oj.uz

Submission #855179

# Submission time Handle Problem Language Result Execution time Memory
855179 2023-09-30T13:02:29 Z FairyWinx Overtaking (IOI23_overtaking) C++17
100 / 100
 2330 ms 179376 KB 
#include <bits/stdc++.h>

#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

using namespace std;

vector<vector<long long>> res;
vector<int> s;
vector<pair<int, long long>> t; // speed, time
int n, m;
int x;

vector<vector<int>> who_layer;
vector<vector<long long>> sorted_layer;
vector<vector<int>> nxt_layer;
vector<vector<long long>> res_layer;

const int K = 10;

vector<vector<vector<pair<int, int>>>> up;

void init(int l, int _n, vector<long long> _t, vector<int> _w, 
            int _x, int _m, vector<int> _s) {

    
    x = _x, n = _n, m = _m;
    s = _s;
    t.resize(n);
    for (int i = 0; i < n; ++i) {
        t[i].first = _w[i];
        t[i].second = _t[i];
    }
    sort(rall(t));
    while (t.size() && t.back().first <= x) {
        t.pop_back();
    }
    n = t.size();

    sorted_layer.resize(m);
    who_layer.resize(m, vector<int> (n));
    nxt_layer.resize(m, vector<int> (n));
    res_layer.resize(m, vector<long long> (n));
    up.resize(m, vector (n, vector<pair<int, int>> (K)));

    res.resize(m, vector<long long> (n, -1));
    s = _s;

    for (int i = 0; i < n; ++i) {
        res[0][i] = t[i].second;
    }
    for (int i = 0; i < m - 1; ++i) { // n^2 log
        vector<pair<long long, int>> value;
        for (int j = 0; j < n; ++j) {
            value.emplace_back(res[i][j], j);
        }
        sort(all(value));
        long long mx = 0;
        for (int j = 0; j < n; ++j) {
            long long tmp_max = mx;
            int k = j;
            for (; k < n; ++k) {
                if (value[k].first != value[j].first)
                    break;
                int ind = value[k].second;
                res[i + 1][ind] = max(res[i][ind] + 1ll * t[ind].first * (s[i + 1] - s[i]), mx);    
                tmp_max = max(tmp_max, res[i + 1][ind]);
            }
            mx = tmp_max;
            j = k - 1;
        }
    }

    for (int i = 0; i < m; ++i) {
        vector<int> p(n);
        iota(all(p), 0);
        sort(p.begin(), p.end(), [&] (const int &a, const int &b) {
            return make_pair(res[i][a], -a) < make_pair(res[i][b], -b);
        });
        for (int j = 0; j < n; ++j) {
            sorted_layer[i].push_back(res[i][p[j]]);
            who_layer[i][j] = p[j];
        }
        if (i != m - 1) {
            map<long long, pair<int, int>> low_speed;
            for (int j = 0; j < n; ++j) {
                low_speed[res[i + 1][j]] = max(make_pair(t[j].first, j), low_speed[res[i + 1][j]]);
            }
            for (int j = 0; j < n; ++j) {
                nxt_layer[i][j] = low_speed[res[i + 1][j]].second;
                up[i][j][0] = {nxt_layer[i][j], i + 1};
            }
        } else {
            for (int j = 0; j < n; ++j) {
                up[i][j][0] = {j, i};
            }
        }
    }
    for (int k = 1; k < K; ++k) {
        for (int i = m - 1; i >= 0; --i) {
            for (int j = 0; j < n; ++j) {
                auto z = up[i][j][k - 1];
                up[i][j][k] = up[z.second][z.first][k - 1];
            }
        }
    }
    for (int i = 0; i < n; ++i) {
        res_layer[m - 1][i] = res[m - 1][i];
    }
    for (int i = m - 2; i >= 0; --i) {
        for (int j = 0; j < n; ++j) {
            int ind_low = lower_bound(all(sorted_layer[i]), res[i][j])
                            - sorted_layer[i].begin() - 1;
            if (ind_low == -1) {
                res_layer[i][j] = res[i][j] + 1ll * x * (s.back() - s[i]);
                continue;
            }
            int ind_less = who_layer[i][ind_low];
            pair<int, int> cur_nxt = {ind_less, i};
            for (int k = K - 1; k >= 0; --k) {
                auto jump = up[cur_nxt.second][cur_nxt.first][k];
                if (res[jump.second][jump.first] < res[i][j] + 1ll * x * (s[jump.second] - s[i])) {
                    cur_nxt = jump;
                }
            }
            if (cur_nxt.second == m - 1) {
                res_layer[i][j] = res[i][j] + 1ll * x * (s.back() - s[i]);
            } else {
                cur_nxt = up[cur_nxt.second][cur_nxt.first][0];
                res_layer[i][j] = res_layer[cur_nxt.second][cur_nxt.first];
            }
        }
    }
}

