PAT 1064 Complete Binary Search Tree(二叉搜索树)

 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

 代码

#include<cstdio>
#include<algorithm>
using namespace std;
const int Max=1005;
//num存储有序数，即是完全二叉树的中序排列
//CBT存放完全二叉树的层次遍历
int N,Num[Max],CBT[Max],index=0;
void inOrder(int root)
{
    if(root>N)
        return;
    inOrder(root*2);
    CBT[root]=Num[index];
    index+=1;
    inOrder(root*2+1);
}

int main()
{
    scanf("%d",&N);
    for(int i=0;i<N;i++)
    {
        scanf("%d",&Num[i]);
    }
    sort(Num,Num+N);
    inOrder(1);
    for(int i=1;i<=N;i++)
    {
        printf("%d",CBT[i]);
        if(i<N)
            printf(" ");
    }
    return 0;
}