PAT A1064 Complete Binary Search Tree(30)[完全二叉搜索树, 数]

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

题意

思路1

二叉排序树的中序遍历序列是有序的，先排序再模拟中序遍历将逐个结果填进去即可的得到层序遍历结果

完全二叉排序树可以只用一个一维数组来存储，下标从 1开始左孩子为 2*n 右孩子为 2*n+1 (若存在)

代码1

#include <iostream>
#include <algorithm>
using namespace std;
const int N = 1010;
int a[N], in[N];
int n, idx;
void inorder(int root)
{
    if(root > n) return;
    inorder(root * 2);
    in[root] = a[idx++];
    inorder(root * 2 + 1);
}
int main()
{

    scanf("%d", &n);
    for(int i = 0; i < n; i++)
        scanf("%d", &a[i]);
    sort(a, a + n);
    inorder(1);
    printf("%d", in[1]);
    for(int i = 2; i <= n; i++)
        printf(" %d", in[i]);
    return 0;
}