// res_layer[2][0] - неверный.

long long arrival_time(long long y) {
    // int ind = lower_bound(all(sorted_layer[0]), y) - sorted_layer[0].begin() - 1;
    // if (ind == -1) {
    //     return 1ll * x * (s.back()) + y;
    // }
    // ind = who_layer[0][ind];
    // for (int i = 1; i < m; ++i) {
    //     ind = nxt_layer[i - 1][ind];
    //     if (1ll * x * s[i] + y <= res[i][ind]) {
    //         return res_layer[i][ind];
    //     }
    // }
    // return 1ll * x * s.back() + y;

    int ind = lower_bound(all(sorted_layer[0]), y) - sorted_layer[0].begin() - 1;
    if (ind == -1) {
        return 1ll * x * (s.back()) + y;
    }
    ind = who_layer[0][ind];
    pair<int, int> cur_nxt = {ind, 0};
    for (int k = K - 1; k >= 0; --k) {
        auto jump = up[cur_nxt.second][cur_nxt.first][k];
        if (res[jump.second][jump.first] < y + 1ll * x * s[jump.second]) {
            cur_nxt = jump;
        }
    }
    if (cur_nxt.second == m - 1) {
        return y + 1ll * x * (s.back() - s[0]);
    } else {
        cur_nxt = up[cur_nxt.second][cur_nxt.first][0];
        return res_layer[cur_nxt.second][cur_nxt.first];
    }
}

#ifdef LOCAL
int main()
{
    // BEGIN SECRET
    const std::string input_secret = "XwWPuInrOjpekAwGKojzwKw3yVDtdkGS";
    const std::string output_secret = "mGlgT4yvr1qPbquFwkxRVh9hMn0Mrxoz";
    char secret[1000];
    assert(1 == scanf("%999s", secret));
    if (std::string(secret) != input_secret)
    {
        printf("%s\n", output_secret.c_str());
        printf("PV\n");
        printf("Possible tampering with the input\n");
        fclose(stdout);
        return 0;
    }
    // END SECRET
    int L, N, X, M, Q;
    assert(5 == scanf("%d %d %d %d %d", &L, &N, &X, &M, &Q));
    std::vector<long long> T(N);
    for (int i = 0; i < N; i++)
        assert(1 == scanf("%lld", &T[i]));
    std::vector<int> W(N);
    for (int i = 0; i < N; i++)
        assert(1 == scanf("%d", &W[i]));
    std::vector<int> S(M);
    for (int i = 0; i < M; i++)
        assert(1 == scanf("%d", &S[i]));
    std::vector<long long> Y(Q);
    for (int i = 0; i < Q; i++)
        assert(1 == scanf("%lld", &Y[i]));

    fclose(stdin);

    init(L, N, T, W, X, M, S);
    std::vector<long long> res(Q);
    for (int i = 0; i < Q; i++)
        res[i] = arrival_time(Y[i]);

    // BEGIN SECRET
    printf("%s\n", output_secret.c_str());
    printf("OK\n");
    // END SECRET
    for (int i = 0; i < Q; i++)
        printf("%lld\n", res[i]);
    fclose(stdout);
    return 0;
}
#endif

