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1064 Complete Binary Search Tree (30 分)

Sky飞羽 2022-02-17 阅读 78
c++算法

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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

#include<iostream>
#include<algorithm>
using namespace std;
int N;
int a[1005];
int b[1005];
int c = 0;
void inorder(int root) {
	if (root >= N) return;
	inorder(root * 2 + 1);
	b[root] = a[c++];
	inorder(root * 2 + 2);
}
int main() {
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> a[i];
	}
	sort(a, a + N);
	inorder(0);
	cout << b[0];
	for (int j = 1; j < N; j++) {
		cout << " " << b[j];
	}
	return 0;
}
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