oj.uz

Submission #966405

# Submission time Handle Problem Language Result Execution time Memory
966405 2024-04-19T20:07:44 Z eysbutno Hard route (IZhO17_road) C++17
100 / 100
 847 ms 178100 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 [len, cnt] : paths) {
					if (len == a) num -= cnt * cnt;
				}
				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 [len, cnt] : paths) {
					if (len == c) num -= cnt * cnt;
				}
				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 1 ms 348 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 432 KB Output is correct
5 Correct 1 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 432 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 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 604 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 600 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 0 ms 596 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 1 ms 604 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 432 KB Output is correct
5 Correct 1 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 432 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 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 604 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 600 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 0 ms 596 KB Output is correct
25 Correct 3 ms 1112 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 1224 KB Output is correct
30 Correct 3 ms 1372 KB Output is correct
31 Correct 4 ms 1372 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 4 ms 1372 KB Output is correct
34 Correct 4 ms 1624 KB Output is correct
35 Correct 3 ms 1468 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 2336 KB Output is correct
39 Correct 4 ms 1216 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 704 KB Output is correct
43 Correct 3 ms 604 KB Output is correct
44 Correct 3 ms 604 KB Output is correct
45 Correct 4 ms 660 KB Output is correct
46 Correct 3 ms 600 KB Output is correct
47 Correct 3 ms 860 KB Output is correct
48 Correct 3 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 1 ms 604 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 432 KB Output is correct
5 Correct 1 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 432 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 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 604 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 600 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 0 ms 596 KB Output is correct
25 Correct 3 ms 1112 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 1224 KB Output is correct
30 Correct 3 ms 1372 KB Output is correct
31 Correct 4 ms 1372 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 4 ms 1372 KB Output is correct
34 Correct 4 ms 1624 KB Output is correct
35 Correct 3 ms 1468 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 2336 KB Output is correct
39 Correct 4 ms 1216 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 704 KB Output is correct
43 Correct 3 ms 604 KB Output is correct
44 Correct 3 ms 604 KB Output is correct
45 Correct 4 ms 660 KB Output is correct
46 Correct 3 ms 600 KB Output is correct
47 Correct 3 ms 860 KB Output is correct
48 Correct 3 ms 860 KB Output is correct
49 Correct 608 ms 90116 KB Output is correct
50 Correct 599 ms 100080 KB Output is correct
51 Correct 588 ms 108396 KB Output is correct
52 Correct 565 ms 78328 KB Output is correct
53 Correct 499 ms 101204 KB Output is correct
54 Correct 537 ms 111264 KB Output is correct
55 Correct 516 ms 86100 KB Output is correct
56 Correct 511 ms 97288 KB Output is correct
57 Correct 584 ms 114612 KB Output is correct
58 Correct 547 ms 103580 KB Output is correct
59 Correct 588 ms 103292 KB Output is correct
60 Correct 543 ms 98204 KB Output is correct
61 Correct 847 ms 178100 KB Output is correct
62 Correct 779 ms 152180 KB Output is correct
63 Correct 747 ms 78164 KB Output is correct
64 Correct 761 ms 60352 KB Output is correct
65 Correct 746 ms 48948 KB Output is correct
66 Correct 704 ms 43140 KB Output is correct
67 Correct 716 ms 39928 KB Output is correct
68 Correct 701 ms 38640 KB Output is correct
69 Correct 683 ms 38224 KB Output is correct
70 Correct 637 ms 37716 KB Output is correct
71 Correct 621 ms 37564 KB Output is correct
72 Correct 667 ms 38024 KB Output is correct
73 Correct 646 ms 38228 KB Output is correct
74 Correct 691 ms 38096 KB Output is correct
75 Correct 684 ms 38976 KB Output is correct
76 Correct 604 ms 40088 KB Output is correct
77 Correct 547 ms 43896 KB Output is correct
78 Correct 436 ms 49048 KB Output is correct