Subtask #0
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 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 1 ms 348 KB Output is correct
6 Correct 1 ms 604 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 860 KB Output is correct
9 Correct 2 ms 1112 KB Output is correct
10 Correct 1 ms 860 KB Output is correct
11 Correct 1 ms 756 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 604 KB Output is correct
6 Correct 2 ms 604 KB Output is correct
7 Correct 2 ms 860 KB Output is correct
8 Correct 2 ms 860 KB Output is correct
9 Correct 2 ms 856 KB Output is correct
10 Correct 1 ms 860 KB Output is correct
11 Correct 1 ms 860 KB Output is correct
12 Correct 2 ms 860 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 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 0 ms 344 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 4 ms 1884 KB Output is correct
10 Correct 4 ms 1884 KB Output is correct
11 Correct 4 ms 1884 KB Output is correct
12 Correct 4 ms 1884 KB Output is correct
13 Correct 4 ms 1884 KB Output is correct
14 Correct 4 ms 1960 KB Output is correct
15 Correct 5 ms 1880 KB Output is correct
16 Correct 6 ms 1880 KB Output is correct
17 Correct 6 ms 1884 KB Output is correct
18 Correct 5 ms 1884 KB Output is correct
19 Correct 6 ms 1884 KB Output is correct
20 Correct 5 ms 1880 KB Output is correct
21 Correct 2 ms 1112 KB Output is correct
22 Correct 3 ms 1116 KB Output is correct
23 Correct 3 ms 1624 KB Output is correct
24 Correct 4 ms 1628 KB Output is correct
25 Correct 4 ms 1628 KB Output is correct
26 Correct 4 ms 1628 KB Output is correct
27 Correct 4 ms 1592 KB Output is correct
28 Correct 3 ms 1116 KB Output is correct
29 Correct 3 ms 1116 KB Output is correct
30 Correct 3 ms 1112 KB Output is correct
31 Correct 3 ms 1116 KB Output is correct
32 Correct 3 ms 1884 KB Output is correct
33 Correct 4 ms 1884 KB Output is correct
34 Correct 4 ms 1884 KB Output is correct
35 Correct 4 ms 1884 KB Output is correct
36 Correct 4 ms 1880 KB Output is correct
37 Correct 4 ms 1884 KB Output is correct
38 Correct 0 ms 344 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 4 ms 1884 KB Output is correct

