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Submission #839710

# Submission time Handle Problem Language Result Execution time Memory
839710 2023-08-30T15:46:26 Z model_code Closing Time (IOI23_closing) C++17
51 / 100
 1000 ms 141612 KB 
// correct/solution-ayaze-brute-linear-knapsack.cpp

// O(N^3)
#include "closing.h"
#include <bits/stdc++.h>
using namespace std;

const int kVisited = 1;
const int kTypeSingle = 1, kTypeBoth = 2;
const long long kInf = 4e18;

vector<vector<pair<int, int>>> adj_list;
vector<long long> dist_from_x, dist_from_y;

void DfsDistance(int now, int prv, long long current_dist, vector<long long> &dist_vec, vector<int> &parent)
{
    dist_vec[now] = current_dist;
    parent[now] = prv;

    for (pair<int, int> edge : adj_list[now])
    {
        int nxt = edge.first;
        if (nxt == prv)
            continue;
        long long new_dist = edge.second + current_dist;
        DfsDistance(nxt, now, new_dist, dist_vec, parent);
    }
}

void DfsComponent(int now, vector<int> &component, vector<int> &state)
{
    state[now] = kVisited;
    for (pair<int, int> edge : adj_list[now])
    {
        int nxt = edge.first;
        if (state[nxt] == kVisited)
            continue;
        DfsComponent(nxt, component, state);
    }
    component.push_back(now);
}

int Knapsack(vector<pair<int, int>> free_nodes, long long K)
{
    int sz = free_nodes.size();
    vector<vector<long long>> dp_mat(sz + 1, vector<long long>(2 * sz + 1, kInf));
    dp_mat[0][0] = 0;

    for (int i = 0; i < sz; i++)
    {
        int node = free_nodes[i].first;
        int typ = free_nodes[i].second;
        long long p = min(dist_from_x[node], dist_from_y[node]);
        long long q = max(dist_from_x[node], dist_from_y[node]);

        for (int j = 0; j <= 2 * i; j++)
        {
            dp_mat[i + 1][j] = min(dp_mat[i + 1][j], dp_mat[i][j]);
            dp_mat[i + 1][j + 1] = min(dp_mat[i + 1][j + 1], dp_mat[i][j] + p);
            if (typ == kTypeBoth)
            {
                dp_mat[i + 1][j + 2] = min(dp_mat[i + 1][j + 2], dp_mat[i][j] + q);
            }
        }
    }

    int ret = 0;
    for (int i = 0; i <= 2 * sz; i++)
    {
        if (dp_mat[sz][i] <= K)
        {
            ret = i;
        }
    }

    return ret;
}

int max_score(int N, int X, int Y, long long K,
              std::vector<int> U, std::vector<int> V, std::vector<int> W)
{
    adj_list.assign(N, vector<pair<int, int>>());
    dist_from_x.resize(N);
    dist_from_y.resize(N);

    for (int i = 0; i < static_cast<int>(U.size()); i++)
    {
        adj_list[U[i]].push_back({V[i], W[i]});
        adj_list[V[i]].push_back({U[i], W[i]});
    }

    vector<int> parent_rooted_x(N);
    DfsDistance(Y, -1, 0, dist_from_y, parent_rooted_x);
    DfsDistance(X, -1, 0, dist_from_x, parent_rooted_x);

    vector<int> path_xy;
    vector<pair<long long, int>> sorted_diff;
    for (int i = Y; i != -1; i = parent_rooted_x[i])
    {
        int idx = path_xy.size();
        path_xy.push_back(i);

        long long diff = dist_from_x[i] - dist_from_y[i];
        if (diff < 0)
            diff = -diff;
        sorted_diff.push_back({diff, idx});
    }
    sort(sorted_diff.begin(), sorted_diff.end());

    int ret = 0;
    int path_xy_size = static_cast<int>(path_xy.size());
    vector<int> node_state(N);

    for (int common_prefix = 0; common_prefix < path_xy_size; common_prefix++)
    {
        fill(node_state.begin(), node_state.end(), 0);
        for (int i = 0; i < path_xy_size; i++)
        {
            node_state[path_xy[i]] = kVisited;
        }

        int common_left = N, common_right = -1;
        for (int i = 0; i <= common_prefix; i++)
        {
            common_left = min(common_left, sorted_diff[i].second);
            common_right = max(common_right, sorted_diff[i].second);
        }

        long long total = 0;
        int score = 0;

        vector<pair<int, int>> free_nodes;
        for (int i = 0; i < path_xy_size; i++)
        {
            int node = path_xy[i];
            int typ = -1;

            if (common_left <= i && i <= common_right)
            {
                total += max(dist_from_x[node], dist_from_y[node]);
                score += 2;
                typ = kTypeBoth;
            }
            else
            {
                total += min(dist_from_x[node], dist_from_y[node]);
                score += 1;
                typ = kTypeSingle;
            }

            vector<int> component;
            DfsComponent(node, component, node_state);
            component.pop_back();

            for (int c : component)
            {
                free_nodes.push_back({c, typ});
            }
        }

        if (total > K)
            continue;
        int opt = Knapsack(free_nodes, K - total);
        ret = max(ret, opt + score);
    }

