04-树6 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 N (≤). 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

  #include<cstdio>
  #include<algorithm>
  using namespace std;
  const int maxn = 2010;
  
  int n;
  int index = 0;
  int CBT[maxn],num[maxn];
  
  void inOrder(int root){
      if(root > n) return;
      inOrder(root*2);
      CBT[root] = num[index++];
      inOrder(root*2+1); 
  }
  
  int main(){
  
      scanf("%d",&n);
      for(int i = 0; i < n; i++){
          scanf("%d",&num[i]);
      }
      sort(num,num+n);
      inOrder(1);
      for(int i = 1; i <= n; i++){
          printf("%d",CBT[i]);
          if(i < n) printf(" ");
      }
      return 0;
  }