# 描述

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))

Your job is to tell if a given complete binary tree is a heap

# 指定输入

Each input file contains one test case. For each case, the first line gives two positive integers: M (≤ 100), the number of trees to be tested; and N (1 < N ≤ 1,000), the number of keys in each tree, respectively. Then M lines follow, each contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.

# 指定输出

For each given tree, 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. Then in the next line print the tree’s postorder traversal sequence. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line.

# 示例

3 8
98 72 86 60 65 12 23 50
8 38 25 58 52 82 70 60
10 28 15 12 34 9 8 56


Max Heap
50 60 65 72 12 23 86 98
Min Heap
60 58 52 38 82 70 25 8
Not Heap
56 12 34 28 9 8 15 10


# 分析

## 分析点二:堆

• 性质一:最大堆的根节点的值是最大的,最小堆的根节点的值是最小的
• 最大堆的定义:每一个节点的值大于等于它的左右子节点的值,且树是最优平衡的,最后一层的叶子节点在最左边(最小堆将大于等于改为小于等于即可,粗体表示暂时还未搞懂)
• 当用数组表示法来表示树时,最大堆判定算法如下

# 代码

class Node:

def __init__(self):
self.data = None
self.left_node = None
self.right_node = None

class GenTree:

def __init__(self, array):
self.array = array
self.root = None
self.max_heap = True
self.min_heap = True
self.result = []

def genbtree(self):
if len(self.array) == 0:
return
count = 0
queue = []
root = Node()
root.data = self.array[0]
self.root = root
queue.append(root)
count += 1
while len(queue) > 0:
current_node = queue.pop(0)
if count < len(self.array):
current_node.left_node = Node()
current_node.left_node.data = self.array[count]
count += 1
queue.append(current_node.left_node)
if count < len(self.array):
current_node.right_node = Node()
current_node.right_node.data = self.array[count]
count += 1
queue.append(current_node.right_node)

def judge(self, root):
if root is None:
return
if root.left_node is not None:
if root.data >= root.left_node.data:
self.min_heap = False
elif root.data <= root.left_node.data:
self.max_heap = False
if root.right_node is not None:
if root.data >= root.right_node.data:
self.min_heap = False
elif root.data <= root.right_node.data:
self.max_heap = False
self.judge(root.left_node)
self.judge(root.right_node)
self.result.append(root.data)

n, m = map(int, input().split(" "))
for i in range(n):
array = list(map(int, input().split(" ")))
gentree = GenTree(array)
gentree.genbtree()
gentree.judge(gentree.root)
if gentree.max_heap and not gentree.min_heap:
print("Max Heap")
for j in range(m):
if j == m - 1:
print(gentree.result[j])
break
print(gentree.result[j], end=" ")
elif gentree.min_heap and not gentree.max_heap:
print("Min Heap")
for j in range(m):
if j == m - 1:
print(gentree.result[j])
break
print(gentree.result[j], end=" ")
else:
print("Not Heap")
for j in range(m):
if j == m - 1:
print(gentree.result[j])
break
print(gentree.result[j], end=" ")


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