pat 5-7 Complete Binary Search Tree (30分)

5-7 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 NN (\le1000≤1000).Then NN distinctnon-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 theend 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

完全二叉树排序后，对于根，左二子是i*2,右儿子是i*2+1

#include <iostream>#include <algorithm>using namespace std;#include <bits/stdc++.h>int a[20005];int b[20005];int len;void dd(int a[20005],int x,int n){if(x*2<=n)dd(a,x*2,n);b[x]=a[len++];// cout<<b<<endl;if(x*2+1<=n)dd(a,x*2+1,n);}int main(){int n;int i;while(cin>>n){len=0;for(i=0; i<n; i++)cin>>a[i];sort(a,a+n);dd(a,1,n);for(i=1; i<=n-1; i++)cout<<b[i]<<" ";cout<<b<<endl;}}