1064 Complete Binary Search Tree （30 分）

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

解析

#include<algorithm>
#include<functional>
#include<cstdio>
#include<iostream>
#include<queue>
#include<string>
#include<cmath>
using namespace std;
vector<int> number,
 
 CBT;
int num=0;
void inorder(int root, int N) {
	if (root > N)
		return;
	inorder(root * 2, N);
	CBT[root] = number[num++];
	inorder(root * 2 + 1, N);
}
int main()
{
	int N;
	scanf("%d", &N);
	number.resize(N, 0), CBT.resize(N+1, 0);
	for (int i = 0; i < N; i++)
		scanf("%d", &number[i]);
	sort(number.begin(), number.end());
	inorder(1,N);
	for (int i = 0; i < N; i++)
		printf("%d%c", CBT[i+1], i == N - 1 ? '\n' : ' ');
}