1064 Complete Binary Search Tree (30 分)

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 N distinct 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

 

#include<bits/stdc++.h>
using namespace std;
const int maxn=1010;
#define  inf  0x3fffffff
int number[maxn],cbt[maxn];
int iindex=0;//注意：定义为index会报错，因为头文件中包含该词语
int n;
void inorder(int root){//中序遍历，假设cbt中已经存入完全二叉树的值，那么它的中序遍历就是number的值
    if(root>n){
        return ;
    }
    inorder(root*2);
    cbt[root]=number[iindex++];
    inorder(root*2+1);
}
int main(){
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&number[i]);
    }
    sort(number,number+n);
    inorder(1);
    for(int i=1;i<=n;i++){
        if(i<=n-1)
        printf("%d ",cbt[i]);
        else
        printf("%d
",cbt[i]);
    }
    return 0;
}