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답안 #966963

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
966963 2024-04-20T17:53:01 Z eysbutno Hard route (IZhO17_road) C++17
100 / 100
 869 ms 179264 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

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 436 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 600 KB Output is correct
7 Correct 1 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 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 352 KB Output is correct
19 Correct 1 ms 344 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 348 KB Output is correct
23 Correct 0 ms 344 KB Output is correct
24 Correct 0 ms 348 KB Output is correct

Subtask #2
33.0 / 33.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 436 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 600 KB Output is correct
7 Correct 1 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 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 352 KB Output is correct
19 Correct 1 ms 344 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 348 KB Output is correct
23 Correct 0 ms 344 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 4 ms 1116 KB Output is correct
26 Correct 3 ms 1372 KB Output is correct
27 Correct 4 ms 1372 KB Output is correct
28 Correct 3 ms 1372 KB Output is correct
29 Correct 3 ms 1372 KB Output is correct
30 Correct 3 ms 1416 KB Output is correct
31 Correct 3 ms 1368 KB Output is correct
32 Correct 3 ms 1112 KB Output is correct
33 Correct 3 ms 1368 KB Output is correct
34 Correct 4 ms 1372 KB Output is correct
35 Correct 4 ms 1372 KB Output is correct
36 Correct 5 ms 1372 KB Output is correct
37 Correct 4 ms 1372 KB Output is correct
38 Correct 4 ms 2140 KB Output is correct
39 Correct 3 ms 1116 KB Output is correct
40 Correct 3 ms 936 KB Output is correct
41 Correct 3 ms 860 KB Output is correct
42 Correct 3 ms 708 KB Output is correct
43 Correct 3 ms 604 KB Output is correct
44 Correct 3 ms 604 KB Output is correct
45 Correct 3 ms 604 KB Output is correct
46 Correct 3 ms 604 KB Output is correct
47 Correct 4 ms 680 KB Output is correct
48 Correct 4 ms 860 KB Output is correct

Subtask #3
48.0 / 48.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 436 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 600 KB Output is correct
7 Correct 1 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 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 352 KB Output is correct
19 Correct 1 ms 344 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 348 KB Output is correct
23 Correct 0 ms 344 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 4 ms 1116 KB Output is correct
26 Correct 3 ms 1372 KB Output is correct
27 Correct 4 ms 1372 KB Output is correct
28 Correct 3 ms 1372 KB Output is correct
29 Correct 3 ms 1372 KB Output is correct
30 Correct 3 ms 1416 KB Output is correct
31 Correct 3 ms 1368 KB Output is correct
32 Correct 3 ms 1112 KB Output is correct
33 Correct 3 ms 1368 KB Output is correct
34 Correct 4 ms 1372 KB Output is correct
35 Correct 4 ms 1372 KB Output is correct
36 Correct 5 ms 1372 KB Output is correct
37 Correct 4 ms 1372 KB Output is correct
38 Correct 4 ms 2140 KB Output is correct
39 Correct 3 ms 1116 KB Output is correct
40 Correct 3 ms 936 KB Output is correct
41 Correct 3 ms 860 KB Output is correct
42 Correct 3 ms 708 KB Output is correct
43 Correct 3 ms 604 KB Output is correct
44 Correct 3 ms 604 KB Output is correct
45 Correct 3 ms 604 KB Output is correct
46 Correct 3 ms 604 KB Output is correct
47 Correct 4 ms 680 KB Output is correct
48 Correct 4 ms 860 KB Output is correct
49 Correct 585 ms 91336 KB Output is correct
50 Correct 568 ms 101460 KB Output is correct
51 Correct 598 ms 109472 KB Output is correct
52 Correct 557 ms 79700 KB Output is correct
53 Correct 515 ms 102224 KB Output is correct
54 Correct 505 ms 112872 KB Output is correct
55 Correct 515 ms 87452 KB Output is correct
56 Correct 510 ms 98364 KB Output is correct
57 Correct 562 ms 115828 KB Output is correct
58 Correct 549 ms 104564 KB Output is correct
59 Correct 553 ms 104344 KB Output is correct
60 Correct 527 ms 99304 KB Output is correct
61 Correct 869 ms 179264 KB Output is correct
62 Correct 795 ms 153460 KB Output is correct
63 Correct 743 ms 79396 KB Output is correct
64 Correct 745 ms 61528 KB Output is correct
65 Correct 722 ms 50004 KB Output is correct
66 Correct 722 ms 44232 KB Output is correct
67 Correct 656 ms 40792 KB Output is correct
68 Correct 664 ms 39660 KB Output is correct
69 Correct 695 ms 39324 KB Output is correct
70 Correct 667 ms 38864 KB Output is correct
71 Correct 671 ms 38904 KB Output is correct
72 Correct 632 ms 39036 KB Output is correct
73 Correct 624 ms 39208 KB Output is correct
74 Correct 622 ms 39572 KB Output is correct
75 Correct 653 ms 40024 KB Output is correct
76 Correct 616 ms 41288 KB Output is correct
77 Correct 589 ms 45668 KB Output is correct
78 Correct 424 ms 49528 KB Output is correct