oj.uz

Submission #965661

# Submission time Handle Problem Language Result Execution time Memory
965661 2024-04-19T04:21:50 Z eysbutno Hard route (IZhO17_road) C++17
100 / 100
 689 ms 140196 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;
#define all(x) begin(x), end(x)
#define sz(x) (int) (x).size()

int main() {
    cin.tie(0) -> sync_with_stdio(0);
    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 hard = 0, cnt = 1;
    auto dfs2 = [&](int u, int p, int parDist, int 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 || sz(adj[u]) == 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(all(paths), greater<>());
        if (sz(adj[u]) >= 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;
            }

            // case 1: all are distinct.
            if (a != b && b != c) {
                num = paths[1][1] * ties;
            }
            // case 2: all are the same.
            else if (a == b && b == c) {
                num = ties * ties;
				for (auto [k, v] : paths) {
					if (k == a) num -= v * v;
				}
				num /= 2; // avoiding double counting
            }
            // case 3: first two are the same.
            else if (a == b) {
                num = (paths[0][1] + paths[1][1]) * ties;
            }
            // case 4: last two are the same.
            else {
               	num = ties * ties;
				for (auto [k, v] : paths) {
					if (k == c) num -= v * v;
				}
				num /= 2;
            }
            if (hard < cur) {
                hard = cur, cnt = num;
            } else if (hard == cur) {
                cnt += num;
            }
        }
        // processing parent dist and parent count.
        ll l1 = 0, l2 = 0, cnt1 = 0, cnt2 = 0;
        for (auto [k, v] : paths) {
            if (k + 1 > l1) {
                swap(l1, l2);
                swap(cnt1, cnt2);
                l1 = k + 1, cnt1 = v;
            } else if (k + 1 == l1) {
                cnt1 += v;
            } else if (k + 1 > l2) {
                l2 = k + 1, cnt2 = v;
            } else if (k + 1 == l2) {
                cnt2 += v;
            }
        }
        for (int v : adj[u]) if (v != p) {
            // using the best parent hardness and parent count possible.
            if (max_length[v] + 2 == l1) {
                (path_count[v] == cnt1) ? dfs2(v, u, l2, cnt2, dfs2) :
                            	          dfs2(v, u, l1, cnt1 - path_count[v], dfs2);
            } else {
                dfs2(v, u, l1, cnt1, dfs2);
            }
        }
    }; dfs2(0, -1, 0, 1, dfs2);
    cout << hard << ' ' << cnt << '\n';
}

Subtask #1
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 344 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 0 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 1 ms 344 KB Output is correct
12 Correct 1 ms 348 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 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 344 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 460 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 344 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 0 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 1 ms 344 KB Output is correct
12 Correct 1 ms 348 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 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 344 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 460 KB Output is correct
25 Correct 3 ms 856 KB Output is correct
26 Correct 4 ms 1116 KB Output is correct
27 Correct 2 ms 1112 KB Output is correct
28 Correct 2 ms 1116 KB Output is correct
29 Correct 2 ms 1116 KB Output is correct
30 Correct 2 ms 1116 KB Output is correct
31 Correct 3 ms 1112 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 2 ms 1112 KB Output is correct
34 Correct 2 ms 1112 KB Output is correct
35 Correct 4 ms 1116 KB Output is correct
36 Correct 2 ms 1116 KB Output is correct
37 Correct 2 ms 1372 KB Output is correct
38 Correct 4 ms 1740 KB Output is correct
39 Correct 2 ms 1116 KB Output is correct
40 Correct 3 ms 856 KB Output is correct
41 Correct 2 ms 860 KB Output is correct
42 Correct 2 ms 604 KB Output is correct
43 Correct 2 ms 604 KB Output is correct
44 Correct 2 ms 604 KB Output is correct
45 Correct 2 ms 604 KB Output is correct
46 Correct 2 ms 604 KB Output is correct
47 Correct 2 ms 848 KB Output is correct
48 Correct 3 ms 856 KB Output is correct

Subtask #3
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 344 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 0 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 1 ms 344 KB Output is correct
12 Correct 1 ms 348 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 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 344 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 460 KB Output is correct
25 Correct 3 ms 856 KB Output is correct
26 Correct 4 ms 1116 KB Output is correct
27 Correct 2 ms 1112 KB Output is correct
28 Correct 2 ms 1116 KB Output is correct
29 Correct 2 ms 1116 KB Output is correct
30 Correct 2 ms 1116 KB Output is correct
31 Correct 3 ms 1112 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 2 ms 1112 KB Output is correct
34 Correct 2 ms 1112 KB Output is correct
35 Correct 4 ms 1116 KB Output is correct
36 Correct 2 ms 1116 KB Output is correct
37 Correct 2 ms 1372 KB Output is correct
38 Correct 4 ms 1740 KB Output is correct
39 Correct 2 ms 1116 KB Output is correct
40 Correct 3 ms 856 KB Output is correct
41 Correct 2 ms 860 KB Output is correct
42 Correct 2 ms 604 KB Output is correct
43 Correct 2 ms 604 KB Output is correct
44 Correct 2 ms 604 KB Output is correct
45 Correct 2 ms 604 KB Output is correct
46 Correct 2 ms 604 KB Output is correct
47 Correct 2 ms 848 KB Output is correct
48 Correct 3 ms 856 KB Output is correct
49 Correct 412 ms 76872 KB Output is correct
50 Correct 385 ms 84100 KB Output is correct
51 Correct 364 ms 89936 KB Output is correct
52 Correct 372 ms 68688 KB Output is correct
53 Correct 333 ms 86496 KB Output is correct
54 Correct 331 ms 94032 KB Output is correct
55 Correct 324 ms 75096 KB Output is correct
56 Correct 414 ms 83416 KB Output is correct
57 Correct 371 ms 94292 KB Output is correct
58 Correct 351 ms 86340 KB Output is correct
59 Correct 330 ms 86324 KB Output is correct
60 Correct 341 ms 82544 KB Output is correct
61 Correct 689 ms 140196 KB Output is correct
62 Correct 634 ms 121616 KB Output is correct
63 Correct 538 ms 68044 KB Output is correct
64 Correct 573 ms 55124 KB Output is correct
65 Correct 543 ms 46972 KB Output is correct
66 Correct 572 ms 42808 KB Output is correct
67 Correct 522 ms 40424 KB Output is correct
68 Correct 504 ms 39356 KB Output is correct
69 Correct 538 ms 39232 KB Output is correct
70 Correct 557 ms 38928 KB Output is correct
71 Correct 551 ms 38768 KB Output is correct
72 Correct 524 ms 39144 KB Output is correct
73 Correct 485 ms 39224 KB Output is correct
74 Correct 462 ms 39544 KB Output is correct
75 Correct 557 ms 40400 KB Output is correct
76 Correct 480 ms 41288 KB Output is correct
77 Correct 372 ms 43760 KB Output is correct
78 Correct 245 ms 49216 KB Output is correct