04-树6 Complete Binary Search Tree (30 分)

Posted 2020-12-02 wanghao-boke

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<cstdio>
#include<algorithm>
using namespace std;
const int maxn = 1010;

int num[maxn];
int CBT[maxn];
int index = 0;

void inOrder(int root, int n);

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

void inOrder(int root, int n)
{
    if (root > n)
    {
        return ;
    }
    
    inOrder(root*2, n);
    CBT[root] = num[index++];
    inOrder(root*2+1, n);
}