PAT Advanced 1064 Complete Binary Search Tree (30分)

Posted 2021-03-13 littlepage

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 (≤). 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

已知一组数据，我们需要进行构成满二叉排序树，并且打印层序遍历。

我们可以进行sort一下，就是中序遍历，然后进行中序遍历插入数据即可。

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int N, index_v = 0 ;
vector<int> v, res;
void inorder(int index_res){
    if(index_res >= N) return ;
    inorder(2 * index_res + 1);
    res[index_res] = v[index_v++];
    inorder(2 * index_res + 2);
}
int main(){
    cin >> N;
    v.resize(N);
    res.resize(N);
    for(int i = 0; i < N; i++)
        cin >> v[i];
    sort(v.begin(),v.end());
    inorder(0);
    cout << res[0];
    for(int i = 1; i < N; i++)
        cout << " " << res[i];
    system("pause");
    return 0;
}