oj.uz

Submission #976684

# Submission time Handle Problem Language Result Execution time Memory
976684 2024-05-07T02:48:52 Z josanneo22 Road Closures (APIO21_roads) C++17
36 / 100
 363 ms 7628 KB 
#include "roads.h"

#include <vector>

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
#define vi vector<int>
vector<i64> N2(int N, vi U, vi V, vi W) {
    vector<vector<pair<int, int>>> G(N);
    for (int i = 0; i < N - 1; i++) {
        G[U[i]].push_back(make_pair(V[i], W[i]));
        G[V[i]].push_back(make_pair(U[i], W[i]));
    }
    auto solve = [&](int k) {
        // cout << k << '\n';
        vector<vector<i64>> dp(N, vector<i64>(2, 100000));
        function<void(int, int)> dfs = [&](int u, int f) {
            // cout << "tree : " << u << ' ' << f << '\n';
            // if (G[u].size() < k) {
            //     dp[u][0] = dp[u][1] = 0;
            // }
            i64 sum = 0;
            vector<i64> wait; 
            for (auto & v : G[u]) {
                if (v.first == f) continue;
                dfs(v.first, u);
                wait.push_back(-dp[v.first][1] + dp[v.first][0] + v.second);
                sum += dp[v.first][0] + v.second;
                // cout << v.first << ' ' << dp[v.first][0] + v.second << ' ' << dp[v.first][1] << '\n';
            }
            // cout << "total: " << sum << '\n';
            sort(wait.begin(), wait.end(), greater<i64>());
            // cout << "wait : ";
            // for (auto & v : wait) cout << v << ' ';
            //     cout << '\n';
            int deg = G[u].size();
            int remain = deg - max(deg - k - 1, 0);
            // cout << "remain: " << remain << '\n';
            i64 res = sum, S = sum;
            for (int i = 0; i < min(remain, (int)wait.size()); i++) {
                S -= wait[i];
                res = min(res, S);
            }
            dp[u][0] = res;
            remain = deg - max(deg - k, 0);
            res = sum; S = sum;
            // cout << "remain: " << remain << '\n';
            // cout << "sums : ";
            for (int i = 0; i < min(remain, (int)wait.size()); i++) {
                S -= wait[i];
                res = min(res, S);
            }
            // cout << '\n';
            dp[u][1] = res;
            // cout << "++++++++++++++\n";
        };  
        dfs(0, -1);
        // for (int i = 0; i < N; i++) {
        //     cout << "dp : " << i << ' ' << dp[i][0] << ' ' << dp[i][1] << '\n';
        // }
        return dp[0][0];
    };  
    vector<i64> ans(N);
    for (int k = 0; k < N; k++) { 
        ans[k] = solve(k - 1);
    }
    return ans;
}
vector<i64> juhua(int N, vi U, vi V, vi W) {
    vector<i64> ans(N);
    ans[0] = accumulate(W.begin(), W.end(), 0LL);
    sort(W.begin(), W.end(), greater<int>());
    for (int i = 1; i < N; i++) {
        ans[i] = ans[i - 1] - W[i - 1];
    }
    return ans;
}
vector<i64> chain(int N, vi U, vi V, vi W) {
    vector<i64> ans(N);
    ans[0] = accumulate(W.begin(), W.end(), 0LL);
    vector<i64> dp(N);
    for (int i = 0; i < N - 1; i++) {
        i64 take = (i == 0 ? 0 : dp[i - 1]) + W[i];
        i64 dun_take = (i - 2 < 0 ? 0 : dp[i - 2]) + (i - 1 < 0 ? 0 : W[i - 1]);
        dp[i] = min(take, dun_take);
    }
    ans[1] = dp[N - 2];
    return ans;
}
vector<i64> minimum_closure_costs(int N, vi U, vi V, vi W) {
    if (N <= 5000) return N2(N, U, V, W);
    if (count(U.begin(), U.end(), 0) == N - 1) return juhua(N, U, V, W);
    return chain(N, U, V, W);
}

