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Submission #959826

# Submission time Handle Problem Language Result Execution time Memory
959826 2024-04-09T07:28:47 Z josanneo22 The Xana coup (BOI21_xanadu) C++17
100 / 100
 49 ms 18772 KB 
#include <bits/stdc++.h>
using namespace std;
using i64 = long long;

#define L(i,j,k) for(int i=(j);i<=(k);++i)
#define R(i,j,k) for(int i=(j);i>=(k);--i)
#define rep(i, n) L(i, 1, n)
#define all(x) x.begin(),x.end()
#define me(x,a) memset(x,a,sizeof(x))

#include<random>
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int nax = 1E5 + 5;
int N, a[nax], dp[nax][2][2];
vector<int> G[nax];
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr); cout.tie(nullptr);
	
	cin >> N;
	L(i, 1, N - 1) {
		int u, v; cin >> u >> v;
		G[u].push_back(v);
		G[v].push_back(u);
	}
	L(i, 1, N) cin >> a[i];
	function<void(int, int)> dfs = [&](int u, int f) {
		for (auto & v : G[u]) {
			if (v == f) continue;
			dfs(v, u);
		}
		/* each node is only pressed once and we need to pass on info to the parent node
		 * dp[u][A][B] = minimum amount of operations done when we have considered node u
		 * and we have A = whether we have pressed node u and B = have we pressed an odd or even number of buttons
		 */
		for (int press = 0; press < 2; press++) { // do I want to press this button
			for (int par = 0; par < 2; par++) { // whether we want to pass on to the parent
				int even = 0, odd = N * 2; // initially we only pressed even number of buttons
				for (auto & v : G[u]) {
					if (v == f) continue;
					// dp[v][whether we pressed child][passing to parent of v that is u (our state whether we want to press)]
					int _od = min(odd + dp[v][0][press], even + dp[v][1][press]); // either odd + 1 -> even or even + 1 -> odd
					int _ev = min(odd + dp[v][1][press], even + dp[v][0][press]); // opposite way
					swap(_od, odd); swap(_ev, even);
				}
				if (press ^ par ^ a[u]) dp[u][press][par] = odd + press; // press ^ par ^ a[u] == 1, we need to perform an operation
				else dp[u][press][par] = even + press; // otherwise
				// the value is stored in odd when we want to change because pressing a odd amount of buttons will cause the button to be flipped
			}
		}
	};
	dfs(1, 1);
	int ans = min(dp[1][1][0], dp[1][0][0]); // since the third one shows how the parent would be pressed, there is no parent so no need to consider
	if (ans > N) cout << "impossible\n";
	else cout << ans << '\n';
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 2 ms 4700 KB Output is correct
7 Correct 1 ms 4700 KB Output is correct
8 Correct 1 ms 4700 KB Output is correct
9 Correct 1 ms 4700 KB Output is correct
10 Correct 1 ms 4700 KB Output is correct
11 Correct 1 ms 4700 KB Output is correct
12 Correct 1 ms 4700 KB Output is correct
13 Correct 1 ms 4700 KB Output is correct
14 Correct 1 ms 4700 KB Output is correct
15 Correct 1 ms 4700 KB Output is correct
16 Correct 1 ms 4700 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 39 ms 18516 KB Output is correct
2 Correct 49 ms 18512 KB Output is correct
3 Correct 38 ms 18680 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 36 ms 18512 KB Output is correct
2 Correct 42 ms 18544 KB Output is correct
3 Correct 37 ms 18768 KB Output is correct
4 Correct 29 ms 7512 KB Output is correct
5 Correct 32 ms 7768 KB Output is correct
6 Correct 34 ms 7772 KB Output is correct
7 Correct 1 ms 4952 KB Output is correct
8 Correct 11 ms 5724 KB Output is correct
9 Correct 33 ms 7828 KB Output is correct
10 Correct 33 ms 7772 KB Output is correct
11 Correct 31 ms 8540 KB Output is correct
12 Correct 32 ms 8796 KB Output is correct
13 Correct 29 ms 7508 KB Output is correct
14 Correct 31 ms 7772 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 2 ms 4700 KB Output is correct
7 Correct 1 ms 4700 KB Output is correct
8 Correct 1 ms 4700 KB Output is correct
9 Correct 1 ms 4700 KB Output is correct
10 Correct 1 ms 4700 KB Output is correct
11 Correct 1 ms 4700 KB Output is correct
12 Correct 1 ms 4700 KB Output is correct
13 Correct 1 ms 4700 KB Output is correct
14 Correct 1 ms 4700 KB Output is correct
15 Correct 1 ms 4700 KB Output is correct
16 Correct 1 ms 4700 KB Output is correct
17 Correct 39 ms 18516 KB Output is correct
18 Correct 49 ms 18512 KB Output is correct
19 Correct 38 ms 18680 KB Output is correct
20 Correct 36 ms 18512 KB Output is correct
21 Correct 42 ms 18544 KB Output is correct
22 Correct 37 ms 18768 KB Output is correct
23 Correct 29 ms 7512 KB Output is correct
24 Correct 32 ms 7768 KB Output is correct
25 Correct 34 ms 7772 KB Output is correct
26 Correct 1 ms 4952 KB Output is correct
27 Correct 11 ms 5724 KB Output is correct
28 Correct 33 ms 7828 KB Output is correct
29 Correct 33 ms 7772 KB Output is correct
30 Correct 31 ms 8540 KB Output is correct
31 Correct 32 ms 8796 KB Output is correct
32 Correct 29 ms 7508 KB Output is correct
33 Correct 31 ms 7772 KB Output is correct
34 Correct 1 ms 4700 KB Output is correct
35 Correct 1 ms 4700 KB Output is correct
36 Correct 1 ms 4700 KB Output is correct
37 Correct 1 ms 4700 KB Output is correct
38 Correct 1 ms 4952 KB Output is correct
39 Correct 1 ms 4700 KB Output is correct
40 Correct 1 ms 4696 KB Output is correct
41 Correct 1 ms 4700 KB Output is correct
42 Correct 1 ms 4700 KB Output is correct
43 Correct 1 ms 4696 KB Output is correct
44 Correct 1 ms 4700 KB Output is correct
45 Correct 38 ms 18684 KB Output is correct
46 Correct 37 ms 18768 KB Output is correct
47 Correct 38 ms 18772 KB Output is correct
48 Correct 29 ms 7516 KB Output is correct
49 Correct 38 ms 7640 KB Output is correct
50 Correct 44 ms 7880 KB Output is correct
51 Correct 1 ms 4700 KB Output is correct
52 Correct 13 ms 5708 KB Output is correct
53 Correct 34 ms 7832 KB Output is correct
54 Correct 32 ms 7768 KB Output is correct
55 Correct 33 ms 8576 KB Output is correct
56 Correct 39 ms 8752 KB Output is correct
57 Correct 40 ms 7608 KB Output is correct
58 Correct 34 ms 7772 KB Output is correct
59 Correct 11 ms 5720 KB Output is correct
60 Correct 29 ms 7512 KB Output is correct
61 Correct 31 ms 7900 KB Output is correct
62 Correct 33 ms 7772 KB Output is correct
63 Correct 36 ms 7876 KB Output is correct
64 Correct 33 ms 7772 KB Output is correct
65 Correct 28 ms 8284 KB Output is correct
66 Correct 31 ms 8280 KB Output is correct
67 Correct 25 ms 8148 KB Output is correct
68 Correct 25 ms 8256 KB Output is correct
69 Correct 27 ms 8148 KB Output is correct
70 Correct 27 ms 8148 KB Output is correct