];
            else for(auto i = 0; i < n; ++ i) prod *= sum[i] -= data[i][j];
            perm += prod;
        }
        return perm * (n & 1 ? -1 : 1);
    }
    template<class output_stream>
    friend output_stream &operator<<(output_stream &out, const matrix &a){
        out << "\n";
        for(auto i = 0; i < a.n; ++ i){
            for(auto j = 0; j < a.m; ++ j) out << a[i][j] << " ";
            out << "\n";
        }
        return out;
    }
    matrix(int n, int m, T init_diagonal = T{0}, T init_off_diagonal = T{0}): n(n), m(m){
        assert(n >= 0 && m >= 0);
        data.assign(n, vector<T>(m, T{0}));
        for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] = i == j ? init_diagonal : init_off_diagonal;
    }
    matrix(int n, int m, const vector<vector<T>> &a): n(n), m(m), data(a){ }
    static matrix additive_identity(int n, int m){
        return matrix(n, m, T{0}, T{0});
    }
    static matrix multiplicative_identity(int n, int m){
        return matrix(n, m, T{1}, T{0});
    }
};
template<class T>
matrix<T> operator*(T c, matrix<T> a){
    for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) a[i][j] = c * a[i][j];
    return a;
}
// Multiply a row vector v on the left
template<class T>
vector<T> operator*(const vector<T> &v, const matrix<T> &a){
    assert(a.n == (int)size(v));
    vector<T> res(a.m, T{0});
    for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) res[j] += v[i] * a[i][j];
    return res;
}

void solve() {
    int K, n, m, q;
    cin >> K >> n >> m >> q;

    int layer = (n - 1) / K;
    vector<matrix<int>> vec(layer, matrix(K, K, inf, inf));
    for (int i = 0; i < m; ++i) {
        int u, v, w;
        cin >> u >> v >> w;
        vec[u / K][u % K][v % K] = min(vec[u / K][u % K][v % K], w);
    }

    // for (int i = 0; i < layer; ++i) {
    //     cout << vec[i] << endl;
    // }

    vector<vector<matrix<int>>> jmp({vec});
    for (int i = 1, p = 1; p << 1 <= layer; ++i, p <<= 1) {
        jmp.emplace_back(isz(jmp[i - 1]) - p, matrix(K, K, inf, inf));
        for (int j = 0; j + p < isz(jmp[i - 1]); ++j) {
            jmp[i][j] = jmp[i - 1][j] * jmp[i - 1][j + p];
            // cout << jmp[i][j] << endl;
        }
    }

    auto query = [&](int l, int r, int st, int en) -> int {
        int len = r - l, cnt = 0;
        matrix res(K, K, inf, inf);
        for (int i = 0; i < K; ++i) {
            res[i][i] = 0;
        }
        while (len) {
            if (len & 1) {
                res *= jmp[cnt][l];
                l += 1 << cnt;
            }
            len >>= 1, ++cnt;
        }
        return (res[st][en] == inf ? -1 : res[st][en]);
    };

    while (q--) {
        int u, v;
        cin >> u >> v;
        cout << query(u / K, v / K, u % K, v % K) << endl;
    }
}

signed main() {

#ifndef CDuongg
    if (fopen(taskname".inp", "r"))
        assert(freopen(taskname".inp", "r", stdin)), assert(freopen(taskname".out", "w", stdout));
#else
    freopen("bai3.inp", "r", stdin);
    freopen("bai3.out", "w", stdout);
    auto start = chrono::high_resolution_clock::now();
#endif

    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int t = 1; //cin >> t;
    while(t--) solve();

#ifdef CDuongg
   auto end = chrono::high_resolution_clock::now();
   cout << "\n"; for(int i = 1; i <= 100; ++i) cout << '=';
   cout << "\nExecution time: " << chrono::duration_cast<chrono::milliseconds> (end - start).count() << "[ms]" << endl;
#endif

}

• Subtask 1: 7 / 7
• Subtask 2: 10 / 10
• Subtask 3: 8 / 8
• Subtask 4: 31 / 31
• Subtask 5: 44 / 44