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Submission #1031049

# Submission time Handle Problem Language Result Execution time Memory
1031049 2024-07-22T13:59:24 Z Thunnus Hard route (IZhO17_road) C++17
100 / 100
 643 ms 179028 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 0 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 0 ms 436 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 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 360 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 428 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 352 KB Output is correct
14 Correct 0 ms 400 KB Output is correct
15 Correct 0 ms 360 KB Output is correct
16 Correct 0 ms 388 KB Output is correct
17 Correct 0 ms 352 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 352 KB Output is correct
20 Correct 0 ms 352 KB Output is correct
21 Correct 0 ms 352 KB Output is correct
22 Correct 1 ms 352 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 352 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 0 ms 436 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 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 360 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 428 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 352 KB Output is correct
14 Correct 0 ms 400 KB Output is correct
15 Correct 0 ms 360 KB Output is correct
16 Correct 0 ms 388 KB Output is correct
17 Correct 0 ms 352 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 352 KB Output is correct
20 Correct 0 ms 352 KB Output is correct
21 Correct 0 ms 352 KB Output is correct
22 Correct 1 ms 352 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 352 KB Output is correct
25 Correct 3 ms 1120 KB Output is correct
26 Correct 3 ms 1372 KB Output is correct
27 Correct 3 ms 1376 KB Output is correct
28 Correct 3 ms 1376 KB Output is correct
29 Correct 3 ms 1372 KB Output is correct
30 Correct 3 ms 1376 KB Output is correct
31 Correct 3 ms 1376 KB Output is correct
32 Correct 3 ms 1368 KB Output is correct
33 Correct 3 ms 1252 KB Output is correct
34 Correct 3 ms 1372 KB Output is correct
35 Correct 3 ms 1372 KB Output is correct
36 Correct 3 ms 1316 KB Output is correct
37 Correct 3 ms 1372 KB Output is correct
38 Correct 3 ms 2140 KB Output is correct
39 Correct 3 ms 1200 KB Output is correct
40 Correct 3 ms 864 KB Output is correct
41 Correct 3 ms 864 KB Output is correct
42 Correct 3 ms 756 KB Output is correct
43 Correct 3 ms 608 KB Output is correct
44 Correct 2 ms 608 KB Output is correct
45 Correct 2 ms 608 KB Output is correct
46 Correct 2 ms 608 KB Output is correct
47 Correct 3 ms 744 KB Output is correct
48 Correct 3 ms 864 KB Output is correct

Subtask #3
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 0 ms 436 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 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 360 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 428 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 352 KB Output is correct
14 Correct 0 ms 400 KB Output is correct
15 Correct 0 ms 360 KB Output is correct
16 Correct 0 ms 388 KB Output is correct
17 Correct 0 ms 352 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 352 KB Output is correct
20 Correct 0 ms 352 KB Output is correct
21 Correct 0 ms 352 KB Output is correct
22 Correct 1 ms 352 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 0 ms 352 KB Output is correct
25 Correct 3 ms 1120 KB Output is correct
26 Correct 3 ms 1372 KB Output is correct
27 Correct 3 ms 1376 KB Output is correct
28 Correct 3 ms 1376 KB Output is correct
29 Correct 3 ms 1372 KB Output is correct
30 Correct 3 ms 1376 KB Output is correct
31 Correct 3 ms 1376 KB Output is correct
32 Correct 3 ms 1368 KB Output is correct
33 Correct 3 ms 1252 KB Output is correct
34 Correct 3 ms 1372 KB Output is correct
35 Correct 3 ms 1372 KB Output is correct
36 Correct 3 ms 1316 KB Output is correct
37 Correct 3 ms 1372 KB Output is correct
38 Correct 3 ms 2140 KB Output is correct
39 Correct 3 ms 1200 KB Output is correct
40 Correct 3 ms 864 KB Output is correct
41 Correct 3 ms 864 KB Output is correct
42 Correct 3 ms 756 KB Output is correct
43 Correct 3 ms 608 KB Output is correct
44 Correct 2 ms 608 KB Output is correct
45 Correct 2 ms 608 KB Output is correct
46 Correct 2 ms 608 KB Output is correct
47 Correct 3 ms 744 KB Output is correct
48 Correct 3 ms 864 KB Output is correct
49 Correct 420 ms 91224 KB Output is correct
50 Correct 429 ms 101036 KB Output is correct
51 Correct 452 ms 109364 KB Output is correct
52 Correct 445 ms 79720 KB Output is correct
53 Correct 398 ms 102236 KB Output is correct
54 Correct 398 ms 112468 KB Output is correct
55 Correct 389 ms 87252 KB Output is correct
56 Correct 397 ms 98384 KB Output is correct
57 Correct 424 ms 115796 KB Output is correct
58 Correct 413 ms 104532 KB Output is correct
59 Correct 434 ms 104524 KB Output is correct
60 Correct 403 ms 99160 KB Output is correct
61 Correct 598 ms 179028 KB Output is correct
62 Correct 623 ms 153516 KB Output is correct
63 Correct 643 ms 79188 KB Output is correct
64 Correct 511 ms 61524 KB Output is correct
65 Correct 506 ms 50004 KB Output is correct
66 Correct 479 ms 44116 KB Output is correct
67 Correct 448 ms 40788 KB Output is correct
68 Correct 474 ms 39652 KB Output is correct
69 Correct 408 ms 39252 KB Output is correct
70 Correct 438 ms 38752 KB Output is correct
71 Correct 428 ms 38740 KB Output is correct
72 Correct 409 ms 39248 KB Output is correct
73 Correct 426 ms 39252 KB Output is correct
74 Correct 458 ms 39376 KB Output is correct
75 Correct 433 ms 40272 KB Output is correct
76 Correct 439 ms 41292 KB Output is correct
77 Correct 403 ms 43740 KB Output is correct
78 Correct 307 ms 49216 KB Output is correct