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

思路

1.二叉搜索树的中序遍历是一个递增的序列，所以先将输入后的节点数组升序排序。
2.完全二叉树以数组描述时，索引为i的节点的左右孩子的索引分别为2 * i和2 * i + 1。
3.将排好序的节点以中序遍历的形式来构造完全二叉搜索树。
4.遍历构造好的数组即为这棵树的层次遍历

代码

#include<iostream>

#include<algorithm>

#include<vector>

using namespace std;

const int MAX = ;

vector<int> nodes(MAX);

vector<int> tree(MAX);

int N,index;   //number of nodes && index of Nodes

void buildtree(int root)

{

    if(root > N)

        return;

    int left = root*,right = root* + ;

    buildtree(left);

    tree[root] = nodes[index++];

    buildtree(right);

}

int main()

{

   while(cin >> N)

   {

    //input

     for(int i = ; i <= N;i++)

        cin >> nodes[i];

     sort(nodes.begin() + ,nodes.begin() +  + N);

     //build tree

     index = ;

     buildtree();

     //print tree

     cout << tree[];

     for(int i = ;i <= N;i++)

        cout <<" " << tree[i];

     cout << endl;

   }

}