PAT 1064 Complete Binary Search Tree (30 分)

• 题目：

  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.

• 题目大意

  给出一个BST树，并且符合完全二叉树的定义，按照层次遍历输出这颗二叉树的节点的值

• 解题思路

  按照完全二叉树的定义，用数组存储节点的值（从1开始）,则2x为x节点的左孩子，2x+1为x节点的右孩子。由于BST树，中序遍历有序，只用中序遍历完全二叉树输入节点的值即可（输入的值存储在数组中，需要按照从小到大排序）。最后只用从前向后输出数组的值，就是这颗树层次遍历的值

• 代码实现：

#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
const int MAX = 10010;
int node[MAX];
int N, k = 0;
vector<int> num;
void mid_order(int root){    //中序遍历，输入节点的值
    if(root > N){
        return;
    }
    mid_order(2 * root);
    node[root] = num[k];
    k++;
    mid_order(2 * root + 1);
}
int main()
{
    scanf("%d", &N);
    for(int i = 0; i < N; i++){
        int temp;
        scanf("%d", &temp);
        num.push_back(temp);
    }
    sort(num.begin(), num.end());                      //排序
    mid_order(1);
    for(int i = 1; i <= N; i++){                           //从前往后输出完全二叉树的值
        if(i != 1){
            printf(" %d", node[i]);
        } else
            printf("%d", node[1]);
    }
    return 0;
}