Subtask #4
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 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 1 ms 348 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 2 ms 1112 KB Output is correct
11 Correct 1 ms 860 KB Output is correct
12 Correct 1 ms 756 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 4 ms 1884 KB Output is correct
17 Correct 4 ms 1884 KB Output is correct
18 Correct 4 ms 1884 KB Output is correct
19 Correct 4 ms 1884 KB Output is correct
20 Correct 4 ms 1884 KB Output is correct
21 Correct 4 ms 1960 KB Output is correct
22 Correct 5 ms 1880 KB Output is correct
23 Correct 6 ms 1880 KB Output is correct
24 Correct 6 ms 1884 KB Output is correct
25 Correct 5 ms 1884 KB Output is correct
26 Correct 6 ms 1884 KB Output is correct
27 Correct 5 ms 1880 KB Output is correct
28 Correct 2 ms 1112 KB Output is correct
29 Correct 3 ms 1116 KB Output is correct
30 Correct 3 ms 1624 KB Output is correct
31 Correct 4 ms 1628 KB Output is correct
32 Correct 4 ms 1628 KB Output is correct
33 Correct 4 ms 1628 KB Output is correct
34 Correct 4 ms 1592 KB Output is correct
35 Correct 3 ms 1116 KB Output is correct
36 Correct 3 ms 1116 KB Output is correct
37 Correct 3 ms 1112 KB Output is correct
38 Correct 3 ms 1116 KB Output is correct
39 Correct 3 ms 1884 KB Output is correct
40 Correct 4 ms 1884 KB Output is correct
41 Correct 4 ms 1884 KB Output is correct
42 Correct 4 ms 1884 KB Output is correct
43 Correct 4 ms 1880 KB Output is correct
44 Correct 4 ms 1884 KB Output is correct
45 Correct 0 ms 344 KB Output is correct
46 Correct 0 ms 348 KB Output is correct
47 Correct 4 ms 1884 KB Output is correct
48 Correct 691 ms 149668 KB Output is correct
49 Correct 715 ms 149700 KB Output is correct
50 Correct 745 ms 149700 KB Output is correct
51 Correct 746 ms 149588 KB Output is correct
52 Correct 701 ms 149744 KB Output is correct
53 Correct 711 ms 149700 KB Output is correct
54 Correct 773 ms 149836 KB Output is correct
55 Correct 617 ms 149620 KB Output is correct
56 Correct 723 ms 149724 KB Output is correct
57 Correct 654 ms 149776 KB Output is correct
58 Correct 756 ms 149736 KB Output is correct
59 Correct 717 ms 149732 KB Output is correct
60 Correct 700 ms 149800 KB Output is correct
61 Correct 739 ms 149744 KB Output is correct
62 Correct 3 ms 860 KB Output is correct
63 Correct 3 ms 860 KB Output is correct
64 Correct 341 ms 75248 KB Output is correct
65 Correct 391 ms 75196 KB Output is correct
66 Correct 517 ms 149896 KB Output is correct
67 Correct 744 ms 149844 KB Output is correct
68 Correct 756 ms 149584 KB Output is correct
69 Correct 442 ms 149588 KB Output is correct
70 Correct 556 ms 149720 KB Output is correct
71 Correct 770 ms 149708 KB Output is correct
72 Correct 954 ms 149712 KB Output is correct
73 Correct 735 ms 149712 KB Output is correct
74 Correct 693 ms 149716 KB Output is correct
75 Correct 2 ms 604 KB Output is correct
76 Correct 2 ms 604 KB Output is correct
77 Correct 1 ms 604 KB Output is correct
78 Correct 447 ms 149736 KB Output is correct

