1064. Complete Binary Search Tree (30)

题意：给出一列数字，可以构成完全二叉搜索树，求构成的完全二叉搜索树的层次遍历

思路：构建树的过程可以看做是不断寻找子树根节点的过程

根据完全二叉树的特征，可以通过确定左子树的子孙节点个数来确定对应的根节点下标

递归构建即可。

代码：

#include<iostream>
#include<vector>
#include<cmath>
#include<algorithm>
#include<fstream>
using namespace std;
vector<int>nodes;

/**
@parm l,r point for nodes
@parm trees store constructed CBT
@parm pos position for trees
*/
void buildCBT(int l,int r,const vector<int> &nodes ,vector<int> &trees,int pos){
if(l>r)return;
if(l==r){
trees[pos] = nodes[l];
}else {
int sumNode = r - l +1;
int level = log((double)sumNode)/log((double)2) +1;
int lastLevelNodes = pow((double)2,level-1);
int knodes=lastLevelNodes-1;//除去最后一行的节点数
int lastRealNodes = sumNode -knodes;
int offset =0;
if(lastRealNodes>=lastLevelNodes/2){
offset = lastLevelNodes/2;
}else{
offset = lastRealNodes;
}
int nodeIndex=l+knodes/2 +offset;
//cout<<"nodeIndex "<<nodeIndex<<" "<<endl;
trees[pos] = nodes[nodeIndex];
//cout<<"trees[pos] "<<trees[pos]<<" ";
buildCBT(l,nodeIndex-1,nodes,trees,2*pos);
buildCBT(nodeIndex+1,r,nodes,trees,2*pos+1);
}
}

int main(){
ifstream cin("data.txt");
int num;
cin>>num;
int k;
for(int i=0;i<num;++i){
cin>>k;
nodes.push_back(k);
}
vector<int>trees(num+1);
sort(nodes.begin(),nodes.end());
buildCBT(0,num-1,nodes,trees,1);
for(int i=1;i<trees.size()-1;++i){
cout<<trees[i]<<" ";
}
cout<<trees[trees.size()-1]<<"\n";
//system("pause");
}