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Submission #958107

# Submission time Handle Problem Language Result Execution time Memory
958107 2024-04-04T23:42:39 Z MinaRagy06 Beads and wires (APIO14_beads) C++17
100 / 100
 149 ms 45756 KB 
#include <bits/stdc++.h>
using namespace std;
#define ll long long
 
const int N = 200'005;
const ll inf = 1e18;
ll dp[N][2];
vector<array<ll, 2>> tadj[N], adj[N];
void build(int i, int p) {
	adj[i].clear();
	for (auto [nxt, w] : tadj[i]) {
		if (nxt == p) continue;
		build(nxt, i);
		adj[i].push_back({nxt, w});
	}
}
void root(int i) {
	for (auto [nxt, w] : adj[i]) {
		root(nxt);
	}
	for (int carry = 0; carry < 2; carry++) {
		ll ans = 0;
		if (carry) {
			ans = -inf;
		}
		ll s = 0;
		for (auto [nxt, w] : adj[i]) {
			s += max(dp[nxt][1] + w, dp[nxt][0]);
		}
		if (!carry) {
			ans = s;
		} else {
			ll mx = -inf;
			for (auto [nxt, w] : adj[i]) {
				mx = max(mx, - max(dp[nxt][1] + w, dp[nxt][0]) + dp[nxt][0] + w);
			}
			ans = s + mx;
		}
		dp[i][carry] = ans;
	}
}
ll ans = 0;
void reroot(int i, array<ll, 3> up) {
	array<ll, 2> newdp = {-inf, -inf};
	for (int carry = 0; carry < 2; carry++) {
		newdp[carry] = 0;
		if (carry) {
			newdp[carry] = -inf;
		}
		ll s = 0;
		for (auto [nxt, w] : adj[i]) {
			s += max(dp[nxt][1] + w, dp[nxt][0]);
		}
		s += max(up[1] + up[2], up[0]);
		if (!carry) {
			newdp[carry] = max(newdp[carry], s);
		} else {
			ll mx = -inf;
			for (auto [nxt, w] : adj[i]) {
				mx = max(mx, - max(dp[nxt][1] + w, dp[nxt][0]) + dp[nxt][0] + w);
			}
			mx = max(mx, - max(up[1] + up[2], up[0]) + up[0] + up[2]);
			newdp[carry] = max(newdp[carry], s + mx);
		}
	}
// 	cout << i << ": " << newdp[0] << '\n';
	ans = max(ans, newdp[0]);
	int m = adj[i].size();
	ll prfmx[m + 1], sufmx[m + 1], prfs[m + 1]{}, sufs[m + 1]{};
	prfmx[0] = - max(up[1] + up[2], up[0]) + up[0] + up[2];
	sufmx[m] = -inf;
	if (max(up[1] + up[2], up[0]) > 0) {
		prfs[0] = max(up[1] + up[2], up[0]);
	}
	for (int j = 0; j < m; j++) {
		auto [nxt, w] = adj[i][j];
		prfmx[j + 1] = max(prfmx[j], - max(dp[nxt][1] + w, dp[nxt][0]) + dp[nxt][0] + w);
		prfs[j + 1] = prfs[j] + max(dp[nxt][1] + w, dp[nxt][0]);
	}
	for (int j = m - 1; j >= 0; j--) {
		auto [nxt, w] = adj[i][j];
		sufmx[j] = max(sufmx[j + 1], - max(dp[nxt][1] + w, dp[nxt][0]) + dp[nxt][0] + w);
		sufs[j] = sufs[j + 1] + max(dp[nxt][1] + w, dp[nxt][0]);
	}
	for (int j = 0; j < m; j++) {
		auto [nxt, w] = adj[i][j];
		ll s = prfs[j] + sufs[j + 1];
		ll mx = max(prfmx[j], sufmx[j + 1]);
// 		cout << j << ' ' << prfmx[j] << ' ' << sufmx[j + 1] << '\n';
		reroot(nxt, {s, s + mx, w});
	}
}
int main() {
	ios_base::sync_with_stdio(0), cin.tie(0);
	memset(dp, -1, sizeof dp);
	int n;
	cin >> n;
	for (int i = 1, u, v, w; i < n; i++) {
		cin >> u >> v >> w;
		tadj[u].push_back({v, w});
		tadj[v].push_back({u, w});
	}
	memset(dp, -1, sizeof dp);
	build(1, 0);
	
	root(1);
	reroot(1, (array<ll, 3>) {-inf, -inf, -inf});	
	cout << ans << '\n';
	return 0;
}

