oj.uz

Submission #966309

# Submission time Handle Problem Language Result Execution time Memory
966309 2024-04-19T16:46:49 Z eysbutno Hard route (IZhO17_road) C++17
100 / 100
 608 ms 140388 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() {
    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, 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;
            }

            // 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 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 1 ms 600 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 376 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 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 0 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 1 ms 344 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 0 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 0 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 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 1 ms 600 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 376 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 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 0 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 1 ms 344 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 0 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 0 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 2 ms 1368 KB Output is correct
26 Correct 2 ms 1116 KB Output is correct
27 Correct 2 ms 1116 KB Output is correct
28 Correct 2 ms 1112 KB Output is correct
29 Correct 2 ms 1116 KB Output is correct
30 Correct 2 ms 1116 KB Output is correct
31 Correct 2 ms 1116 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 2 ms 1116 KB Output is correct
34 Correct 2 ms 1116 KB Output is correct
35 Correct 2 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 3 ms 1780 KB Output is correct
39 Correct 2 ms 1116 KB Output is correct
40 Correct 2 ms 860 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 860 KB Output is correct
48 Correct 2 ms 860 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 1 ms 600 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 376 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 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 0 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 1 ms 344 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 0 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 0 ms 348 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 2 ms 1368 KB Output is correct
26 Correct 2 ms 1116 KB Output is correct
27 Correct 2 ms 1116 KB Output is correct
28 Correct 2 ms 1112 KB Output is correct
29 Correct 2 ms 1116 KB Output is correct
30 Correct 2 ms 1116 KB Output is correct
31 Correct 2 ms 1116 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 2 ms 1116 KB Output is correct
34 Correct 2 ms 1116 KB Output is correct
35 Correct 2 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 3 ms 1780 KB Output is correct
39 Correct 2 ms 1116 KB Output is correct
40 Correct 2 ms 860 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 860 KB Output is correct
48 Correct 2 ms 860 KB Output is correct
49 Correct 408 ms 76708 KB Output is correct
50 Correct 372 ms 83916 KB Output is correct
51 Correct 354 ms 90004 KB Output is correct
52 Correct 386 ms 68416 KB Output is correct
53 Correct 299 ms 86352 KB Output is correct
54 Correct 299 ms 94196 KB Output is correct
55 Correct 325 ms 75328 KB Output is correct
56 Correct 280 ms 83536 KB Output is correct
57 Correct 325 ms 94508 KB Output is correct
58 Correct 298 ms 86400 KB Output is correct
59 Correct 332 ms 86576 KB Output is correct
60 Correct 314 ms 82532 KB Output is correct
61 Correct 608 ms 140388 KB Output is correct
62 Correct 577 ms 121768 KB Output is correct
63 Correct 546 ms 67964 KB Output is correct
64 Correct 592 ms 55448 KB Output is correct
65 Correct 541 ms 47180 KB Output is correct
66 Correct 485 ms 42580 KB Output is correct
67 Correct 524 ms 40204 KB Output is correct
68 Correct 519 ms 39748 KB Output is correct
69 Correct 454 ms 39212 KB Output is correct
70 Correct 475 ms 38920 KB Output is correct
71 Correct 481 ms 38816 KB Output is correct
72 Correct 480 ms 38992 KB Output is correct
73 Correct 493 ms 39556 KB Output is correct
74 Correct 452 ms 39384 KB Output is correct
75 Correct 513 ms 40136 KB Output is correct
76 Correct 458 ms 41368 KB Output is correct
77 Correct 397 ms 44176 KB Output is correct
78 Correct 238 ms 51048 KB Output is correct