题目

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.

输入

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.

输出

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.

样例输入 

10
1 2 3 4 5 6 7 8 9 0

样例输出 

6 3 8 1 5 7 9 0 2 4

题意理解

给你n个节点 然后让你输出完全二叉排序树的层序遍历

我们先来明确什么是完全二叉排序树 只有叶子节点和度为2的节点 并且小于根节点的节点放入左子树 大于等于根节点的节点放入右子树 并且我们还要知道 完全二叉排序树的中序遍历是完全有序的 那么我们直接用数组模拟会更加的方便

代码 

#include<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
int a[N],ans[N];
int n,k;
void build(int root){
    if(root>n)return;
    build(root<<1);
    ans[root]=a[++k];
    build(root<<1|1);
}
int main(){
    cin>>n;
    for(int i=1,x;i<=n;i++){
        scanf("%d",&a[i]);
    }
    sort(a+1,a+1+n);
    build(1);
    for(int i=1;i<=n;i++){
        if(i>1)printf(" ");
        printf("%d",ans[i]);
    }
    return 0;
}