1022 Complete Binary Search Tree

利用了完全二叉树的性质：满二叉树表现在可用下标寻左右子节点。根节点为0时，节点i的左右子节点为（2*i+1）和（2*i+2）；同理：反过来按这个性质构造出来的树就是一个完全二叉树

以及性质：二叉搜索树表现在中序遍历是有序的

所以思路是：重新构造一个数组，index就按照层序遍历的标号来，但是原始拍好序的数组是按照中序遍历来的，那就按照中序遍历吧数据填充进去就好了。填的方式就按照递归来就是了

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.

输入描述:

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.

输出描述:

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.

输入例子:

10

1 2 3 4 5 6 7 8 9 0

输出例子:

6 3 8 1 5 7 9 0 2 4

package p1064;

import java.util.Arrays;
import java.util.Scanner;

public class Main {

static int[] built_cbs;
static int[] nums;
static int pos = 0, n = 0;

public static void main(String[] args) {
Scanner sc = new Scanner(System.in);

n = sc.nextInt();
nums = new int
;

for(int i=0 ;i<n; i++)
nums[i] = sc.nextInt();

Arrays.sort(nums);
built_cbs = new int
;
LDR_build(0);

for(int i=0; i<n-1; i++)
System.out.print(built_cbs[i] + " ");
System.out.println(built_cbs[n-1]);
}

public static void LDR_build(int i) {
if(i >= n)  return;
LDR_build(2 * i + 1);
built_cbs[i] = nums[pos++];
LDR_build(2 * i + 2);
}
}

另外附上C++：

#include <iostream>
#include <algorithm>

using namespace std;
int N;
int nums[1002], cbs[1002];
int pos = 0;

void built_cbs(int f) {
if(f >= N)      return;
built_cbs(2 * f + 1);
cbs[f] = nums[pos++];
built_cbs(2 * f + 2);
}

int main()
{
cin >> N;
for(int i=0; i<N; i++) {
cin >> nums[i];
}
sort(nums, nums + N);

built_cbs(0);

for(int i=0; i<N-1; i++)
cout << cbs[i] << " ";
cout << cbs[N-1];

return 0;
}

有一篇文章讲的不错：

浙大PAT 1064. Complete Binary Search Tree