题目如下：
A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:
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 0Sample Output:
6 3 8 1 5 7 9 0 2 4
题目要求对给定的序列建立完全二叉搜索树，所谓完全二叉搜索树就是要满足完全二叉树的搜索树。
我们知道，完全二叉树的结点i如果从1开始编号，那么左儿子为2*i，右儿子为2*i+1；而二叉搜索树的中序遍历为升序，因此只需要对输入序列按照升序排序，然后对完全二叉树进行中序遍历，填入相应的元素即可。
#include <iostream>
#include <vector>
#include <stdio.h>
#include <algorithm>
using namespace std;
vector<int> tree;
vector<int> nodes;
int N;
void buildTree(int root){
static int index = 1;
if(root > N) return;
buildTree(root * 2);
tree[root] = nodes[index++];
buildTree(root * 2 + 1);
}
int main()
{
cin >> N;
nodes.resize(N+1);
tree.resize(N+1);
for(int i = 1; i <= N; i++){
scanf("%d",&nodes[i]);
}
sort(nodes.begin(),nodes.end());
buildTree(1);
printf("%d",tree[1]);
for(int i = 2; i <= N; i++)
printf(" %d",tree[i]);
cout << endl;
return 0;
}
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1064. Complete Binary Search Tree (30)
原文地址：http://blog.csdn.net/xyt8023y/article/details/47177853
