oj.uz

Submission #966365

# Submission time Handle Problem Language Result Execution time Memory
966365 2024-04-19T18:19:08 Z eysbutno Hard route (IZhO17_road) C++17
100 / 100
 769 ms 175940 KB 
/**
 * Assume there is some hard route that goes from vertex
 * u to vertex v. Let the node that the path from u to v and the
 * furthest node from the hard route meet be node x. Use rerooting
 * DP to calculate the hardest route and the # of such hardest routes
 * for every node x.
 * 
 * Time Complexity: O(n log(n))
*/
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
    int n; 
    cin >> n;
    vector<vector<int>> adj(n);
    for (int i = 1; i < n; i++) {
        int x, y; 
        cin >> x >> y;
        --x, --y;
        adj[x].push_back(y);
        adj[y].push_back(x);
    }

    vector<int> max_length(n), path_count(n);
    function<void(int, int)> dfs = [&](int u, int p) {
		/**
         * Calculates the longest path from vertex u,
         * and the number of such paths.
        */
        max_length[u] = 0;
        path_count[u] = 1;
        for (int v : adj[u]) if (v != p) {
            dfs(v, u);
            if (max_length[u] < max_length[v] + 1) {
                max_length[u] = max_length[v] + 1;
                path_count[u] = path_count[v];
            } else if (max_length[v] + 1 == max_length[u]) {
                path_count[u] += path_count[v];
            }
        }
    }; 
    dfs(0, -1);

    ll max_hardness = 0, hardest_path_count = 1; 
    function<void(int, int, ll, ll)> dfs2 = [&](int u, int p, ll parDist, ll parCnt) {
		/**
         * Performs the rerooting, to count the hardest
         * path and the # of such paths at this vertex.
        */
        vector<array<ll, 2>> paths; // {distance, count}
        if (u > 0 || (int) adj[u].size() == 1) {
            paths.push_back({parDist, parCnt});
        }
        for (int v : adj[u]) if (v != p) {
            paths.push_back({max_length[v] + 1, path_count[v]});
        }
        sort(paths.begin(), paths.end(), greater<>());
        if ((int) adj[u].size() >= 3) { // can form a nonzero hard route
            /**
             * Let the 3 longest path lengths be a, b, c, with a > b > c.
             * The optimal hard route "hardness" is a * (b + c).
            */
            ll a = paths[0][0], b = paths[1][0], c = paths[2][0];
            ll cur = a * (b + c), num = 0, ties = 0;
            for (auto [k, v] : paths) {
                if (k == c) ties += v;
            }

            if (a != b && b != c) {
                // case 1: all are distinct.
                num = paths[1][1] * ties;
            } else if (a == b && b == c) {
                // case 2: all are the same.
                num = ties * ties;
				for (auto [k, v] : paths) {
					if (k == a) num -= v * v;
				}
				num /= 2; // avoiding double counting
            } else if (a == b) {
                // case 3: first two are the same.
                num = (paths[0][1] + paths[1][1]) * ties;
            } else {
                // case 4: last two are the same.
               	num = ties * ties;
				for (auto [k, v] : paths) {
					if (k == c) num -= v * v;
				}
				num /= 2; // avoiding double counting
            }
            if (max_hardness < cur) {
                max_hardness = cur;
                hardest_path_count = num;
            } else if (max_hardness == cur) {
                hardest_path_count += num;
            }
        }
        // processing parent dist and parent count.
        ll longest1 = 0;
        ll longest2 = 0;
        ll count1 = 0;
        ll count2 = 0;
        for (auto [k, v] : paths) {
            if (k + 1 > longest1) {
                swap(longest1, longest2);
                swap(count1, count2);
                longest1 = k + 1, count1 = v;
            } else if (k + 1 == longest1) {
                count1 += v;
            } else if (k + 1 > longest2) {
                longest2 = k + 1, count2 = v;
            } else if (k + 1 == longest2) {
                count2 += v;
            }
        }
        for (int v : adj[u]) if (v != p) {
            // using the best parent hardness and parent count possible.
            if (max_length[v] + 2 == longest1) {
                (path_count[v] == count1) ? dfs2(v, u, longest2, count2) :
                            	            dfs2(v, u, longest1, count1 - path_count[v]);
            } else {
                dfs2(v, u, longest1, count1);
            }
        }
    }; 
    dfs2(0, -1, 0, 1);
    
