#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MAXN (200005)
ll N,D;
vector<pair<ll,ll> > sortbydepth;
vector<pair<ll,ll> > DIST[MAXN];
vector<pair<ll,ll> > v[MAXN];
ll sub[MAXN], par[MAXN], lvl[MAXN], dist[MAXN][20], m[MAXN];
bool cannot[MAXN];
void calcdepth(ll x,ll p,ll level){
sortbydepth.push_back({level,x});
for(auto u : v[x]){
if(u.first != p){
calcdepth(u.first,x,level + 1);
}
}
}
ll dfs1(ll x,ll p,ll l){
sub[x] = 1;
for(auto u : v[x]){
if(u.first != p && lvl[u.first] == -1){ //unvisited
sub[x] += dfs1(u.first,x,l);
}
}
return sub[x];
}
ll dfs2(ll x,ll p,ll siz){ //siz is total size of this centroid tree
for(auto u : v[x]){
if(u.first != p && lvl[u.first] == -1 && sub[u.first] > siz / 2){
return dfs2(u.first,x,siz); //remember that siz remains constant
}
}
return x;
}
void dfsdist(ll x,ll p,ll centroid,ll curlvl,ll curdist){
dist[x][curlvl] = curdist;
DIST[centroid].push_back({curdist,x});
for(auto u : v[x]){
if(u.first != p && lvl[u.first] == -1){ //unvisited
dfsdist(u.first,x,centroid,curlvl,curdist + u.second);
//Note: curlvl is unchanged since we are moving down so
//the relative lvl has already changed
}
}
}
void build(ll x,ll p,ll l){
ll siz = dfs1(x,p,l);
ll cent = dfs2(x,p,siz);
if(p == -1) p = cent;
par[cent] = p;
lvl[cent] = l;
dfsdist(cent,-1,cent,l,0);
sort(DIST[cent].begin(),DIST[cent].end(),greater<pair<ll,ll> >());
for(auto u : v[cent]){
if(lvl[u.first] == -1){ //unvisited
build(u.first,cent,l + 1);
}
}
}
int main() {
ios_base::sync_with_stdio(false);cin.tie(0);
cin>>N>>D;
for(ll i = 1;i < N;i++){
ll p;
cin>>p;
v[p].push_back({i,1});
v[i].push_back({p,1});
}
calcdepth(0,-1,0);
sort(sortbydepth.begin(),sortbydepth.end(),greater<pair<ll,ll> >());
for(ll i = 0;i < MAXN;i++){
for(ll j = 0;j < 20;j++){
dist[i][j] = 1e18;
}
}
memset(lvl,-1,sizeof(lvl)); //need lvl to find dist[i][lvl]
build(0,-1,0);
for(ll i = 0;i < MAXN;i++){
m[i] = 1e18;
}
ll ans = 0;
for(auto u : sortbydepth){
if(cannot[u.second]) continue;
ll x = u.second;
while(true){
ll distjumped = dist[u.second][lvl[x]];
while(!DIST[x].empty()){
if(DIST[x].back().first + distjumped < D){ //node DIST[x].back().second cannot be picked as distance < D from a node that is already selected, we can greedily prove that it is not optimal to delete the selected node (with greater depth) and replace it with node DIST[x].back().second (with lower depth)
cannot[DIST[x].back().second] = true;
DIST[x].pop_back();
}else{
break;
}
}
if(par[x] == x) break; //x is the root node in the centroid tree
x = par[x]; //in the centroid tree, height is at most log2(N) so node x has at most log2(N) ancestors in total
}
ans++;
}
cout<<ans<<'\n';
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
12 ms |
47192 KB |
Output is correct |
| 2 |
Correct |
11 ms |
47192 KB |
Output is correct |
| 3 |
Correct |
11 ms |
47196 KB |
Output is correct |
| 4 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 5 |
Correct |
10 ms |
47196 KB |
Output is correct |
| 6 |
Correct |
11 ms |
47448 KB |
Output is correct |
| 7 |
Correct |
10 ms |
47196 KB |
Output is correct |
| 8 |
Correct |
11 ms |
47376 KB |
Output is correct |
| 9 |
Correct |
10 ms |
47436 KB |
Output is correct |
| 10 |
Correct |
11 ms |
47412 KB |
Output is correct |
| 11 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 12 |
Correct |
11 ms |
47372 KB |
Output is correct |
| 13 |
Correct |
11 ms |
47448 KB |
Output is correct |
| 14 |
Correct |
10 ms |
47388 KB |
Output is correct |
| 15 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 16 |
Correct |
12 ms |
47452 KB |
Output is correct |
| 17 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 18 |
Correct |
12 ms |
47448 KB |
Output is correct |
| 19 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 20 |
Correct |
12 ms |
47440 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
12 ms |
47192 KB |
Output is correct |
| 2 |
Correct |
11 ms |
47192 KB |
Output is correct |
| 3 |
Correct |
11 ms |
47196 KB |
Output is correct |
| 4 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 5 |
Correct |
10 ms |
47196 KB |
Output is correct |
| 6 |
Correct |
11 ms |
47448 KB |
Output is correct |
| 7 |
Correct |
10 ms |
47196 KB |
Output is correct |
| 8 |
Correct |
11 ms |
47376 KB |
Output is correct |
| 9 |
Correct |
10 ms |
47436 KB |
Output is correct |
| 10 |
Correct |
11 ms |
47412 KB |
Output is correct |
| 11 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 12 |
Correct |
11 ms |
47372 KB |
Output is correct |
| 13 |
Correct |
11 ms |
47448 KB |
Output is correct |
| 14 |
Correct |
10 ms |
47388 KB |
Output is correct |
| 15 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 16 |
Correct |
12 ms |
47452 KB |
Output is correct |
| 17 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 18 |
