oj.uz

Submission #966317

# Submission time Handle Problem Language Result Execution time Memory
966317 2024-04-19T17:17:12 Z eysbutno Hard route (IZhO17_road) C++17
100 / 100
 787 ms 133488 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);
    auto dfs = [&](int u, int p, auto&& dfs) -> void {
		/**
         * 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, dfs);
            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, dfs);

    ll max_hardness = 0, hardest_path_count = 1;
    auto dfs2 = [&](int u, int p, ll parDist, ll parCnt, 
                    auto&& dfs2) -> void {
		/**
         * 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) :
                            	            dfs2(v, u, longest1, count1 - path_count[v], dfs2);
            } else {
                dfs2(v, u, longest1, count1, dfs2);
            }
        }
    }; dfs2(0, -1, 0, 1, dfs2);
    cout << max_hardness << ' ' << hardest_path_count << '\n';
}

Subtask #1
19.0 / 19.0

# 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 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 344 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 0 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 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 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 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 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 344 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 0 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 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 3 ms 856 KB Output is correct
26 Correct 3 ms 1116 KB Output is correct
27 Correct 4 ms 1116 KB Output is correct
28 Correct 3 ms 1116 KB Output is correct
29 Correct 4 ms 1112 KB Output is correct
30 Correct 4 ms 1116 KB Output is correct
31 Correct 3 ms 1116 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 4 ms 1112 KB Output is correct
34 Correct 4 ms 1216 KB Output is correct
35 Correct 3 ms 1116 KB Output is correct
36 Correct 3 ms 1116 KB Output is correct
37 Correct 4 ms 1116 KB Output is correct
38 Correct 4 ms 1628 KB Output is correct
39 Correct 4 ms 860 KB Output is correct
40 Correct 3 ms 860 KB Output is correct
41 Correct 3 ms 600 KB Output is correct
42 Correct 3 ms 604 KB Output is correct
43 Correct 3 ms 604 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 604 KB Output is correct
48 Correct 3 ms 916 KB Output is correct

Subtask #3
48.0 / 48.0

# 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 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 344 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 0 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 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 3 ms 856 KB Output is correct
26 Correct 3 ms 1116 KB Output is correct
27 Correct 4 ms 1116 KB Output is correct
28 Correct 3 ms 1116 KB Output is correct
29 Correct 4 ms 1112 KB Output is correct
30 Correct 4 ms 1116 KB Output is correct
31 Correct 3 ms 1116 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 4 ms 1112 KB Output is correct
34 Correct 4 ms 1216 KB Output is correct
35 Correct 3 ms 1116 KB Output is correct
36 Correct 3 ms 1116 KB Output is correct
37 Correct 4 ms 1116 KB Output is correct
38 Correct 4 ms 1628 KB Output is correct
39 Correct 4 ms 860 KB Output is correct
40 Correct 3 ms 860 KB Output is correct
41 Correct 3 ms 600 KB Output is correct
42 Correct 3 ms 604 KB Output is correct
43 Correct 3 ms 604 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 604 KB Output is correct
48 Correct 3 ms 916 KB Output is correct
49 Correct 570 ms 69936 KB Output is correct
50 Correct 514 ms 76788 KB Output is correct
51 Correct 543 ms 82904 KB Output is correct
52 Correct 554 ms 61292 KB Output is correct
53 Correct 539 ms 79348 KB Output is correct
54 Correct 465 ms 87104 KB Output is correct
55 Correct 471 ms 68192 KB Output is correct
56 Correct 496 ms 76412 KB Output is correct
57 Correct 560 ms 87284 KB Output is correct
58 Correct 540 ms 79248 KB Output is correct
59 Correct 522 ms 79188 KB Output is correct
60 Correct 562 ms 75324 KB Output is correct
61 Correct 787 ms 133488 KB Output is correct
62 Correct 760 ms 114688 KB Output is correct
63 Correct 715 ms 61108 KB Output is correct
64 Correct 760 ms 48152 KB Output is correct
65 Correct 693 ms 39760 KB Output is correct
66 Correct 719 ms 35468 KB Output is correct
67 Correct 655 ms 33216 KB Output is correct
68 Correct 713 ms 32608 KB Output is correct
69 Correct 669 ms 32076 KB Output is correct
70 Correct 653 ms 31568 KB Output is correct
71 Correct 630 ms 31728 KB Output is correct
72 Correct 644 ms 31740 KB Output is correct
73 Correct 642 ms 32084 KB Output is correct
74 Correct 658 ms 32460 KB Output is correct
75 Correct 668 ms 33104 KB Output is correct
76 Correct 601 ms 34084 KB Output is correct
77 Correct 529 ms 38164 KB Output is correct
78 Correct 405 ms 43844 KB Output is correct