/*
ST1: 菊花图
直接一个一个贪心移除

ST2: 链
我们可以直接dp, 从i - 1/i - 2转移过来

ST3 & 4:
对于每个K, 我们可以单独solve
就是说如果我们让dp[i] = 整个i的子树里最小价格满足, deg[i] <= k
发现到其实这样的存储方式不足以满足dp转移方式
dp[u][0/1] = 和父亲节点是否有边
    如果我们拿这个边那么我们会得到dp[v][1]
    如果我们不要这个边我们得到dp[v][0] + W[i]
        如果我们现在和父亲节点连边: 需要移除min(deg[u] - k, 0)
                   没和父亲连边： 需要移除min(deg[u] - k - 1, 0)
                   那么我们可以拿的边 = deg[u] - 移除
    我们先把dp[v][1] - (dp[v][0] + W[i])排序， ans = sum(dp[v][0] + W[i])
    然后我们降序排序然后直接贪心取

O(N ^ 2) 24分

若W[i] = 1, 就是说我们只是求最少移除多少遍使得
max deg <= k 
erm....
有没有可能是贪心？
    猜测: 如果现在这个边的deg > k, 移除是最优的
    然后就是贪心

*/

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 299 ms 792 KB Output is correct
3 Correct 323 ms 852 KB Output is correct
4 Correct 213 ms 604 KB Output is correct
5 Correct 1 ms 344 KB Output is correct
6 Correct 3 ms 348 KB Output is correct
7 Correct 3 ms 472 KB Output is correct
8 Correct 158 ms 724 KB Output is correct
9 Correct 247 ms 776 KB Output is correct
10 Correct 3 ms 344 KB Output is correct
11 Correct 3 ms 348 KB Output is correct
12 Correct 19 ms 3636 KB Output is correct
13 Correct 34 ms 5568 KB Output is correct
14 Correct 35 ms 5724 KB Output is correct
15 Correct 41 ms 6324 KB Output is correct
16 Correct 40 ms 6484 KB Output is correct
17 Correct 35 ms 6480 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 27 ms 5200 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 28 ms 6280 KB Output is correct
3 Correct 33 ms 7028 KB Output is correct
4 Correct 33 ms 7512 KB Output is correct
5 Correct 34 ms 7628 KB Output is correct
6 Correct 210 ms 860 KB Output is correct
7 Correct 284 ms 1020 KB Output is correct
8 Correct 221 ms 856 KB Output is correct
9 Correct 3 ms 348 KB Output is correct
10 Correct 3 ms 348 KB Output is correct
11 Correct 3 ms 348 KB Output is correct
12 Correct 18 ms 4204 KB Output is correct
13 Correct 33 ms 6748 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 27 ms 5968 KB Output is correct
16 Correct 30 ms 6744 KB Output is correct

