04-树6 Complete Binary Search Tree

Posted 2020-06-29 kuotian

刚开始只发现了中序遍历是从小到大顺序的。一直在找完全二叉树的层结点间规律。。。放弃了

不曾想，完全二叉树的规律早就知道啊。根结点为i，其左孩子结点2*i, 右孩子结点2*i+1。

结合此两者即可解决问题！

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 NN 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 <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 using namespace std;
 5 
 6 #define MaxSize 1005
 7 int sortNum[MaxSize] = {0};
 8 int CBTreeNode[MaxSize] = {0};
 9 int countNum = 0;
10 void CreatCBTree(int root,int N)
11 {
12     if(root > N)
13         return;
14     int left = root * 2;
15     int right = root * 2 + 1;
16     CreatCBTree(left,N);        //中序遍历LGR从小到大 小的先
17     CBTreeNode[root] = sortNum[countNum++];
18     CreatCBTree(right,N);
19 }
20 
21 int main()
22 {
23     int N;
24     scanf("%d",&N);
25     for(int i = 0; i < N; i++) 
26         scanf("%d",&sortNum[i]);
27     
28     sort(sortNum,sortNum + N);//按从小到大排序 
29     CreatCBTree(1,N);
30     for(int i = 1; i <= N; i++) {
31         if(i != N)
32             printf("%d ",CBTreeNode[i]);
33         else
34             printf("%d",CBTreeNode[i]);
35     }
36     return 0;
37 }