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Submission #265554

# Submission time Handle Problem Language Result Execution time Memory
265554 2020-08-15T01:05:29 Z square1001 Beads and wires (APIO14_beads) C++14
100 / 100
 172 ms 23408 KB 
// APIO 2014 Problem 3 - Beads and Wires

#include <vector>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std;
const int inf = 2012345678;
int main() {
	// step #1. read input
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	int N;
	cin >> N;
	vector<int> ga(N - 1), gb(N - 1), gw(N - 1);
	for(int i = 0; i < N - 1; ++i) {
		cin >> ga[i] >> gb[i] >> gw[i];
		--ga[i], --gb[i];
	}
	// step #2. construct a graph
	vector<int> sep(N + 1);
	for(int i = 0; i < N - 1; ++i) {
		++sep[ga[i] + 1];
		++sep[gb[i] + 1];
	}
	for(int i = 0; i < N; ++i) {
		sep[i + 1] += sep[i];
	}
	vector<int> ctr(sep);
	vector<int> to(2 * N - 2), cost(2 * N - 2);
	for(int i = 0; i < N - 1; ++i) {
		to[ctr[ga[i]]] = gb[i]; cost[ctr[ga[i]]++] = gw[i];
		to[ctr[gb[i]]] = ga[i]; cost[ctr[gb[i]]++] = gw[i];
	}
	// step #3. calculation (zenhoui-tree-dp part 1)
	vector<int> par(N);
	vector<pair<int, int> > dp1(N);
	function<void(int, int)> solve1 = [&](int pos, int pre) {
		// returns = (no mid-blue, one mid-blue)
		par[pos] = pre;
		int sumcost = 0, delta = -inf;
		for(int i = sep[pos]; i < sep[pos + 1]; ++i) {
			if(to[i] == pre) continue;
			solve1(to[i], pos);
			sumcost += max(dp1[to[i]].first, dp1[to[i]].second + cost[i]);
			delta = max(delta, min(dp1[to[i]].first - dp1[to[i]].second, cost[i]));
		}
		dp1[pos] = make_pair(sumcost, sumcost + delta);
	};
	solve1(0, -1);
	// step #4. calculation (zenhoui-tree-dp part 2)
	vector<pair<int, int> > dp2(N);
	function<void(int, int)> solve2 = [&](int pos, int pre) {
		int sumcost = 0;
		vector<pair<int, int> > deltas;
		for(int i = sep[pos]; i < sep[pos + 1]; ++i) {
			if(to[i] == pre) {
				sumcost += max(dp2[pos].first, dp2[pos].second + cost[i]);
				deltas.push_back(make_pair(min(dp2[pos].first - dp2[pos].second, cost[i]), -1));
			}
			else {
				sumcost += max(dp1[to[i]].first, dp1[to[i]].second + cost[i]);
				deltas.push_back(make_pair(min(dp1[to[i]].first - dp1[to[i]].second, cost[i]), i));
			}
		}
		sort(deltas.begin(), deltas.end(), greater<pair<int, int> >());
		for(int i = sep[pos]; i < sep[pos + 1]; ++i) {
			if(to[i] == pre) continue;
			pair<int, int> dm = make_pair(min(dp1[to[i]].first - dp1[to[i]].second, cost[i]), i);
			int sc = sumcost - max(dp1[to[i]].first, dp1[to[i]].second + cost[i]);
			dp2[to[i]] = make_pair(sc, sc + (dm != deltas[0] ? deltas[0].first : (deltas.size() != 1 ? deltas[1].first : -inf)));
			solve2(to[i], pos);
		}
	};
	dp2[0] = make_pair(0, -inf);
	solve2(0, -1);
	// step #5. calculate and print the answer
	int ans = 0;
	for(int i = 0; i < N; ++i) {
		int sumcost = 0;
		for(int j = sep[i]; j < sep[i + 1]; ++j) {
			if(to[j] == par[i]) {
				sumcost += max(dp2[i].first, dp2[i].second + cost[j]);
			}
			else {
				sumcost += max(dp1[to[j]].first, dp1[to[j]].second + cost[j]);
			}
		}
		ans = max(ans, sumcost);
	}
	cout << ans << endl;
	return 0;
}

