oj.uz

Submission #110856

# Submission time Handle Problem Language Result Execution time Memory
110856 2019-05-12T15:29:06 Z user202729 Beads and wires (APIO14_beads) C++17
100 / 100
 354 ms 22508 KB 
#include<iostream>
#include<cassert>
#include<vector>
#include<array>
#include<algorithm>
#include<climits>

struct edge{
	int n,w;
};
static std::vector<std::vector<edge>> ad;
static std::vector<int> parw;

static std::vector<int> f0,f1,g0,g1;
// f_rf[i]: max value of subtree rooted at i,
// g_rf[i] = ~ but also include edge from i to parent
// where rf = must the component be done first? (0/1)

static auto const b1=[](edge e){
	int j=e.n;
	return f1[j]+e.w-g0[j];
};
static auto const b2=[](edge e){
	int j=e.n;
	return f0[j]+e.w-g0[j];
};

static auto const compb1=[](edge a,edge b){
	return b1(a)<b1(b);
};
static auto const compb2=[](edge a,edge b){
	return b2(a)<b2(b);
};

static void dfs(int i){
	int sg0=0; // sum of g0[j] for j in child[i]
	int m=INT_MIN; // max cost when use f0 instead of g0 and pair the edge
	int m1=INT_MIN; // max cost when use f**1** instead of g0 and pair the edge

	int mgf=INT_MIN;

	for(edge e:ad[i]){
		int j=e.n,w=e.w;
		// par[j]=i;
		parw[j]=e.w;
		ad[j].erase(
				std::find_if(begin(ad[j]),end(ad[j]),[i](edge e){
					return e.n==i;
					}));
		dfs(j);

		sg0+=g0[j];
		m=std::max(m,f0[j]-g0[j]+w);
		m1=std::max(m1,f1[j]-g0[j]+w);

		mgf=std::max(mgf,g1[j]-g0[j]);
	}

	f0[i]=sg0; // i cannot be the center of any pair

	g0[i]=sg0;
	if(m+parw[i]>0)g0[i]+=m+parw[i];

	f1[i]=sg0; // if i is constructed first

	if(ad[i].size()>=2){ // otherwise, if i is a pair center, one get benefit f1+w-g0 (B1) and another get f0+w-g0 (B2)

		// case 1: best B1 get B1, best B2 (except <) get B2
		auto const& ai=ad[i];
		auto bb1=std::max_element(begin(ai),end(ai),compb1);
		int mb2=INT_MIN;
		if(bb1!=begin(ai))
			mb2=std::max(mb2,
				b2(*std::max_element(begin(ai),bb1,compb2)));
		if(bb1+1!=end(ai))
			mb2=std::max(mb2,
				b2(*std::max_element(bb1+1,end(ai),compb2)));
		f1[i]=std::max(f1[i],sg0+b1(*bb1)+mb2);

		// case 2: best B1 get B2, best B1 of rest get B1
		int mb1r=INT_MIN;
		if(bb1!=begin(ai))
			mb1r=std::max(mb1r,
				b1(*std::max_element(begin(ai),bb1,compb1)));
		if(bb1+1!=end(ai))
			mb1r=std::max(mb1r,
				b1(*std::max_element(bb1+1,end(ai),compb1)));
		f1[i]=std::max(f1[i],sg0+b2(*bb1)+mb1r);
	}

	// otherwise (i is not constructed first and not paired) just add max g1-g0
	f1[i]=std::max(f1[i],sg0+mgf);

	g1[i]=f1[i];
	// in case i is a pair center with one leg upward,
	// the first vertex constructed must be inside the other leg
	g1[i]=std::max(g1[i],sg0+m1+parw[i]);

	assert(f1[i]>=f0[i]);
	assert(g1[i]>=g0[i]);
	assert(g0[i]>=f0[i]);
	assert(g1[i]>=f1[i]);
}

int main(){
	int n;std::cin>>n;
	ad.resize(n);
	for(int _=n-1;_--;){
		int a,b,w;std::cin>>a>>b>>w;--a;--b;
		ad[a].push_back({b,w});
		ad[b].push_back({a,w});
	}
	// par.resize(n);
	parw.resize(n);
	f0.resize(n);
	f1.resize(n);
	g0.resize(n);
	g1.resize(n);
	dfs(0);
	std::cout<<f1[0]<<'\n';
}

