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Submission #959823

# Submission time Handle Problem Language Result Execution time Memory
959823 2024-04-09T07:26:58 Z josanneo22 The Xana coup (BOI21_xanadu) C++17
100 / 100
 47 ms 18816 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 + 500;
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 2 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 4696 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 2 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 4696 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 1 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 4952 KB Output is correct
10 Correct 1 ms 4700 KB Output is correct
11 Correct 1 ms 4952 KB Output is correct
12 Correct 1 ms 4696 KB Output is correct
13 Correct 1 ms 4712 KB Output is correct
14 Correct 1 ms 4948 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 37 ms 18780 KB Output is correct
2 Correct 37 ms 18524 KB Output is correct
3 Correct 37 ms 18728 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 39 ms 18712 KB Output is correct
2 Correct 39 ms 18588 KB Output is correct
3 Correct 41 ms 18772 KB Output is correct
4 Correct 28 ms 7512 KB Output is correct
5 Correct 32 ms 7768 KB Output is correct
6 Correct 32 ms 7812 KB Output is correct
7 Correct 1 ms 4700 KB Output is correct
8 Correct 11 ms 5724 KB Output is correct
9 Correct 32 ms 7772 KB Output is correct
10 Correct 34 ms 8020 KB Output is correct
11 Correct 37 ms 8612 KB Output is correct
12 Correct 33 ms 8796 KB Output is correct
13 Correct 28 ms 7452 KB Output is correct
14 Correct 33 ms 7764 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 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 4696 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 1 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 4952 KB Output is correct
10 Correct 1 ms 4700 KB Output is correct
11 Correct 1 ms 4952 KB Output is correct
12 Correct 1 ms 4696 KB Output is correct
13 Correct 1 ms 4712 KB Output is correct
14 Correct 1 ms 4948 KB Output is correct
15 Correct 1 ms 4700 KB Output is correct
16 Correct 1 ms 4700 KB Output is correct
17 Correct 37 ms 18780 KB Output is correct
18 Correct 37 ms 18524 KB Output is correct
19 Correct 37 ms 18728 KB Output is correct
20 Correct 39 ms 18712 KB Output is correct
21 Correct 39 ms 18588 KB Output is correct
22 Correct 41 ms 18772 KB Output is correct
23 Correct 28 ms 7512 KB Output is correct
24 Correct 32 ms 7768 KB Output is correct
25 Correct 32 ms 7812 KB Output is correct
26 Correct 1 ms 4700 KB Output is correct
27 Correct 11 ms 5724 KB Output is correct
28 Correct 32 ms 7772 KB Output is correct
29 Correct 34 ms 8020 KB Output is correct
30 Correct 37 ms 8612 KB Output is correct
31 Correct 33 ms 8796 KB Output is correct
32 Correct 28 ms 7452 KB Output is correct
33 Correct 33 ms 7764 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 4696 KB Output is correct
37 Correct 1 ms 4696 KB Output is correct
38 Correct 1 ms 4696 KB Output is correct
39 Correct 1 ms 4696 KB Output is correct
40 Correct 1 ms 4700 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 4700 KB Output is correct
44 Correct 1 ms 4700 KB Output is correct
45 Correct 37 ms 18620 KB Output is correct
46 Correct 35 ms 18520 KB Output is correct
47 Correct 37 ms 18816 KB Output is correct
48 Correct 33 ms 7296 KB Output is correct
49 Correct 41 ms 7772 KB Output is correct
50 Correct 33 ms 7772 KB Output is correct
51 Correct 1 ms 4700 KB Output is correct
52 Correct 11 ms 5724 KB Output is correct
53 Correct 35 ms 7740 KB Output is correct
54 Correct 34 ms 8028 KB Output is correct
55 Correct 32 ms 8540 KB Output is correct
56 Correct 33 ms 8796 KB Output is correct
57 Correct 47 ms 7484 KB Output is correct
58 Correct 32 ms 7692 KB Output is correct
59 Correct 11 ms 5724 KB Output is correct
60 Correct 30 ms 7516 KB Output is correct
61 Correct 32 ms 7852 KB Output is correct
62 Correct 32 ms 8028 KB Output is correct
63 Correct 34 ms 7904 KB Output is correct
64 Correct 32 ms 7784 KB Output is correct
65 Correct 31 ms 8284 KB Output is correct
66 Correct 36 ms 8532 KB Output is correct
67 Correct 26 ms 8148 KB Output is correct
68 Correct 26 ms 8284 KB Output is correct
69 Correct 27 ms 8152 KB Output is correct
70 Correct 29 ms 8276 KB Output is correct