    cout << max_hardness << ' ' << hardest_path_count << '\n';
}

Subtask #1
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 344 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 436 KB Output is correct
20 Correct 1 ms 436 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 1 ms 344 KB Output is correct
24 Correct 0 ms 348 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 344 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 436 KB Output is correct
20 Correct 1 ms 436 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 1 ms 344 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 3 ms 1116 KB Output is correct
26 Correct 4 ms 1372 KB Output is correct
27 Correct 3 ms 1372 KB Output is correct
28 Correct 4 ms 1372 KB Output is correct
29 Correct 4 ms 1372 KB Output is correct
30 Correct 4 ms 1448 KB Output is correct
31 Correct 4 ms 1372 KB Output is correct
32 Correct 3 ms 1260 KB Output is correct
33 Correct 4 ms 1368 KB Output is correct
34 Correct 4 ms 1540 KB Output is correct
35 Correct 3 ms 1412 KB Output is correct
36 Correct 3 ms 1372 KB Output is correct
37 Correct 4 ms 1372 KB Output is correct
38 Correct 4 ms 2088 KB Output is correct
39 Correct 4 ms 1212 KB Output is correct
40 Correct 3 ms 860 KB Output is correct
41 Correct 4 ms 704 KB Output is correct
42 Correct 3 ms 760 KB Output is correct
43 Correct 3 ms 856 KB Output is correct
44 Correct 3 ms 604 KB Output is correct
45 Correct 3 ms 604 KB Output is correct
46 Correct 3 ms 604 KB Output is correct
47 Correct 3 ms 896 KB Output is correct
48 Correct 3 ms 928 KB Output is correct

Subtask #3
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 344 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 436 KB Output is correct
20 Correct 1 ms 436 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 1 ms 344 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 3 ms 1116 KB Output is correct
26 Correct 4 ms 1372 KB Output is correct
27 Correct 3 ms 1372 KB Output is correct
28 Correct 4 ms 1372 KB Output is correct
29 Correct 4 ms 1372 KB Output is correct
30 Correct 4 ms 1448 KB Output is correct
31 Correct 4 ms 1372 KB Output is correct
32 Correct 3 ms 1260 KB Output is correct
33 Correct 4 ms 1368 KB Output is correct
34 Correct 4 ms 1540 KB Output is correct
35 Correct 3 ms 1412 KB Output is correct
36 Correct 3 ms 1372 KB Output is correct
37 Correct 4 ms 1372 KB Output is correct
38 Correct 4 ms 2088 KB Output is correct
39 Correct 4 ms 1212 KB Output is correct
40 Correct 3 ms 860 KB Output is correct
41 Correct 4 ms 704 KB Output is correct
42 Correct 3 ms 760 KB Output is correct
43 Correct 3 ms 856 KB Output is correct
44 Correct 3 ms 604 KB Output is correct
45 Correct 3 ms 604 KB Output is correct
46 Correct 3 ms 604 KB Output is correct
47 Correct 3 ms 896 KB Output is correct
48 Correct 3 ms 928 KB Output is correct
49 Correct 558 ms 88064 KB Output is correct
50 Correct 564 ms 97716 KB Output is correct
51 Correct 632 ms 106320 KB Output is correct
52 Correct 546 ms 76456 KB Output is correct
53 Correct 535 ms 99244 KB Output is correct
54 Correct 505 ms 109392 KB Output is correct
55 Correct 518 ms 84048 KB Output is correct
56 Correct 481 ms 95060 KB Output is correct
57 Correct 520 ms 112364 KB Output is correct
58 Correct 511 ms 101204 KB Output is correct
59 Correct 530 ms 101224 KB Output is correct
60 Correct 571 ms 95840 KB Output is correct
61 Correct 769 ms 175940 KB Output is correct
62 Correct 759 ms 150324 KB Output is correct
63 Correct 723 ms 75856 KB Output is correct
64 Correct 722 ms 58184 KB Output is correct
65 Correct 731 ms 46908 KB Output is correct
66 Correct 649 ms 41236 KB Output is correct
67 Correct 639 ms 37576 KB Output is correct
68 Correct 666 ms 36692 KB Output is correct
69 Correct 627 ms 35928 KB Output is correct
70 Correct 633 ms 35484 KB Output is correct
71 Correct 602 ms 35532 KB Output is correct
72 Correct 643 ms 35736 KB Output is correct
73 Correct 649 ms 36060 KB Output is correct
74 Correct 603 ms 36300 KB Output is correct
75 Correct 666 ms 36928 KB Output is correct
76 Correct 587 ms 38224 KB Output is correct
77 Correct 595 ms 41284 KB Output is correct
78 Correct 413 ms 47308 KB Output is correct