CF 1311 E. Construct the Binary Tree (Tree)

link

 Solution: https://codeforces.com/blog/entry/74224

#include <bits/stdc++.h>
# define LL long long
using namespace std;

string s;

int main(){
    int T;
    scanf("%d", &T);
    while(T--){
        int n,d;
        scanf("%d %d", &n, &d);
        int hi=n*(n-1)/2;
        int lo=0;
        int h=0;
        for(int i=2;i<=n;++i){
            if((i&(i-1))==0) h++;
            lo+=h;
        }
        if(!(d>=lo && d<=hi)) {printf("NO
");continue;}
        printf("YES
");
        vector<int> parent(n+1);
        for(int i=2;i<=n;++i) parent[i]=i-1;
        vector<int> numOfCd(n+1,1);
        numOfCd[n]=0;
        int cur=hi;
        vector<int> checked(n+1,0);
        vector<int> dep(n+1);
        for(int i=1;i<=n;++i) dep[i]=i-1;
        while(cur>d){
            int v=-1;
            for(int i=2;i<=n;++i){
                if(checked[i]==1) continue;
                if(numOfCd[i]==0 && (v==-1 || dep[i]<dep[v])){
                    v=i;
                }
            }
            int p=-1;
            for(int i=1;i<=n;++i){
                if(numOfCd[i]<2 && dep[i]==dep[v]-2){
                    p=i;
                }
            }
            if(p==-1){
                checked[v]=1;
                continue;
            }
            numOfCd[parent[v]]--;
            numOfCd[p]++;
            parent[v]=p;
            dep[v]--;
            cur--;
        }
        for(int i=2;i<=n;++i){
            printf("%d ", parent[i]);
        }
        printf("
");
    }
    return 0;
}