    // no common
    {
        vector<long long> sorted_dist;
        for (int i = 0; i < N; i++)
        {
            sorted_dist.push_back(dist_from_y[i]);
            sorted_dist.push_back(dist_from_x[i]);
        }
        sort(sorted_dist.begin(), sorted_dist.end());

        int score = 0;
        long long total = 0;
        for (long long d : sorted_dist)
        {
            if (total + d <= K)
            {
                score++;
                total += d;
            }
        }
        ret = max(ret, score);
    }

    return ret;
}

Subtask #0
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct

Subtask #1
0.0 / 8.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1077 ms 31516 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #2
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 300 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 368 KB Output is correct
5 Correct 1 ms 300 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 296 KB Output is correct
11 Correct 1 ms 300 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 300 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 368 KB Output is correct
5 Correct 1 ms 300 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 296 KB Output is correct
11 Correct 1 ms 300 KB Output is correct
12 Correct 1 ms 488 KB Output is correct
13 Correct 1 ms 448 KB Output is correct
14 Correct 1 ms 300 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 300 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 5 ms 4248 KB Output is correct
20 Correct 4 ms 3592 KB Output is correct
21 Correct 43 ms 1864 KB Output is correct
22 Correct 3 ms 304 KB Output is correct
23 Correct 8 ms 300 KB Output is correct
24 Correct 9 ms 396 KB Output is correct

Subtask #4
0.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 300 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 368 KB Output is correct
5 Correct 1 ms 300 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 296 KB Output is correct
11 Correct 1 ms 300 KB Output is correct
12 Correct 1 ms 488 KB Output is correct
13 Correct 1 ms 448 KB Output is correct
14 Correct 1 ms 300 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 300 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 5 ms 4248 KB Output is correct
20 Correct 4 ms 3592 KB Output is correct
21 Correct 43 ms 1864 KB Output is correct
22 Correct 3 ms 304 KB Output is correct
23 Correct 8 ms 300 KB Output is correct
24 Correct 9 ms 396 KB Output is correct
25 Correct 5 ms 436 KB Output is correct
26 Correct 241 ms 141612 KB Output is correct
27 Correct 139 ms 122480 KB Output is correct
28 Correct 239 ms 904 KB Output is correct
29 Execution timed out 1081 ms 18512 KB Time limit exceeded
30 Halted 0 ms 0 KB -

Subtask #5
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 300 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 368 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 0 ms 212 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 0 ms 304 KB Output is correct
22 Correct 1 ms 300 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct

Subtask #6
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 300 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 368 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 296 KB Output is correct
12 Correct 1 ms 300 KB Output is correct
13 Correct 1 ms 488 KB Output is correct
14 Correct 1 ms 448 KB Output is correct
15 Correct 1 ms 300 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 300 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 0 ms 212 KB Output is correct
27 Correct 0 ms 212 KB Output is correct
28 Correct 0 ms 212 KB Output is correct
29 Correct 0 ms 212 KB Output is correct
30 Correct 0 ms 212 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 0 ms 304 KB Output is correct
34 Correct 1 ms 300 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 0 ms 212 KB Output is correct
37 Correct 0 ms 212 KB Output is correct
38 Correct 1 ms 212 KB Output is correct
39 Correct 1 ms 444 KB Output is correct
40 Correct 1 ms 340 KB Output is correct
41 Correct 1 ms 440 KB Output is correct
42 Correct 0 ms 212 KB Output is correct
43 Correct 1 ms 212 KB Output is correct
44 Correct 1 ms 340 KB Output is correct
45 Correct 1 ms 256 KB Output is correct
46 Correct 1 ms 340 KB Output is correct
47 Correct 2 ms 444 KB Output is correct
48 Correct 1 ms 340 KB Output is correct
49 Correct 1 ms 340 KB Output is correct
50 Correct 0 ms 212 KB Output is correct

