oj.uz

Submission #646171

# Submission time Handle Problem Language Result Execution time Memory
646171 2022-09-28T21:56:55 Z dutinmeow Fireworks (APIO16_fireworks) C++17
100 / 100
 207 ms 80520 KB 
#include <bits/stdc++.h>
using namespace std;

template<typename T>
struct Line {
	T m, b;

	Line() : m(T()), b(T()) {}

	Line(T _m, T _b) : m(_m), b(_b) {}

	T operator()(long long x) { return m * x + b; }

	friend long double intersect(const Line &l1, const Line &l2) { 
		return (long double)(l2.b - l1.b) / (long double)(l1.m - l2.m); 
	}

	friend ostream& operator<<(ostream &os, const Line &l) { 
		return os << '{' << l.m << "x + " << l.b << '}'; 
	}
};

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);

	int N, M;
	cin >> N >> M;
	M += N;
	vector<long long> C(M);	
	vector<vector<int>> T(M);
	for (int i = 1; i < M; i++) {
		int p;
		long long c;
		cin >> p >> c;
		T[p - 1].push_back(i);
		C[i] = c;
	}

	vector<Line<long long>> L(M);
	vector<priority_queue<long long>> Q(M);

	const auto dfs = [&](const auto &self, int u) -> void {
		priority_queue<long long> &pq = Q[u];
		if (T[u].empty()) {
			L[u].m = 1, L[u].b = -C[u];
			pq.push(C[u]);
			pq.push(C[u]);
			return;
		}

		for (int v : T[u]) {
			self(self, v);
			L[u].m += L[v].m, L[u].b += L[v].b;
			if (Q[v].size() > pq.size())
				pq.swap(Q[v]);
			while (!Q[v].empty()) {
				pq.push(Q[v].top());
				Q[v].pop();
			}
		}
		while (L[u].m > 1) { // slope is never greater than 1
			long long x = pq.top(); pq.pop();
			L[u].m--, L[u].b += x; // compensate for change in slope
		}
		long long t0 = pq.top(); pq.pop(); // location of slope 0 -> 1
		long long t1 = pq.top(); pq.pop(); // location of slope -1 -> 0
		pq.push(t0 + C[u]); // slope = -1 section increases by C[u]
		pq.push(t1 + C[u]); // slope = 0 section increases by C[u]
		L[u].b -= C[u]; // L[u].m = 1, compensate for adding C[u] to previous sections
	};

	dfs(dfs, 0);

	// since f(x) is CCU <-> f"(x) >= 0, max f(x) for all x is at f'(x) = 0
	priority_queue<long long> &pq = Q[0];
	while (L[0].m > 0) { 
		long long x = pq.top(); pq.pop();
		L[0].m--, L[0].b += x;
	}
	cout << L[0].b << '\n';
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 316 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 212 KB Output is correct

Subtask #2
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 316 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 316 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 0 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 0 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 316 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 340 KB Output is correct
31 Correct 1 ms 468 KB Output is correct
32 Correct 1 ms 468 KB Output is correct
33 Correct 2 ms 576 KB Output is correct
34 Correct 2 ms 724 KB Output is correct
35 Correct 2 ms 720 KB Output is correct
36 Correct 2 ms 844 KB Output is correct
37 Correct 3 ms 980 KB Output is correct
38 Correct 3 ms 972 KB Output is correct
39 Correct 3 ms 980 KB Output is correct
40 Correct 2 ms 1616 KB Output is correct
41 Correct 3 ms 1620 KB Output is correct
42 Correct 2 ms 852 KB Output is correct
43 Correct 3 ms 1236 KB Output is correct
44 Correct 3 ms 1108 KB Output is correct
45 Correct 3 ms 1108 KB Output is correct
46 Correct 3 ms 1116 KB Output is correct
47 Correct 3 ms 1108 KB Output is correct
48 Correct 3 ms 980 KB Output is correct
49 Correct 3 ms 972 KB Output is correct
50 Correct 2 ms 852 KB Output is correct
51 Correct 2 ms 852 KB Output is correct
52 Correct 3 ms 928 KB Output is correct
53 Correct 3 ms 980 KB Output is correct
54 Correct 3 ms 980 KB Output is correct

Subtask #4
45.0 / 45.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 316 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 0 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 0 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 316 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 340 KB Output is correct
31 Correct 1 ms 468 KB Output is correct
32 Correct 1 ms 468 KB Output is correct
33 Correct 2 ms 576 KB Output is correct
34 Correct 2 ms 724 KB Output is correct
35 Correct 2 ms 720 KB Output is correct
36 Correct 2 ms 844 KB Output is correct
37 Correct 3 ms 980 KB Output is correct
38 Correct 3 ms 972 KB Output is correct
39 Correct 3 ms 980 KB Output is correct
40 Correct 2 ms 1616 KB Output is correct
41 Correct 3 ms 1620 KB Output is correct
42 Correct 2 ms 852 KB Output is correct
43 Correct 3 ms 1236 KB Output is correct
44 Correct 3 ms 1108 KB Output is correct
45 Correct 3 ms 1108 KB Output is correct
46 Correct 3 ms 1116 KB Output is correct
47 Correct 3 ms 1108 KB Output is correct
48 Correct 3 ms 980 KB Output is correct
49 Correct 3 ms 972 KB Output is correct
50 Correct 2 ms 852 KB Output is correct
51 Correct 2 ms 852 KB Output is correct
52 Correct 3 ms 928 KB Output is correct
53 Correct 3 ms 980 KB Output is correct
54 Correct 3 ms 980 KB Output is correct
55 Correct 7 ms 2116 KB Output is correct
56 Correct 26 ms 7160 KB Output is correct
57 Correct 53 ms 12056 KB Output is correct
58 Correct 72 ms 15320 KB Output is correct
59 Correct 97 ms 20356 KB Output is correct
60 Correct 123 ms 25412 KB Output is correct
61 Correct 146 ms 29364 KB Output is correct
62 Correct 160 ms 32192 KB Output is correct
63 Correct 202 ms 38100 KB Output is correct
64 Correct 207 ms 40000 KB Output is correct
65 Correct 109 ms 80520 KB Output is correct
66 Correct 108 ms 80444 KB Output is correct
67 Correct 103 ms 38092 KB Output is correct
68 Correct 144 ms 60484 KB Output is correct
69 Correct 183 ms 56928 KB Output is correct
70 Correct 170 ms 56892 KB Output is correct
71 Correct 163 ms 50400 KB Output is correct
72 Correct 159 ms 50832 KB Output is correct
73 Correct 143 ms 46920 KB Output is correct
74 Correct 144 ms 47160 KB Output is correct
75 Correct 146 ms 45940 KB Output is correct
76 Correct 144 ms 46012 KB Output is correct
77 Correct 153 ms 45224 KB Output is correct
78 Correct 151 ms 43296 KB Output is correct
79 Correct 135 ms 44872 KB Output is correct