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
#include<cstdio> #include<algorithm> using namespace std; const int maxn = 1100; //num存储有序数,即是完全二叉树的中序排列 //CBT存放完全二叉树的层次遍历 int n,num[maxn],CBT[maxn],index = 0; 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; }