Submission #1093531

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1093531	2024-09-27T02:39:54 Z	vjudge1	Toll (BOI17_toll)	C++17	100 / 100	220 ms	75068 KB

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

7.0 / 7.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	202 ms	75064 KB	Output is correct
2	Correct	1 ms	344 KB	Output is correct
3	Correct	0 ms	344 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	4 ms	1372 KB	Output is correct
6	Correct	4 ms	1236 KB	Output is correct
7	Correct	4 ms	1384 KB	Output is correct
8	Correct	205 ms	75068 KB	Output is correct
9	Correct	200 ms	74804 KB	Output is correct
10	Correct	220 ms	74276 KB	Output is correct

Subtask #2

10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	150 ms	59460 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	0 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	19 ms	1488 KB	Output is correct
8	Correct	21 ms	1112 KB	Output is correct
9	Correct	189 ms	75048 KB	Output is correct
10	Correct	157 ms	50388 KB	Output is correct
11	Correct	149 ms	59540 KB	Output is correct
12	Correct	158 ms	49252 KB	Output is correct
13	Correct	97 ms	26556 KB	Output is correct
14	Correct	83 ms	28868 KB	Output is correct
15	Correct	93 ms	25236 KB	Output is correct
16	Correct	90 ms	25236 KB	Output is correct

Subtask #3

8.0 / 8.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	348 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	1 ms	348 KB	Output is correct
5	Correct	0 ms	348 KB	Output is correct
6	Correct	4 ms	1372 KB	Output is correct
7	Correct	3 ms	1116 KB	Output is correct
8	Correct	3 ms	860 KB	Output is correct
9	Correct	2 ms	980 KB	Output is correct
10	Correct	176 ms	74752 KB	Output is correct
11	Correct	124 ms	59384 KB	Output is correct
12	Correct	130 ms	49984 KB	Output is correct
13	Correct	136 ms	50216 KB	Output is correct
14	Correct	126 ms	49736 KB	Output is correct
15	Correct	74 ms	25200 KB	Output is correct
16	Correct	72 ms	25196 KB	Output is correct

Subtask #4

31.0 / 31.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	348 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	1 ms	348 KB	Output is correct
5	Correct	0 ms	348 KB	Output is correct
6	Correct	4 ms	1372 KB	Output is correct
7	Correct	3 ms	1116 KB	Output is correct
8	Correct	3 ms	860 KB	Output is correct
9	Correct	2 ms	980 KB	Output is correct
10	Correct	176 ms	74752 KB	Output is correct
11	Correct	124 ms	59384 KB	Output is correct
12	Correct	130 ms	49984 KB	Output is correct
13	Correct	136 ms	50216 KB	Output is correct
14	Correct	126 ms	49736 KB	Output is correct
15	Correct	74 ms	25200 KB	Output is correct
16	Correct	72 ms	25196 KB	Output is correct
17	Correct	146 ms	59720 KB	Output is correct
18	Correct	1 ms	348 KB	Output is correct
19	Correct	1 ms	348 KB	Output is correct
20	Correct	0 ms	348 KB	Output is correct
21	Correct	0 ms	348 KB	Output is correct
22	Correct	0 ms	348 KB	Output is correct
23	Correct	8 ms	1372 KB	Output is correct
24	Correct	7 ms	1228 KB	Output is correct
25	Correct	11 ms	860 KB	Output is correct
26	Correct	9 ms	1068 KB	Output is correct
27	Correct	183 ms	74868 KB	Output is correct
28	Correct	142 ms	50252 KB	Output is correct
29	Correct	143 ms	50460 KB	Output is correct
30	Correct	138 ms	49732 KB	Output is correct

Subtask #5

44.0 / 44.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	202 ms	75064 KB	Output is correct
2	Correct	1 ms	344 KB	Output is correct
3	Correct	0 ms	344 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	4 ms	1372 KB	Output is correct
6	Correct	4 ms	1236 KB	Output is correct
7	Correct	4 ms	1384 KB	Output is correct
8	Correct	205 ms	75068 KB	Output is correct
9	Correct	200 ms	74804 KB	Output is correct
10	Correct	220 ms	74276 KB	Output is correct
11	Correct	150 ms	59460 KB	Output is correct
12	Correct	0 ms	348 KB	Output is correct
13	Correct	0 ms	348 KB	Output is correct
14	Correct	0 ms	348 KB	Output is correct
15	Correct	0 ms	348 KB	Output is correct
16	Correct	0 ms	348 KB	Output is correct
17	Correct	19 ms	1488 KB	Output is correct
18	Correct	21 ms	1112 KB	Output is correct
19	Correct	189 ms	75048 KB	Output is correct
20	Correct	157 ms	50388 KB	Output is correct
21	Correct	149 ms	59540 KB	Output is correct
22	Correct	158 ms	49252 KB	Output is correct
23	Correct	97 ms	26556 KB	Output is correct
24	Correct	83 ms	28868 KB	Output is correct
25	Correct	93 ms	25236 KB	Output is correct
26	Correct	90 ms	25236 KB	Output is correct
27	Correct	0 ms	348 KB	Output is correct
28	Correct	1 ms	348 KB	Output is correct
29	Correct	0 ms	348 KB	Output is correct
30	Correct	1 ms	348 KB	Output is correct
31	Correct	0 ms	348 KB	Output is correct
32	Correct	4 ms	1372 KB	Output is correct
33	Correct	3 ms	1116 KB	Output is correct
34	Correct	3 ms	860 KB	Output is correct
35	Correct	2 ms	980 KB	Output is correct
36	Correct	176 ms	74752 KB	Output is correct
37	Correct	124 ms	59384 KB	Output is correct
38	Correct	130 ms	49984 KB	Output is correct
39	Correct	136 ms	50216 KB	Output is correct
40	Correct	126 ms	49736 KB	Output is correct
41	Correct	74 ms	25200 KB	Output is correct
42	Correct	72 ms	25196 KB	Output is correct
43	Correct	146 ms	59720 KB	Output is correct
44	Correct	1 ms	348 KB	Output is correct
45	Correct	1 ms	348 KB	Output is correct
46	Correct	0 ms	348 KB	Output is correct
47	Correct	0 ms	348 KB	Output is correct
48	Correct	0 ms	348 KB	Output is correct
49	Correct	8 ms	1372 KB	Output is correct
50	Correct	7 ms	1228 KB	Output is correct
51	Correct	11 ms	860 KB	Output is correct
52	Correct	9 ms	1068 KB	Output is correct
53	Correct	183 ms	74868 KB	Output is correct
54	Correct	142 ms	50252 KB	Output is correct
55	Correct	143 ms	50460 KB	Output is correct
56	Correct	138 ms	49732 KB	Output is correct
57	Correct	189 ms	49352 KB	Output is correct
58	Correct	206 ms	74868 KB	Output is correct
59	Correct	162 ms	59740 KB	Output is correct