Subtask #3
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 352 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 3 ms 352 KB Output is correct
5 Correct 4 ms 348 KB Output is correct
6 Correct 3 ms 416 KB Output is correct
7 Correct 3 ms 352 KB Output is correct
8 Correct 3 ms 344 KB Output is correct
9 Correct 3 ms 348 KB Output is correct
10 Correct 3 ms 352 KB Output is correct
11 Correct 3 ms 604 KB Output is correct
12 Correct 3 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 3 ms 384 KB Output is correct
15 Correct 3 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 4 ms 348 KB Output is correct
18 Correct 4 ms 348 KB Output is correct
19 Correct 2 ms 344 KB Output is correct
20 Correct 3 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 352 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 3 ms 352 KB Output is correct
5 Correct 4 ms 348 KB Output is correct
6 Correct 3 ms 416 KB Output is correct
7 Correct 3 ms 352 KB Output is correct
8 Correct 3 ms 344 KB Output is correct
9 Correct 3 ms 348 KB Output is correct
10 Correct 3 ms 352 KB Output is correct
11 Correct 3 ms 604 KB Output is correct
12 Correct 3 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 3 ms 384 KB Output is correct
15 Correct 3 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 4 ms 348 KB Output is correct
18 Correct 4 ms 348 KB Output is correct
19 Correct 2 ms 344 KB Output is correct
20 Correct 3 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 1 ms 600 KB Output is correct
23 Correct 130 ms 636 KB Output is correct
24 Correct 363 ms 784 KB Output is correct
25 Correct 260 ms 604 KB Output is correct
26 Correct 296 ms 600 KB Output is correct
27 Correct 289 ms 812 KB Output is correct
28 Correct 219 ms 780 KB Output is correct
29 Correct 295 ms 608 KB Output is correct
30 Correct 250 ms 852 KB Output is correct
31 Correct 261 ms 780 KB Output is correct
32 Correct 222 ms 792 KB Output is correct
33 Correct 230 ms 916 KB Output is correct
34 Correct 270 ms 856 KB Output is correct
35 Correct 219 ms 860 KB Output is correct
36 Correct 275 ms 780 KB Output is correct
37 Correct 318 ms 796 KB Output is correct
38 Correct 210 ms 1048 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 2 ms 348 KB Output is correct
42 Correct 4 ms 600 KB Output is correct
43 Correct 3 ms 348 KB Output is correct
44 Correct 4 ms 344 KB Output is correct
45 Correct 5 ms 604 KB Output is correct
46 Correct 5 ms 468 KB Output is correct
47 Correct 2 ms 440 KB Output is correct
48 Correct 3 ms 348 KB Output is correct
49 Correct 3 ms 348 KB Output is correct
50 Correct 2 ms 348 KB Output is correct
51 Correct 3 ms 468 KB Output is correct
52 Correct 3 ms 348 KB Output is correct
53 Correct 207 ms 684 KB Output is correct
54 Correct 358 ms 760 KB Output is correct
55 Correct 241 ms 788 KB Output is correct
56 Correct 158 ms 724 KB Output is correct
57 Correct 235 ms 604 KB Output is correct
58 Correct 1 ms 760 KB Output is correct
59 Correct 4 ms 344 KB Output is correct
60 Correct 3 ms 344 KB Output is correct
61 Correct 2 ms 348 KB Output is correct
62 Correct 3 ms 472 KB Output is correct
63 Correct 1 ms 348 KB Output is correct
64 Correct 344 ms 756 KB Output is correct
65 Correct 348 ms 604 KB Output is correct
66 Correct 238 ms 768 KB Output is correct
67 Correct 222 ms 772 KB Output is correct
68 Correct 229 ms 604 KB Output is correct

Subtask #5
0 / 17.0

# Verdict Execution time Memory Grader output
1 Incorrect 32 ms 6748 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #6
0 / 25.0

