PAT 1064. Complete Binary Search Tree (30) 快速建立完全二叉树

1064. Complete Binary Search Tree (30)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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:

101 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

哇，这个解法太骚了。不废话，上干货。

题目要求对给定的序列建立完全二叉搜索树，所谓完全二叉搜索树就是要满足完全二叉树的搜索树。

我们知道，完全二叉树的结点i如果从1开始编号，那么左儿子为2*i，右儿子为2*i+1；而二叉搜索树的中序遍历为升序，因此只需要对输入序列按照升序排序，然后对完全二叉树进行中序遍历，填入相应的元素即可。

[cpp] view plain copy

1. #include <iostream>  
2. #include <vector>  
3. #include <stdio.h>  
4. #include <algorithm>  
5.   
6. using namespace std;  
7.   
8. vector<int> tree;  
9. vector<int> nodes;  
10. int N;  
11.   
12. void buildTree(int root){  
13.     static int index = 1;  
14.     if(root > N) return;  
15.     buildTree(root * 2);  
16.     tree[root] = nodes[index++];  
17.     buildTree(root * 2 + 1);  
18. }  
19.   
20. int main()  
21. {  
22.     cin >> N;  
23.     nodes.resize(N+1);  
24.     tree.resize(N+1);  
25.     for(int i = 1; i <= N; i++){  
26.         scanf("%d",&nodes[i]);  
27.     }  
28.     sort(nodes.begin(),nodes.end());  
29.     buildTree(1);  
30.     printf("%d",tree[1]);  
31.     for(int i = 2; i <= N; i++)  
32.         printf(" %d",tree[i]);  
33.     cout << endl;  
34.     return 0;  
35. }  

我的仿写：

#include<string>#include<stdio.h>#include<iostream>#include<string.h>#include<queue>#include<algorithm>#include<map>#include<set>#include<math.h>#include<stack>#include<vector>using namespace std;int num[1001];int tree[1001];int n;int p=0;void buildtree(int x) {     if(x>n) return;     buildtree(2*x);       tree[x]=num[p++];     buildtree(2*x+1); }int main(){    cin>>n;    for(int i=0;i<n;i++)      cin>>num[i];      sort(num,num+n);       buildtree(1);        cout<<tree[1];        for(int i=2;i<=n;i++)          cout<<' '<<tree[i];     return 0;}