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