# Verdict Execution time Memory Grader output
1 Incorrect 32 ms 6748 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #7
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 299 ms 792 KB Output is correct
3 Correct 323 ms 852 KB Output is correct
4 Correct 213 ms 604 KB Output is correct
5 Correct 1 ms 344 KB Output is correct
6 Correct 3 ms 348 KB Output is correct
7 Correct 3 ms 472 KB Output is correct
8 Correct 158 ms 724 KB Output is correct
9 Correct 247 ms 776 KB Output is correct
10 Correct 3 ms 344 KB Output is correct
11 Correct 3 ms 348 KB Output is correct
12 Correct 19 ms 3636 KB Output is correct
13 Correct 34 ms 5568 KB Output is correct
14 Correct 35 ms 5724 KB Output is correct
15 Correct 41 ms 6324 KB Output is correct
16 Correct 40 ms 6484 KB Output is correct
17 Correct 35 ms 6480 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 27 ms 5200 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 28 ms 6280 KB Output is correct
22 Correct 33 ms 7028 KB Output is correct
23 Correct 33 ms 7512 KB Output is correct
24 Correct 34 ms 7628 KB Output is correct
25 Correct 210 ms 860 KB Output is correct
26 Correct 284 ms 1020 KB Output is correct
27 Correct 221 ms 856 KB Output is correct
28 Correct 3 ms 348 KB Output is correct
29 Correct 3 ms 348 KB Output is correct
30 Correct 3 ms 348 KB Output is correct
31 Correct 18 ms 4204 KB Output is correct
32 Correct 33 ms 6748 KB Output is correct
33 Correct 0 ms 344 KB Output is correct
34 Correct 27 ms 5968 KB Output is correct
35 Correct 30 ms 6744 KB Output is correct
36 Correct 0 ms 352 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 3 ms 352 KB Output is correct
40 Correct 4 ms 348 KB Output is correct
41 Correct 3 ms 416 KB Output is correct
42 Correct 3 ms 352 KB Output is correct
43 Correct 3 ms 344 KB Output is correct
44 Correct 3 ms 348 KB Output is correct
45 Correct 3 ms 352 KB Output is correct
46 Correct 3 ms 604 KB Output is correct
47 Correct 3 ms 348 KB Output is correct
48 Correct 1 ms 348 KB Output is correct
49 Correct 3 ms 384 KB Output is correct
50 Correct 3 ms 348 KB Output is correct
51 Correct 1 ms 348 KB Output is correct
52 Correct 4 ms 348 KB Output is correct
53 Correct 4 ms 348 KB Output is correct
54 Correct 2 ms 344 KB Output is correct
55 Correct 3 ms 348 KB Output is correct
56 Correct 0 ms 348 KB Output is correct
57 Correct 1 ms 600 KB Output is correct
58 Correct 130 ms 636 KB Output is correct
59 Correct 363 ms 784 KB Output is correct
60 Correct 260 ms 604 KB Output is correct
61 Correct 296 ms 600 KB Output is correct
62 Correct 289 ms 812 KB Output is correct
63 Correct 219 ms 780 KB Output is correct
64 Correct 295 ms 608 KB Output is correct
65 Correct 250 ms 852 KB Output is correct
66 Correct 261 ms 780 KB Output is correct
67 Correct 222 ms 792 KB Output is correct
68 Correct 230 ms 916 KB Output is correct
69 Correct 270 ms 856 KB Output is correct
70 Correct 219 ms 860 KB Output is correct
71 Correct 275 ms 780 KB Output is correct
72 Correct 318 ms 796 KB Output is correct
73 Correct 210 ms 1048 KB Output is correct
74 Correct 0 ms 348 KB Output is correct
75 Correct 0 ms 348 KB Output is correct
76 Correct 2 ms 348 KB Output is correct
77 Correct 4 ms 600 KB Output is correct
78 Correct 3 ms 348 KB Output is correct
79 Correct 4 ms 344 KB Output is correct
80 Correct 5 ms 604 KB Output is correct
81 Correct 5 ms 468 KB Output is correct
82 Correct 2 ms 440 KB Output is correct
83 Correct 3 ms 348 KB Output is correct
84 Correct 3 ms 348 KB Output is correct
85 Correct 2 ms 348 KB Output is correct
86 Correct 3 ms 468 KB Output is correct
87 Correct 3 ms 348 KB Output is correct
88 Correct 207 ms 684 KB Output is correct
89 Correct 358 ms 760 KB Output is correct
90 Correct 241 ms 788 KB Output is correct
91 Correct 158 ms 724 KB Output is correct
92 Correct 235 ms 604 KB Output is correct
93 Correct 1 ms 760 KB Output is correct
94 Correct 4 ms 344 KB Output is correct
95 Correct 3 ms 344 KB Output is correct
96 Correct 2 ms 348 KB Output is correct
97 Correct 3 ms 472 KB Output is correct
98 Correct 1 ms 348 KB Output is correct
99 Correct 344 ms 756 KB Output is correct
100 Correct 348 ms 604 KB Output is correct
101 Correct 238 ms 768 KB Output is correct
102 Correct 222 ms 772 KB Output is correct
103 Correct 229 ms 604 KB Output is correct
104 Incorrect 32 ms 6748 KB Output isn't correct
105 Halted 0 ms 0 KB -