PAT 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

题目大意：构建一颗完全二叉树， 输出二叉树层序遍历；
思路： 因为是完全二叉树， 又要求输出层序遍历， 可以用一个数组来构建树， 根节点和子节点的下标关系式:左子树：2*i+1, 右子树: 2*i+2;
      通过下标对二叉树进行中序遍历， 且中序遍历二叉树得到的是递增数列，所以记录中序遍历的下标顺序； 
      把数组排序后， 按照中序遍历得到的顺序依次填入到保存二叉树的数组中， 得到的就是层序遍历了

 1 #include<iostream>
 2 #include<vector>
 3 #include<algorithm>
 4 using namespace std;
 5 int n;
 6 vector<int> t, temp;
 7 void inorder(int index){
 8   if(index>=n) return;
 9   if(index*2+1<n) inorder(index*2+1);
10   t.push_back(index); //记录中序遍历的节点下标
11   if(index*2+2<n) inorder(index*2+2);
12 }
13 int main(){
14   int  i;
15   scanf("%d", &n);
16   vector<int> v(n);
17   temp.resize(n);
18   for(i=0; i<n; i++) scanf("%d", &v[i]);
19   inorder(0);
20   sort(v.begin(), v.end());
21   for(i=0; i<n; i++)  temp[t[i]] = v[i]; //按照中序遍历的顺序把排序后的数据填入到数组中
22   printf("%d", temp[0]);
23   for(i=1; i<n; i++) printf(" %d", temp[i]);
24   return 0;
25 }