/*
5
1 2 10
1 3 40
1 4 15
1 5 20

10
4 10 2
1 2 21
1 3 13
6 7 1
7 9 5
2 4 3
2 5 8
1 6 55
6 8 34
*/

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 4 ms 256 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 256 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 256 KB Output is correct
9 Correct 2 ms 384 KB Output is correct
10 Correct 2 ms 384 KB Output is correct
11 Correct 2 ms 256 KB Output is correct
12 Correct 2 ms 256 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 4 ms 256 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 256 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 256 KB Output is correct
9 Correct 2 ms 384 KB Output is correct
10 Correct 2 ms 384 KB Output is correct
11 Correct 2 ms 256 KB Output is correct
12 Correct 2 ms 256 KB Output is correct
13 Correct 2 ms 384 KB Output is correct
14 Correct 2 ms 384 KB Output is correct
15 Correct 2 ms 384 KB Output is correct
16 Correct 2 ms 384 KB Output is correct
17 Correct 3 ms 384 KB Output is correct
18 Correct 2 ms 384 KB Output is correct
19 Correct 2 ms 256 KB Output is correct
20 Correct 2 ms 384 KB Output is correct
21 Correct 2 ms 384 KB Output is correct
22 Correct 2 ms 384 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 4 ms 256 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 256 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 256 KB Output is correct
9 Correct 2 ms 384 KB Output is correct
10 Correct 2 ms 384 KB Output is correct
11 Correct 2 ms 256 KB Output is correct
12 Correct 2 ms 256 KB Output is correct
13 Correct 2 ms 384 KB Output is correct
14 Correct 2 ms 384 KB Output is correct
15 Correct 2 ms 384 KB Output is correct
16 Correct 2 ms 384 KB Output is correct
17 Correct 3 ms 384 KB Output is correct
18 Correct 2 ms 384 KB Output is correct
19 Correct 2 ms 256 KB Output is correct
20 Correct 2 ms 384 KB Output is correct
21 Correct 2 ms 384 KB Output is correct
22 Correct 2 ms 384 KB Output is correct
23 Correct 6 ms 768 KB Output is correct
24 Correct 7 ms 768 KB Output is correct
25 Correct 6 ms 768 KB Output is correct
26 Correct 12 ms 1152 KB Output is correct
27 Correct 13 ms 1152 KB Output is correct
28 Correct 11 ms 1152 KB Output is correct
29 Correct 11 ms 1152 KB Output is correct
30 Correct 12 ms 1152 KB Output is correct
31 Correct 14 ms 1664 KB Output is correct

Subtask #4
43.0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 4 ms 256 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 256 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 256 KB Output is correct
9 Correct 2 ms 384 KB Output is correct
10 Correct 2 ms 384 KB Output is correct
11 Correct 2 ms 256 KB Output is correct
12 Correct 2 ms 256 KB Output is correct
13 Correct 2 ms 384 KB Output is correct
14 Correct 2 ms 384 KB Output is correct
15 Correct 2 ms 384 KB Output is correct
16 Correct 2 ms 384 KB Output is correct
17 Correct 3 ms 384 KB Output is correct
18 Correct 2 ms 384 KB Output is correct
19 Correct 2 ms 256 KB Output is correct
20 Correct 2 ms 384 KB Output is correct
21 Correct 2 ms 384 KB Output is correct
22 Correct 2 ms 384 KB Output is correct
23 Correct 6 ms 768 KB Output is correct
24 Correct 7 ms 768 KB Output is correct
25 Correct 6 ms 768 KB Output is correct
26 Correct 12 ms 1152 KB Output is correct
27 Correct 13 ms 1152 KB Output is correct
28 Correct 11 ms 1152 KB Output is correct
29 Correct 11 ms 1152 KB Output is correct
30 Correct 12 ms 1152 KB Output is correct
31 Correct 14 ms 1664 KB Output is correct
32 Correct 66 ms 4344 KB Output is correct
33 Correct 71 ms 4344 KB Output is correct
34 Correct 70 ms 4344 KB Output is correct
35 Correct 335 ms 16472 KB Output is correct
36 Correct 341 ms 16504 KB Output is correct
37 Correct 354 ms 16376 KB Output is correct
38 Correct 272 ms 16748 KB Output is correct
39 Correct 293 ms 16868 KB Output is correct
40 Correct 282 ms 16736 KB Output is correct
41 Correct 331 ms 22508 KB Output is correct