1064. Complete Binary Search Tree (30)
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 0Sample Output:
6 3 8 1 5 7 9 0 2 4
注：利用完全二叉树数组的特性，i的左子树是2i，右子树是2i+1
#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<map>
#define MAXSIZE 100005
typedef long long ll;
using namespace std;
int current=0;
int cmp(const void *a,const void *b)
{
return *(int *)a-*(int *)b;
}
//构建完全二叉树
void BuildTree(int point,int *Get,int *Tree,int n)//point当前结点，Get是存放有序数列的数组
{
if(point<=n)
{
BuildTree(point<<1,Get,Tree,n);//左子树
Tree[point]=Get[current++];
BuildTree((point<<1)+1,Get,Tree,n);//左子树
}
}
int main()
{
int Get[MAXSIZE];
int Tree[MAXSIZE];
int N;
cin>>N;
for(int i=0;i<N;i++)cin>>Get[i];
qsort(Get,N,sizeof(Get[0]),cmp);
//for(int i=0;i<N;i++)cout<<Get[i]<<" ";
BuildTree(1,Get,Tree,N);
for(int i=1;i<N;i++)cout<<Tree[i]<<" ";
cout<<Tree[N]<<endl;
return 0;
}