PAT 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 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

题目大意：构建一颗完全二叉树， 输出二叉树层序遍历；
思路： 因为是完全二叉树， 又要求输出层序遍历， 可以用一个数组来构建树， 根节点和子节点的下标关系式:左子树：2*i+1, 右子树: 2*i+2;
      通过下标对二叉树进行中序遍历， 且中序遍历二叉树得到的是递增数列，所以记录中序遍历的下标顺序； 
      把数组排序后， 按照中序遍历得到的顺序依次填入到保存二叉树的数组中， 得到的就是层序遍历了

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
int n;
vector<int> t, temp;
void inorder(int index){
  if(index>=n) return;
  if(index*2+1<n) inorder(index*2+1);
  t.push_back(index); //记录中序遍历的节点下标
  if(index*2+2<n) inorder(index*2+2);
}
int main(){
  int  i;
  scanf("%d", &n);
  vector<int> v(n);
  temp.resize(n);
  for(i=0; i<n; i++) scanf("%d", &v[i]);
  inorder(0);
  sort(v.begin(), v.end());
  for(i=0; i<n; i++)  temp[t[i]] = v[i]; //按照中序遍历的顺序把排序后的数据填入到数组中
  printf("%d", temp[0]);
  for(i=1; i<n; i++) printf(" %d", temp[i]);
  return 0;
}