浙大PAT 1064. Complete Binary Search Tree

064. Complete Binary Search Tree (30)

时间限制

100 ms

内存限制

32000 kB

代码长度限制

16000 B

判题程序

Standard

作者

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

0 1 2 3 4 5 6 7 8 9

Sample Output:

6 3 8 1 5 7 9 0 2 4

分析：这道题的意思是建立完全二叉树并按中序输出，参考了别人的答案发现可以按照完全二叉树的性质来建树。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，从根节点下标为1，按照对应下标存入数组。最后输出时按照数组下表从小到大输出即中序输出

#include <iostream>  #include <vector>  #include <stdio.h>  #include <algorithm>    using namespace std;    vector<int> tree;  vector<int> nodes;  int N;    void buildTree(int root){      static int index = 1;      if(root > N) return;      buildTree(root * 2);      tree[root] = nodes[index++];      buildTree(root * 2 + 1);  }    int main()  {      cin >> N;      nodes.resize(N+1);      tree.resize(N+1);      for(int i = 1; i <= N; i++){          scanf("%d",&nodes[i]);      }      sort(nodes.begin(),nodes.end());      buildTree(1);       for(int i = 1; i <= N; i++)          printf(" %d",tree[i]);      cout << endl;      return 0;  }