oj.uz

Submission #991739

# Submission time Handle Problem Language Result Execution time Memory
991739 2024-06-03T04:12:17 Z xjonwang Hard route (IZhO17_road) C++17
100 / 100
 609 ms 179012 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;
		adj[--x].push_back(--y);
		adj[y].push_back(x);
	}

	vector<int> max_length(n);
	vector<int> path_count(n);
	/**
	 * Calculates the longest path from vertex u,
	 * and the number of such paths.
	 */
	function<void(int, int)> dfs = [&](int u, int p) {
		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;
	/**
	 * Performs the rerooting, to count the hardest
	 * path and the # of such paths at this vertex.
	 */
	function<void(int, int, ll, ll)> dfs2 = [&](int u, int p, ll parent_dist,
	                                            ll parent_count) {
		vector<array<ll, 2>> paths;  // {distance, count}
		if (u > 0 || (int)adj[u].size() == 1) {
			paths.push_back({parent_dist, parent_count});
		}
		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 current_hardness = a * (b + c);
			ll current_path_count = 0;
			ll ties = 0;
			for (auto [len, amt] : paths) {
				if (len == c) { ties += amt; }
			}

			if (a != b && b != c) {
				// case 1: all are distinct.
				current_path_count = paths[1][1] * ties;
			} else if (a == b && b == c) {
				// case 2: all are the same.
				current_path_count = ties * ties;
				for (auto [len, amt] : paths) {
					if (len == a) { current_path_count -= amt * amt; }
				}
				current_path_count /= 2;  // avoiding double counting
			} else if (a == b) {
				// case 3: first two are the same.
				current_path_count = (paths[0][1] + paths[1][1]) * ties;
			} else {
				// case 4: last two are the same.
				current_path_count = ties * ties;
				for (auto [len, amt] : paths) {
					if (len == c) { current_path_count -= amt * amt; }
				}
				current_path_count /= 2;  // avoiding double counting
			}

			if (max_hardness < current_hardness) {
				max_hardness = current_hardness;
				hardest_path_count = current_path_count;
			} else if (max_hardness == current_hardness) {
				hardest_path_count += current_path_count;
			}
		}

		// processing parent dist and parent count.
		ll longest1 = 0;
		ll longest2 = 0;
		ll count1 = 0;
		ll count2 = 0;
		for (auto [len, amt] : paths) {
			if (len + 1 > longest1) {
				swap(longest1, longest2);
				swap(count1, count2);
				longest1 = len + 1;
				count1 = amt;
			} else if (len + 1 == longest1) {
				count1 += amt;
			} else if (len + 1 > longest2) {
				longest2 = len + 1;
				count2 = amt;
			} else if (len + 1 == longest2) {
				count2 += amt;
			}
		}

		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 344 KB Output is correct
2 Correct 0 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 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 348 KB Output is correct
11 Correct 1 ms 344 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 344 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 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 1 ms 344 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 344 KB Output is correct
2 Correct 0 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 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 348 KB Output is correct
11 Correct 1 ms 344 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 344 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 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 1 ms 344 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 1372 KB Output is correct
28 Correct 4 ms 1372 KB Output is correct
29 Correct 5 ms 1116 KB Output is correct
30 Correct 4 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 3 ms 1116 KB Output is correct
34 Correct 3 ms 1424 KB Output is correct
35 Correct 3 ms 1372 KB Output is correct
36 Correct 5 ms 1372 KB Output is correct
37 Correct 3 ms 1372 KB Output is correct
38 Correct 4 ms 2040 KB Output is correct
39 Correct 3 ms 1116 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 2 ms 600 KB Output is correct
46 Correct 3 ms 592 KB Output is correct
47 Correct 3 ms 604 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 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 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 348 KB Output is correct
11 Correct 1 ms 344 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 344 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 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 1 ms 344 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 1372 KB Output is correct
28 Correct 4 ms 1372 KB Output is correct
29 Correct 5 ms 1116 KB Output is correct
30 Correct 4 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 3 ms 1116 KB Output is correct
34 Correct 3 ms 1424 KB Output is correct
35 Correct 3 ms 1372 KB Output is correct
36 Correct 5 ms 1372 KB Output is correct
37 Correct 3 ms 1372 KB Output is correct
38 Correct 4 ms 2040 KB Output is correct
39 Correct 3 ms 1116 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 2 ms 600 KB Output is correct
46 Correct 3 ms 592 KB Output is correct
47 Correct 3 ms 604 KB Output is correct
48 Correct 3 ms 856 KB Output is correct
49 Correct 477 ms 84160 KB Output is correct
50 Correct 430 ms 94036 KB Output is correct
51 Correct 434 ms 102440 KB Output is correct
52 Correct 411 ms 72396 KB Output is correct
53 Correct 399 ms 95316 KB Output is correct
54 Correct 383 ms 105552 KB Output is correct
55 Correct 378 ms 80144 KB Output is correct
56 Correct 378 ms 91216 KB Output is correct
57 Correct 441 ms 108520 KB Output is correct
58 Correct 466 ms 97360 KB Output is correct
59 Correct 426 ms 97364 KB Output is correct
60 Correct 409 ms 91984 KB Output is correct
61 Correct 597 ms 179012 KB Output is correct
62 Correct 607 ms 153428 KB Output is correct
63 Correct 609 ms 79188 KB Output is correct
64 Correct 557 ms 61332 KB Output is correct
65 Correct 532 ms 50052 KB Output is correct
66 Correct 525 ms 44064 KB Output is correct
67 Correct 498 ms 40788 KB Output is correct
68 Correct 575 ms 39572 KB Output is correct
69 Correct 464 ms 39252 KB Output is correct
70 Correct 451 ms 38740 KB Output is correct
71 Correct 468 ms 38740 KB Output is correct
72 Correct 444 ms 38996 KB Output is correct
73 Correct 475 ms 39384 KB Output is correct
74 Correct 514 ms 39380 KB Output is correct
75 Correct 424 ms 40160 KB Output is correct
76 Correct 430 ms 41292 KB Output is correct
77 Correct 401 ms 44464 KB Output is correct
78 Correct 325 ms 50500 KB Output is correct