oj.uz

Submission #993474

# Submission time Handle Problem Language Result Execution time Memory
993474 2024-06-05T18:00:15 Z doducanh Hard route (IZhO17_road) C++14
100 / 100
 578 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[0][1]*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';
}

Compilation message

road.cpp: In lambda function:
road.cpp:67:14: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   67 |    for (auto [len, amt] : paths) {
      |              ^
road.cpp:77:15: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   77 |     for (auto [len, amt] : paths) {
      |               ^
road.cpp:87:15: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   87 |     for (auto [len, amt] : paths) {
      |               ^
road.cpp:106:13: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
  106 |   for (auto [len, amt] : paths) {
      |             ^

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 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 1 ms 348 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 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 436 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 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 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 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 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 1 ms 348 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 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 436 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 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 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 1132 KB Output is correct
26 Correct 3 ms 1372 KB Output is correct
27 Correct 3 ms 1372 KB Output is correct
28 Correct 3 ms 1428 KB Output is correct
29 Correct 3 ms 1200 KB Output is correct
30 Correct 3 ms 1372 KB Output is correct
31 Correct 3 ms 1412 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 3 ms 1372 KB Output is correct
34 Correct 3 ms 1372 KB Output is correct
35 Correct 3 ms 1384 KB Output is correct
36 Correct 3 ms 1368 KB Output is correct
37 Correct 3 ms 1628 KB Output is correct
38 Correct 5 ms 2140 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 680 KB Output is correct
42 Correct 3 ms 604 KB Output is correct
43 Correct 3 ms 740 KB Output is correct
44 Correct 5 ms 604 KB Output is correct
45 Correct 3 ms 604 KB Output is correct
46 Correct 3 ms 700 KB Output is correct
47 Correct 4 ms 668 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 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 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 1 ms 348 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 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 436 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 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 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 1132 KB Output is correct
26 Correct 3 ms 1372 KB Output is correct
27 Correct 3 ms 1372 KB Output is correct
28 Correct 3 ms 1428 KB Output is correct
29 Correct 3 ms 1200 KB Output is correct
30 Correct 3 ms 1372 KB Output is correct
31 Correct 3 ms 1412 KB Output is correct
32 Correct 3 ms 1116 KB Output is correct
33 Correct 3 ms 1372 KB Output is correct
34 Correct 3 ms 1372 KB Output is correct
35 Correct 3 ms 1384 KB Output is correct
36 Correct 3 ms 1368 KB Output is correct
37 Correct 3 ms 1628 KB Output is correct
38 Correct 5 ms 2140 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 680 KB Output is correct
42 Correct 3 ms 604 KB Output is correct
43 Correct 3 ms 740 KB Output is correct
44 Correct 5 ms 604 KB Output is correct
45 Correct 3 ms 604 KB Output is correct
46 Correct 3 ms 700 KB Output is correct
47 Correct 4 ms 668 KB Output is correct
48 Correct 3 ms 860 KB Output is correct
49 Correct 406 ms 91216 KB Output is correct
50 Correct 409 ms 101136 KB Output is correct
51 Correct 402 ms 109396 KB Output is correct
52 Correct 412 ms 79700 KB Output is correct
53 Correct 396 ms 102296 KB Output is correct
54 Correct 389 ms 112524 KB Output is correct
55 Correct 367 ms 87252 KB Output is correct
56 Correct 362 ms 98380 KB Output is correct
57 Correct 425 ms 115792 KB Output is correct
58 Correct 398 ms 104528 KB Output is correct
59 Correct 408 ms 104276 KB Output is correct
60 Correct 407 ms 99156 KB Output is correct
61 Correct 560 ms 179028 KB Output is correct
62 Correct 577 ms 153424 KB Output is correct
63 Correct 578 ms 79184 KB Output is correct
64 Correct 501 ms 61520 KB Output is correct
65 Correct 441 ms 50008 KB Output is correct
66 Correct 427 ms 44112 KB Output is correct
67 Correct 419 ms 40832 KB Output is correct
68 Correct 428 ms 39764 KB Output is correct
69 Correct 421 ms 39224 KB Output is correct
70 Correct 396 ms 38820 KB Output is correct
71 Correct 390 ms 38592 KB Output is correct
72 Correct 422 ms 38992 KB Output is correct
73 Correct 399 ms 39252 KB Output is correct
74 Correct 376 ms 39376 KB Output is correct
75 Correct 381 ms 40164 KB Output is correct
76 Correct 372 ms 41116 KB Output is correct
77 Correct 369 ms 44120 KB Output is correct
78 Correct 278 ms 49988 KB Output is correct