04-树6 Complete Binary Search Tree

完全二叉树

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

 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 using namespace std;

 #define MaxSize 1005
 int sortNum[MaxSize] = {};
 int CBTreeNode[MaxSize] = {};
 int countNum = ;
 void CreatCBTree(int root,int N)
 {
     if(root > N)
         return;
     int left = root * ;
     int right = root *  + ;
     CreatCBTree(left,N);        //中序遍历LGR从小到大 小的先
     CBTreeNode[root] = sortNum[countNum++];
     CreatCBTree(right,N);
 }

 int main()
 {
     int N;
     scanf("%d",&N);
     for(int i = ; i < N; i++)
         scanf("%d",&sortNum[i]);

     sort(sortNum,sortNum + N);//按从小到大排序
     CreatCBTree(,N);
     for(int i = ; i <= N; i++) {
         if(i != N)
             printf("%d ",CBTreeNode[i]);
         else
             printf("%d",CBTreeNode[i]);
     }
     return ;
 }