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 288 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 0 ms 384 KB Output is correct
6 Correct 0 ms 384 KB Output is correct
7 Correct 1 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 0 ms 384 KB Output is correct
12 Correct 0 ms 384 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 288 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 0 ms 384 KB Output is correct
6 Correct 0 ms 384 KB Output is correct
7 Correct 1 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 0 ms 384 KB Output is correct
12 Correct 0 ms 384 KB Output is correct
13 Correct 0 ms 384 KB Output is correct
14 Correct 0 ms 384 KB Output is correct
15 Correct 1 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 1 ms 384 KB Output is correct
19 Correct 0 ms 384 KB Output is correct
20 Correct 1 ms 384 KB Output is correct
21 Correct 0 ms 384 KB Output is correct
22 Correct 0 ms 384 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 288 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 0 ms 384 KB Output is correct
6 Correct 0 ms 384 KB Output is correct
7 Correct 1 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 0 ms 384 KB Output is correct
12 Correct 0 ms 384 KB Output is correct
13 Correct 0 ms 384 KB Output is correct
14 Correct 0 ms 384 KB Output is correct
15 Correct 1 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 1 ms 384 KB Output is correct
19 Correct 0 ms 384 KB Output is correct
20 Correct 1 ms 384 KB Output is correct
21 Correct 0 ms 384 KB Output is correct
22 Correct 0 ms 384 KB Output is correct
23 Correct 3 ms 640 KB Output is correct
24 Correct 3 ms 640 KB Output is correct
25 Correct 4 ms 640 KB Output is correct
26 Correct 6 ms 896 KB Output is correct
27 Correct 6 ms 1024 KB Output is correct
28 Correct 6 ms 1280 KB Output is correct
29 Correct 6 ms 1152 KB Output is correct
30 Correct 6 ms 1152 KB Output is correct
31 Correct 6 ms 1792 KB Output is correct

Subtask #4
43.0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 288 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 0 ms 384 KB Output is correct
6 Correct 0 ms 384 KB Output is correct
7 Correct 1 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 0 ms 384 KB Output is correct
12 Correct 0 ms 384 KB Output is correct
13 Correct 0 ms 384 KB Output is correct
14 Correct 0 ms 384 KB Output is correct
15 Correct 1 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 1 ms 384 KB Output is correct
19 Correct 0 ms 384 KB Output is correct
20 Correct 1 ms 384 KB Output is correct
21 Correct 0 ms 384 KB Output is correct
22 Correct 0 ms 384 KB Output is correct
23 Correct 3 ms 640 KB Output is correct
24 Correct 3 ms 640 KB Output is correct
25 Correct 4 ms 640 KB Output is correct
26 Correct 6 ms 896 KB Output is correct
27 Correct 6 ms 1024 KB Output is correct
28 Correct 6 ms 1280 KB Output is correct
29 Correct 6 ms 1152 KB Output is correct
30 Correct 6 ms 1152 KB Output is correct
31 Correct 6 ms 1792 KB Output is correct
32 Correct 31 ms 3832 KB Output is correct
33 Correct 36 ms 3840 KB Output is correct
34 Correct 31 ms 3832 KB Output is correct
35 Correct 152 ms 14840 KB Output is correct
36 Correct 164 ms 14968 KB Output is correct
37 Correct 149 ms 14840 KB Output is correct
38 Correct 140 ms 17136 KB Output is correct
39 Correct 139 ms 17008 KB Output is correct
40 Correct 140 ms 16628 KB Output is correct
41 Correct 172 ms 23408 KB Output is correct