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Submission #966373

# Submission time Handle Problem Language Result Execution time Memory
966373 2024-04-19T18:45:29 Z eysbutno Hard route (IZhO17_road) C++17
100 / 100
 825 ms 171832 KB 
#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;
    ll 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 hardness 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];
            ll b = paths[1][0];
            ll c = paths[2][0];
            ll cur = a * (b + c);
            ll num = 0;
            ll ties = 0;
            for (auto [len, cnt] : paths) {
                if (len == c) ties += cnt;
            }

            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 [len, cnt] : paths) {
            if (len + 1 > longest1) {
                swap(longest1, longest2);
                swap(count1, count2);
                longest1 = len + 1;
                count1 = cnt;
            } else if (len + 1 == longest1) {
                count1 += cnt;
            } else if (len + 1 > longest2) {
                longest2 = len + 1;
                count2 = cnt;
            } else if (len + 1 == longest2) {
                count2 += cnt;
            }
        }
        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 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 420 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 0 ms 344 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 344 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 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 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 344 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 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 348 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 420 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 0 ms 344 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 344 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 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 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 344 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 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 348 KB Output is correct
25 Correct 3 ms 1116 KB Output is correct
26 Correct 3 ms 1116 KB Output is correct
27 Correct 3 ms 1624 KB Output is correct
28 Correct 4 ms 1448 KB Output is correct
29 Correct 4 ms 1116 KB Output is correct
30 Correct 3 ms 1372 KB Output is correct
31 Correct 3 ms 1372 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 3 ms 1116 KB Output is correct
34 Correct 4 ms 1372 KB Output is correct
35 Correct 3 ms 1372 KB Output is correct
36 Correct 3 ms 1152 KB Output is correct
37 Correct 4 ms 1372 KB Output is correct
38 Correct 4 ms 1884 KB Output is correct
39 Correct 4 ms 1112 KB Output is correct
40 Correct 3 ms 860 KB Output is correct
41 Correct 3 ms 860 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 5 ms 604 KB Output is correct
46 Correct 3 ms 624 KB Output is correct
47 Correct 5 ms 852 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 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 420 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 0 ms 344 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 344 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 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 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1 ms 344 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 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 348 KB Output is correct
25 Correct 3 ms 1116 KB Output is correct
26 Correct 3 ms 1116 KB Output is correct
27 Correct 3 ms 1624 KB Output is correct
28 Correct 4 ms 1448 KB Output is correct
29 Correct 4 ms 1116 KB Output is correct
30 Correct 3 ms 1372 KB Output is correct
31 Correct 3 ms 1372 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 3 ms 1116 KB Output is correct
34 Correct 4 ms 1372 KB Output is correct
35 Correct 3 ms 1372 KB Output is correct
36 Correct 3 ms 1152 KB Output is correct
37 Correct 4 ms 1372 KB Output is correct
38 Correct 4 ms 1884 KB Output is correct
39 Correct 4 ms 1112 KB Output is correct
40 Correct 3 ms 860 KB Output is correct
41 Correct 3 ms 860 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 5 ms 604 KB Output is correct
46 Correct 3 ms 624 KB Output is correct
47 Correct 5 ms 852 KB Output is correct
48 Correct 3 ms 856 KB Output is correct
49 Correct 539 ms 84052 KB Output is correct
50 Correct 571 ms 93968 KB Output is correct
51 Correct 572 ms 102596 KB Output is correct
52 Correct 614 ms 72528 KB Output is correct
53 Correct 481 ms 95264 KB Output is correct
54 Correct 559 ms 105392 KB Output is correct
55 Correct 521 ms 80196 KB Output is correct
56 Correct 532 ms 91304 KB Output is correct
57 Correct 519 ms 108752 KB Output is correct
58 Correct 575 ms 97400 KB Output is correct
59 Correct 527 ms 97348 KB Output is correct
60 Correct 587 ms 92232 KB Output is correct
61 Correct 820 ms 171832 KB Output is correct
62 Correct 801 ms 146532 KB Output is correct
63 Correct 747 ms 72244 KB Output is correct
64 Correct 825 ms 54568 KB Output is correct
65 Correct 690 ms 42832 KB Output is correct
66 Correct 655 ms 37164 KB Output is correct
67 Correct 696 ms 33900 KB Output is correct
68 Correct 629 ms 32608 KB Output is correct
69 Correct 715 ms 32572 KB Output is correct
70 Correct 649 ms 32176 KB Output is correct
71 Correct 598 ms 31740 KB Output is correct
72 Correct 640 ms 31720 KB Output is correct
73 Correct 653 ms 32088 KB Output is correct
74 Correct 661 ms 32816 KB Output is correct
75 Correct 639 ms 32892 KB Output is correct
76 Correct 623 ms 34316 KB Output is correct
77 Correct 535 ms 37976 KB Output is correct
78 Correct 453 ms 42152 KB Output is correct