1064 Complete Binary Search Tree (30)（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 (<=1000). 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

 

题意：

给定一串非负整数序列（保证每个数都不同），构建二叉树使其满足既是二叉查找树，也是完全二叉树。输出层序序列。

 

思路：

利用完全二叉树顺序存储时的性质

 

代码：

#include 
      
       #include 
       
        using namespace std;const int N=1010;int CBT[N],data[N];int n;void inOrderTraversal(int root){    static int cnt=1;    if(root<=n){
    //注意边界条件        inOrderTraversal(root*2);//左子树        CBT[root]=data[cnt++];        inOrderTraversal(root*2+1);    }}int main(){    scanf("%d",&n);    for(int i=1;i<=n;i++) scanf("%d",&data[i]);    sort(data+1,data+n+1);    inOrderTraversal(1);        for(int i=1;i<=n;i++){        printf("%d",CBT[i]);        if(i