Subtask #5
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 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 1 ms 348 KB Output is correct
7 Correct 1 ms 604 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 2 ms 1112 KB Output is correct
11 Correct 1 ms 860 KB Output is correct
12 Correct 1 ms 756 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 604 KB Output is correct
18 Correct 2 ms 604 KB Output is correct
19 Correct 2 ms 860 KB Output is correct
20 Correct 2 ms 860 KB Output is correct
21 Correct 2 ms 856 KB Output is correct
22 Correct 1 ms 860 KB Output is correct
23 Correct 1 ms 860 KB Output is correct
24 Correct 2 ms 860 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 4 ms 1884 KB Output is correct
28 Correct 4 ms 1884 KB Output is correct
29 Correct 4 ms 1884 KB Output is correct
30 Correct 4 ms 1884 KB Output is correct
31 Correct 4 ms 1884 KB Output is correct
32 Correct 4 ms 1960 KB Output is correct
33 Correct 5 ms 1880 KB Output is correct
34 Correct 6 ms 1880 KB Output is correct
35 Correct 6 ms 1884 KB Output is correct
36 Correct 5 ms 1884 KB Output is correct
37 Correct 6 ms 1884 KB Output is correct
38 Correct 5 ms 1880 KB Output is correct
39 Correct 2 ms 1112 KB Output is correct
40 Correct 3 ms 1116 KB Output is correct
41 Correct 3 ms 1624 KB Output is correct
42 Correct 4 ms 1628 KB Output is correct
43 Correct 4 ms 1628 KB Output is correct
44 Correct 4 ms 1628 KB Output is correct
45 Correct 4 ms 1592 KB Output is correct
46 Correct 3 ms 1116 KB Output is correct
47 Correct 3 ms 1116 KB Output is correct
48 Correct 3 ms 1112 KB Output is correct
49 Correct 3 ms 1116 KB Output is correct
50 Correct 3 ms 1884 KB Output is correct
51 Correct 4 ms 1884 KB Output is correct
52 Correct 4 ms 1884 KB Output is correct
53 Correct 4 ms 1884 KB Output is correct
54 Correct 4 ms 1880 KB Output is correct
55 Correct 4 ms 1884 KB Output is correct
56 Correct 0 ms 344 KB Output is correct
57 Correct 0 ms 348 KB Output is correct
58 Correct 4 ms 1884 KB Output is correct
59 Correct 691 ms 149668 KB Output is correct
60 Correct 715 ms 149700 KB Output is correct
61 Correct 745 ms 149700 KB Output is correct
62 Correct 746 ms 149588 KB Output is correct
63 Correct 701 ms 149744 KB Output is correct
64 Correct 711 ms 149700 KB Output is correct
65 Correct 773 ms 149836 KB Output is correct
66 Correct 617 ms 149620 KB Output is correct
67 Correct 723 ms 149724 KB Output is correct
68 Correct 654 ms 149776 KB Output is correct
69 Correct 756 ms 149736 KB Output is correct
70 Correct 717 ms 149732 KB Output is correct
71 Correct 700 ms 149800 KB Output is correct
72 Correct 739 ms 149744 KB Output is correct
73 Correct 3 ms 860 KB Output is correct
74 Correct 3 ms 860 KB Output is correct
75 Correct 341 ms 75248 KB Output is correct
76 Correct 391 ms 75196 KB Output is correct
77 Correct 517 ms 149896 KB Output is correct
78 Correct 744 ms 149844 KB Output is correct
79 Correct 756 ms 149584 KB Output is correct
80 Correct 442 ms 149588 KB Output is correct
81 Correct 556 ms 149720 KB Output is correct
82 Correct 770 ms 149708 KB Output is correct
83 Correct 954 ms 149712 KB Output is correct
84 Correct 735 ms 149712 KB Output is correct
85 Correct 693 ms 149716 KB Output is correct
86 Correct 2 ms 604 KB Output is correct
87 Correct 2 ms 604 KB Output is correct
88 Correct 1 ms 604 KB Output is correct
89 Correct 447 ms 149736 KB Output is correct
90 Correct 728 ms 152000 KB Output is correct
91 Correct 1151 ms 175060 KB Output is correct
92 Correct 1186 ms 174916 KB Output is correct
93 Correct 1162 ms 175176 KB Output is correct
94 Correct 1173 ms 175072 KB Output is correct
95 Correct 1094 ms 174996 KB Output is correct
96 Correct 1184 ms 175176 KB Output is correct
97 Correct 693 ms 152000 KB Output is correct
98 Correct 1134 ms 174816 KB Output is correct
99 Correct 1133 ms 175304 KB Output is correct
100 Correct 1143 ms 175020 KB Output is correct
101 Correct 1151 ms 174804 KB Output is correct
102 Correct 1144 ms 174940 KB Output is correct
103 Correct 1196 ms 174996 KB Output is correct
104 Correct 663 ms 99664 KB Output is correct
105 Correct 745 ms 101864 KB Output is correct
106 Correct 903 ms 179376 KB Output is correct
107 Correct 1117 ms 179232 KB Output is correct
108 Correct 1161 ms 179160 KB Output is correct
109 Correct 1148 ms 179364 KB Output is correct
110 Correct 1181 ms 179280 KB Output is correct
111 Correct 852 ms 175380 KB Output is correct
112 Correct 1014 ms 175948 KB Output is correct
113 Correct 1725 ms 177064 KB Output is correct
114 Correct 2222 ms 178004 KB Output is correct
115 Correct 1516 ms 177092 KB Output is correct
116 Correct 1215 ms 176980 KB Output is correct
117 Correct 204 ms 29272 KB Output is correct
118 Correct 181 ms 29056 KB Output is correct
119 Correct 176 ms 27980 KB Output is correct
120 Correct 191 ms 29248 KB Output is correct
121 Correct 188 ms 30024 KB Output is correct
122 Correct 1343 ms 172492 KB Output is correct
123 Correct 2330 ms 178000 KB Output is correct
124 Correct 2291 ms 178204 KB Output is correct
125 Correct 2284 ms 178100 KB Output is correct