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 12892 KB Output is correct
2 Correct 2 ms 12892 KB Output is correct
3 Correct 3 ms 12960 KB Output is correct
4 Correct 3 ms 12892 KB Output is correct
5 Correct 3 ms 12892 KB Output is correct
6 Correct 2 ms 12892 KB Output is correct
7 Correct 3 ms 12892 KB Output is correct
8 Correct 3 ms 12888 KB Output is correct
9 Correct 4 ms 12892 KB Output is correct
10 Correct 3 ms 12892 KB Output is correct
11 Correct 3 ms 12892 KB Output is correct
12 Correct 3 ms 12892 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 12892 KB Output is correct
2 Correct 2 ms 12892 KB Output is correct
3 Correct 3 ms 12960 KB Output is correct
4 Correct 3 ms 12892 KB Output is correct
5 Correct 3 ms 12892 KB Output is correct
6 Correct 2 ms 12892 KB Output is correct
7 Correct 3 ms 12892 KB Output is correct
8 Correct 3 ms 12888 KB Output is correct
9 Correct 4 ms 12892 KB Output is correct
10 Correct 3 ms 12892 KB Output is correct
11 Correct 3 ms 12892 KB Output is correct
12 Correct 3 ms 12892 KB Output is correct
13 Correct 3 ms 12892 KB Output is correct
14 Correct 3 ms 12892 KB Output is correct
15 Correct 3 ms 12892 KB Output is correct
16 Correct 3 ms 12892 KB Output is correct
17 Correct 3 ms 12892 KB Output is correct
18 Correct 3 ms 12888 KB Output is correct
19 Correct 3 ms 12892 KB Output is correct
20 Correct 3 ms 12892 KB Output is correct
21 Correct 3 ms 12892 KB Output is correct
22 Correct 3 ms 12892 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 12892 KB Output is correct
2 Correct 2 ms 12892 KB Output is correct
3 Correct 3 ms 12960 KB Output is correct
4 Correct 3 ms 12892 KB Output is correct
5 Correct 3 ms 12892 KB Output is correct
6 Correct 2 ms 12892 KB Output is correct
7 Correct 3 ms 12892 KB Output is correct
8 Correct 3 ms 12888 KB Output is correct
9 Correct 4 ms 12892 KB Output is correct
10 Correct 3 ms 12892 KB Output is correct
11 Correct 3 ms 12892 KB Output is correct
12 Correct 3 ms 12892 KB Output is correct
13 Correct 3 ms 12892 KB Output is correct
14 Correct 3 ms 12892 KB Output is correct
15 Correct 3 ms 12892 KB Output is correct
16 Correct 3 ms 12892 KB Output is correct
17 Correct 3 ms 12892 KB Output is correct
18 Correct 3 ms 12888 KB Output is correct
19 Correct 3 ms 12892 KB Output is correct
20 Correct 3 ms 12892 KB Output is correct
21 Correct 3 ms 12892 KB Output is correct
22 Correct 3 ms 12892 KB Output is correct
23 Correct 5 ms 13404 KB Output is correct
24 Correct 5 ms 13404 KB Output is correct
25 Correct 6 ms 13404 KB Output is correct
26 Correct 8 ms 13660 KB Output is correct
27 Correct 7 ms 13656 KB Output is correct
28 Correct 6 ms 14168 KB Output is correct
29 Correct 7 ms 13916 KB Output is correct
30 Correct 6 ms 13916 KB Output is correct
31 Correct 7 ms 14940 KB Output is correct

Subtask #4
43.0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 12892 KB Output is correct
2 Correct 2 ms 12892 KB Output is correct
3 Correct 3 ms 12960 KB Output is correct
4 Correct 3 ms 12892 KB Output is correct
5 Correct 3 ms 12892 KB Output is correct
6 Correct 2 ms 12892 KB Output is correct
7 Correct 3 ms 12892 KB Output is correct
8 Correct 3 ms 12888 KB Output is correct
9 Correct 4 ms 12892 KB Output is correct
10 Correct 3 ms 12892 KB Output is correct
11 Correct 3 ms 12892 KB Output is correct
12 Correct 3 ms 12892 KB Output is correct
13 Correct 3 ms 12892 KB Output is correct
14 Correct 3 ms 12892 KB Output is correct
15 Correct 3 ms 12892 KB Output is correct
16 Correct 3 ms 12892 KB Output is correct
17 Correct 3 ms 12892 KB Output is correct
18 Correct 3 ms 12888 KB Output is correct
19 Correct 3 ms 12892 KB Output is correct
20 Correct 3 ms 12892 KB Output is correct
21 Correct 3 ms 12892 KB Output is correct
22 Correct 3 ms 12892 KB Output is correct
23 Correct 5 ms 13404 KB Output is correct
24 Correct 5 ms 13404 KB Output is correct
25 Correct 6 ms 13404 KB Output is correct
26 Correct 8 ms 13660 KB Output is correct
27 Correct 7 ms 13656 KB Output is correct
28 Correct 6 ms 14168 KB Output is correct
29 Correct 7 ms 13916 KB Output is correct
30 Correct 6 ms 13916 KB Output is correct
31 Correct 7 ms 14940 KB Output is correct
32 Correct 24 ms 17596 KB Output is correct
33 Correct 25 ms 17488 KB Output is correct
34 Correct 26 ms 17500 KB Output is correct
35 Correct 135 ms 31832 KB Output is correct
36 Correct 149 ms 32084 KB Output is correct
37 Correct 144 ms 31688 KB Output is correct
38 Correct 113 ms 39608 KB Output is correct
39 Correct 90 ms 37576 KB Output is correct
40 Correct 97 ms 34916 KB Output is correct
41 Correct 144 ms 45756 KB Output is correct