Complete Binary Search Tree

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than the node's key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
• Both the left and right subtrees must also be binary search trees.

A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.

Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤). Then Ndistinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.

Output Specification:

For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

Sample Input:

10
1 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

AC代码

#include<stdio.h>
#include<iostream>
#include<algorithm>
//using namespece std;

typedef struct TreeNode{
  int left;
  int right;
  int key;
}CBT;

void AddKeytoCBT(CBT T[],int i,int data[],int *k,int N){
    if(i<=N){
      AddKeytoCBT(T,2*i,data,k,N);
      T[i].key = data[*k];
      (*k)++;
      AddKeytoCBT(T,2*i+1,data,k,N);
    }
    return;
}


int main(){
  int N;
  int k = 1;
  scanf("%d",&N);
  CBT T[N+1];
  int data[N+1];
  for(int i = 1;i<N+1;i++){
    scanf("%d",&data[i]);
    
  }
  for(int i = 1; i <=N;i++){
    T[i].left = 2*i;
    T[i].right = 2*i+1;
  }
  std::sort(&data[1],&data[1]+N);   //特别注意
  AddKeytoCBT(T,1,data,&k,N);
  for(int i = 1; i <= N; i++){
    if(i==1){
      printf("%d",T[i].key);
    }else{
      printf(" %d",T[i].key);
    }
  }
  return 0;
}