# 题目

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

### Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (1<N≤1,000), the number of keys in the tree. Then the next line contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.

### Output Specification:

For each given tree, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally print in a line `Max Heap` if it is a max heap, or `Min Heap` for a min heap, or `Not Heap` if it is not a heap at all.

# 题解

## 思路

• 根本是考你堆的存储
• 堆的存储是一个数组，第一个0下标为空。真正的根在下标1。
• 这样就可以保证，任何下标乘以2就是它的左孩子，乘以2+1就是它的右孩子
• 然后题目考你DFS和maxheap还是minheap的判断，分开来都不难
• DFS遍历树就是维护一个路径，能右就右，然后能左就左，注意回溯。
• 判断heap先判断前两项的关系，然后看后面每项和它的父亲比大小即可。

## 数据结构

• nodes 是一个堆
• path 记录DFS的路径
• isMax 记录是不是大顶堆

• 照着思路走一遍就OK。

## 代码

• 由于使用Python可以AC，因此只放了Python的题解。