Correct |
12 ms |
47448 KB |
Output is correct |
| 19 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 20 |
Correct |
12 ms |
47440 KB |
Output is correct |
| 21 |
Correct |
13 ms |
47964 KB |
Output is correct |
| 22 |
Correct |
12 ms |
47448 KB |
Output is correct |
| 23 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 24 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 25 |
Correct |
14 ms |
47496 KB |
Output is correct |
| 26 |
Correct |
14 ms |
47408 KB |
Output is correct |
| 27 |
Correct |
12 ms |
47452 KB |
Output is correct |
| 28 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 29 |
Correct |
12 ms |
47768 KB |
Output is correct |
| 30 |
Correct |
12 ms |
47564 KB |
Output is correct |
| 31 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 32 |
Correct |
11 ms |
47708 KB |
Output is correct |
| 33 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 34 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 35 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 36 |
Correct |
12 ms |
47704 KB |
Output is correct |
| 37 |
Correct |
11 ms |
47708 KB |
Output is correct |
| 38 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 39 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 40 |
Correct |
14 ms |
47960 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
12 ms |
47192 KB |
Output is correct |
| 2 |
Correct |
11 ms |
47192 KB |
Output is correct |
| 3 |
Correct |
11 ms |
47196 KB |
Output is correct |
| 4 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 5 |
Correct |
10 ms |
47196 KB |
Output is correct |
| 6 |
Correct |
11 ms |
47448 KB |
Output is correct |
| 7 |
Correct |
10 ms |
47196 KB |
Output is correct |
| 8 |
Correct |
11 ms |
47376 KB |
Output is correct |
| 9 |
Correct |
10 ms |
47436 KB |
Output is correct |
| 10 |
Correct |
11 ms |
47412 KB |
Output is correct |
| 11 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 12 |
Correct |
11 ms |
47372 KB |
Output is correct |
| 13 |
Correct |
11 ms |
47448 KB |
Output is correct |
| 14 |
Correct |
10 ms |
47388 KB |
Output is correct |
| 15 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 16 |
Correct |
12 ms |
47452 KB |
Output is correct |
| 17 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 18 |
Correct |
12 ms |
47448 KB |
Output is correct |
| 19 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 20 |
Correct |
12 ms |
47440 KB |
Output is correct |
| 21 |
Correct |
13 ms |
47964 KB |
Output is correct |
| 22 |
Correct |
12 ms |
47448 KB |
Output is correct |
| 23 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 24 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 25 |
Correct |
14 ms |
47496 KB |
Output is correct |
| 26 |
Correct |
14 ms |
47408 KB |
Output is correct |
| 27 |
Correct |
12 ms |
47452 KB |
Output is correct |
| 28 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 29 |
Correct |
12 ms |
47768 KB |
Output is correct |
| 30 |
Correct |
12 ms |
47564 KB |
Output is correct |
| 31 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 32 |
Correct |
11 ms |
47708 KB |
Output is correct |
| 33 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 34 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 35 |
Correct |
11 ms |
47452 KB |
Output is correct |
| 36 |
Correct |
12 ms |
47704 KB |
Output is correct |
| 37 |
Correct |
11 ms |
47708 KB |
Output is correct |
| 38 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 39 |
Correct |
12 ms |
47708 KB |
Output is correct |
| 40 |
Correct |
14 ms |
47960 KB |
Output is correct |
| 41 |
Correct |
196 ms |
74420 KB |
Output is correct |
| 42 |
Correct |
200 ms |
74044 KB |
Output is correct |
| 43 |
Correct |
203 ms |
74412 KB |
Output is correct |
| 44 |
Correct |
174 ms |
74048 KB |
Output is correct |
| 45 |
Correct |
176 ms |
73496 KB |
Output is correct |
| 46 |
Correct |
517 ms |
100656 KB |
Output is correct |
| 47 |
Correct |
504 ms |
101804 KB |
Output is correct |
| 48 |
Correct |
466 ms |
103824 KB |
Output is correct |
| 49 |
Correct |
489 ms |
104232 KB |
Output is correct |
| 50 |
Correct |
119 ms |
68536 KB |
Output is correct |
| 51 |
Correct |
148 ms |
68692 KB |
Output is correct |
| 52 |
Correct |
122 ms |
68336 KB |
Output is correct |
| 53 |
Correct |
302 ms |
91952 KB |
Output is correct |
| 54 |
Correct |
285 ms |
89652 KB |
Output is correct |
| 55 |
Correct |
277 ms |
90180 KB |
Output is correct |
| 56 |
Correct |
13 ms |
48212 KB |
Output is correct |
| 57 |
Correct |
36 ms |
56912 KB |
Output is correct |
| 58 |
Correct |
174 ms |
93516 KB |
Output is correct |
| 59 |
Correct |
531 ms |
136512 KB |
Output is correct |
| 60 |
Correct |
164 ms |
76552 KB |
Output is correct |
| 61 |
Correct |
245 ms |
92144 KB |
Output is correct |
