oj.uz

Submission #706226

# Submission time Handle Problem Language Result Execution time Memory
706226 2023-03-06T06:52:16 Z alvingogo Mergers (JOI19_mergers) C++14
10 / 100
 267 ms 29292 KB 
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#define AquA cin.tie(0);ios_base::sync_with_stdio(0);
#define fs first
#define sc second
#define p_q priority_queue
using namespace std;

/* Merger:
first, find out the LCA of all stages

second, for each node find out whether we can cut the edge its father to the node, which can be done by storing every node's stage's LCA
if all its subtree's node's stage's LCA is in its subtree then we can cut it

last, for all the node we can build a virtual tree
we know that if we see the edges between virtual tree's node to node as a stage, the answer won't change

if we merge two stages, then the nodes on the path of the two stages are all uncuttable, so we only have to find out the minimum path cover

and i think it's equal to (the number of leaf (deg == 1) + 1) / 2, done!

guess a few coding will lead us to the ac :happy_mention:
*/
vector<int> e;
struct no{
	vector<int> ch,ch2;
	int as[21]={0};
	int dep=-1;
	int md=1e9;
	int in=0;
	int t;
};
vector<no> v;
vector<int> can;
int cnt=0;
void dfs(int r,int f){
	v[r].dep=v[f].dep+1;
	v[r].as[0]=f;
	v[r].in=cnt;
	cnt++;
	for(auto h:v[r].ch){
		if(h!=f){
			dfs(h,r);
		}
	}
}
void dfs2(int r,int f){
	v[r].md=v[e[v[r].t]].dep;
	for(auto h:v[r].ch){
		if(h!=f){
			dfs2(h,r);
			v[r].md=min(v[r].md,v[h].md);
		}
	}
	if(r!=f){
		if(v[r].md>=v[r].dep){
			can.push_back(r);
		}
	}
}
int lca(int a,int b){
	if(v[a].dep<v[b].dep){
		swap(a,b);
	}
	for(int i=20;i>=0;i--){
		if(v[v[a].as[i]].dep>=v[b].dep){
			a=v[a].as[i];
		}
	}
	if(a==b){
		return a;
	}
	for(int i=20;i>=0;i--){
		if(v[a].as[i]!=v[b].as[i]){
			a=v[a].as[i];
			b=v[b].as[i];
		}
	}
	return v[a].as[0];
}
bool cmp(int a,int b){
	return v[a].in<v[b].in;
}
int bvt(vector<int> x,int flag){
	sort(x.begin(),x.end(),cmp);
	int u=x.size();
	for(int i=1;i<u;i++){
		x.push_back(lca(x[i],x[i-1]));
	}
	sort(x.begin(),x.end(),cmp);
	if(flag==1){	
		x.erase(unique(x.begin(),x.end()),x.end());
		u=x.size();
		for(int i=0;i<u-1;i++){
			int z=lca(x[i],x[i+1]);
			v[z].ch2.push_back(x[i+1]);
			v[x[i+1]].ch2.push_back(z);
		}
		can=x;
	}
	return x[0];
}
int main(){
	AquA;
	int n,k;
	cin >> n >> k;
	v.resize(n);
	e.resize(k);
	for(int i=1;i<n;i++){
		int a,b;
		cin >> a >> b;
		a--;
		b--;
		v[a].ch.push_back(b);
		v[b].ch.push_back(a);
	}
	dfs(0,0);
	for(int i=1;i<21;i++){
		for(int j=0;j<n;j++){
			v[j].as[i]=v[v[j].as[i-1]].as[i-1];
		}
	}
	vector<vector<int> > gg(k);
	for(int i=0;i<n;i++){
		int a;
		cin >> a;
		a--;
		v[i].t=a;
		gg[a].push_back(i);
	}
	for(int i=0;i<k;i++){
		e[i]=bvt(gg[i],0);
	}
	dfs2(0,0);
	if(!can.size()){
		cout << 0 << "\n";
		return 0;
	}
	if(can.size()==1){
		cout << 1 << "\n";
		return 0;
	}
	bvt(can,1);
	int ans=0;
	for(auto h:can){
		if(v[h].ch2.size()==1){
			ans++;
		}
	}
	cout << (ans+1)/2 << '\n';
	return 0;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 324 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 320 KB Output is correct
8 Correct 1 ms 320 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 0 ms 340 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct

Subtask #2
0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 324 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 320 KB Output is correct
8 Correct 1 ms 320 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 0 ms 340 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Incorrect 0 ms 340 KB Output isn't correct
26 Halted 0 ms 0 KB -

Subtask #3
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 324 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 320 KB Output is correct
8 Correct 1 ms 320 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 0 ms 340 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Incorrect 0 ms 340 KB Output isn't correct
26 Halted 0 ms 0 KB -

Subtask #4
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 122 ms 19332 KB Output is correct
2 Incorrect 267 ms 29292 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #5
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 324 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 320 KB Output is correct
8 Correct 1 ms 320 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 0 ms 340 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Incorrect 0 ms 340 KB Output isn't correct
26 Halted 0 ms 0 KB -