树6 Complete Binary Search Tree

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
  

#include<iostream>
#include<algorithm>
using namespace std;
int B[1002],j=0;
void inorder(int root, int N, int a[])
{
	if (root <= N) {
		inorder(2 * root, N, a);
		B[root] = a[j++];
		inorder(2 * root + 1, N, a);
	}
}
int main()
{
	int N;
	cin >> N;
	int *a = new int[N];
	for (int i = 0; i < N; i++)
	{
		cin >> a[i];
	}
	sort(a, a + N);
	inorder(1, N, a);
	cout << B[1];
	for (int i = 2; i <N+1; i++)
	{	
		cout <<' '<< B[i];
	}
	return 0;
}