题目描述

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

考点

完全二叉搜索树

思路

二叉搜索树中序遍历的结果就是由小到大排列的，因此将数组排序之后方可一一对应。由于是完全二叉树，因此可以使用一维数组存储树。

代码

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
vector<int> sq, bt;
int n, c=1;
void buildtree(int r) {
    if (r > n) return;
    buildtree(r * 2);
    bt[r] = sq[c++];
    buildtree(r * 2 + 1);
}
int main() {
    int i;
    cin >> n;
    sq.resize(n + 1); bt.resize(n + 1);
    for (i = 1; i <= n; i++)  cin >> sq[i];
    sort(sq.begin(), sq.end());
    buildtree(1);
    cout << bt[1];
    for (i = 2; i <= n; i++)  cout << " " << bt[i];
    return 0;
}