Complete Binary Search Tree

Posted 2021-10-28 jiamian

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

   

 

 

 1 #include <cstdio> 
 2 #include <math.h>
 3 #include <algorithm> 
 4 
 5 using namespace std;
 6 
 7 int a[1010];
 8 int T[1010];
 9 
10 int GetLeftLength(int n)
11 {
12     int H=log(n+1)/log(2);
13     int X=n+1-pow(2,H);
14     if(X>pow(2,H-1))
15         X=pow(2,H-1);
16     int L=pow(2,H-1)-1+X;
17     return L;
18 }
19 
20 void solve(int ALeft,int ARight,int TRoot)
21 {
22     int n=ARight-ALeft+1;
23     if(n==0) return;
24     int L=GetLeftLength(n);
25     T[TRoot]=a[ALeft+L];
26     int LeftTRoot=TRoot*2+1;
27     int RightTRoot=LeftTRoot+1;
28     solve(ALeft,ALeft+L-1,LeftTRoot);
29     solve(ALeft+L+1,ARight,RightTRoot);
30 }
31 
32 int main()
33 {
34     int n;
35     scanf("%d",&n);
36     for(int i=0;i<n;i++)
37     {
38         scanf("%d",&a[i]);
39     }
40     sort(a,a+n);
41     solve(0,n-1,0);
42     for(int i=0;i<n;i++)
43     {
44         if(i==0)
45             printf("%d",T[i]);
46         else printf(" %d",T[i]);
47     }
48     return 0;
49 }