Subtask #7
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 300 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 368 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 296 KB Output is correct
12 Correct 1 ms 300 KB Output is correct
13 Correct 1 ms 488 KB Output is correct
14 Correct 1 ms 448 KB Output is correct
15 Correct 1 ms 300 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 300 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 5 ms 4248 KB Output is correct
21 Correct 4 ms 3592 KB Output is correct
22 Correct 43 ms 1864 KB Output is correct
23 Correct 3 ms 304 KB Output is correct
24 Correct 8 ms 300 KB Output is correct
25 Correct 9 ms 396 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 0 ms 212 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 1 ms 340 KB Output is correct
33 Correct 0 ms 212 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 0 ms 212 KB Output is correct
36 Correct 0 ms 212 KB Output is correct
37 Correct 0 ms 212 KB Output is correct
38 Correct 1 ms 212 KB Output is correct
39 Correct 1 ms 212 KB Output is correct
40 Correct 0 ms 304 KB Output is correct
41 Correct 1 ms 300 KB Output is correct
42 Correct 1 ms 212 KB Output is correct
43 Correct 0 ms 212 KB Output is correct
44 Correct 0 ms 212 KB Output is correct
45 Correct 1 ms 212 KB Output is correct
46 Correct 1 ms 444 KB Output is correct
47 Correct 1 ms 340 KB Output is correct
48 Correct 1 ms 440 KB Output is correct
49 Correct 0 ms 212 KB Output is correct
50 Correct 1 ms 212 KB Output is correct
51 Correct 1 ms 340 KB Output is correct
52 Correct 1 ms 256 KB Output is correct
53 Correct 1 ms 340 KB Output is correct
54 Correct 2 ms 444 KB Output is correct
55 Correct 1 ms 340 KB Output is correct
56 Correct 1 ms 340 KB Output is correct
57 Correct 0 ms 212 KB Output is correct
58 Correct 1 ms 340 KB Output is correct
59 Correct 2 ms 340 KB Output is correct
60 Correct 4 ms 468 KB Output is correct
61 Correct 8 ms 552 KB Output is correct
62 Correct 10 ms 896 KB Output is correct
63 Correct 6 ms 4288 KB Output is correct
64 Correct 22 ms 3660 KB Output is correct
65 Correct 44 ms 3072 KB Output is correct
66 Correct 4 ms 3804 KB Output is correct
67 Correct 1 ms 340 KB Output is correct
68 Correct 9 ms 304 KB Output is correct
69 Correct 37 ms 564 KB Output is correct
70 Correct 2 ms 340 KB Output is correct
71 Correct 4 ms 300 KB Output is correct
72 Correct 32 ms 3888 KB Output is correct
73 Correct 6 ms 2720 KB Output is correct
74 Correct 4 ms 2972 KB Output is correct
75 Correct 2 ms 468 KB Output is correct

Subtask #8
0.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 300 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 368 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 296 KB Output is correct
12 Correct 1 ms 300 KB Output is correct
13 Correct 1 ms 488 KB Output is correct
14 Correct 1 ms 448 KB Output is correct
15 Correct 1 ms 300 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 300 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 5 ms 4248 KB Output is correct
21 Correct 4 ms 3592 KB Output is correct
22 Correct 43 ms 1864 KB Output is correct
23 Correct 3 ms 304 KB Output is correct
24 Correct 8 ms 300 KB Output is correct
25 Correct 9 ms 396 KB Output is correct
26 Correct 5 ms 436 KB Output is correct
27 Correct 241 ms 141612 KB Output is correct
28 Correct 139 ms 122480 KB Output is correct
29 Correct 239 ms 904 KB Output is correct
30 Execution timed out 1081 ms 18512 KB Time limit exceeded
31 Halted 0 ms 0 KB -

Subtask #9
0.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 300 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 368 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 296 KB Output is correct
12 Correct 1 ms 300 KB Output is correct
13 Correct 1 ms 488 KB Output is correct
14 Correct 1 ms 448 KB Output is correct
15 Correct 1 ms 300 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 300 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 5 ms 4248 KB Output is correct
21 Correct 4 ms 3592 KB Output is correct
22 Correct 43 ms 1864 KB Output is correct
23 Correct 3 ms 304 KB Output is correct
24 Correct 8 ms 300 KB Output is correct
25 Correct 9 ms 396 KB Output is correct
26 Correct 5 ms 436 KB Output is correct
27 Correct 241 ms 141612 KB Output is correct
28 Correct 139 ms 122480 KB Output is correct
29 Correct 239 ms 904 KB Output is correct
30 Execution timed out 1081 ms 18512 KB Time limit exceeded
31 Halted 0 ms 0 KB -