Max-Heap 是一个完整的二叉树，其中每个内部节点中的值大于或等于该节点的子节点中的值。
将堆的元素映射到数组是微不足道的：如果一个节点存储在索引 k 中，那么它的左子节点存储在索引2k + 1 处，其右子节点存储在索引2k + 2 处。
最大堆示例： 
最大堆是如何表示的?
最大堆是一棵完全二叉树。 Max heap 通常表示为一个数组。根元素将在Arr[0] 。下表显示了第 i 个节点的其他节点的索引，即Arr[i] ：
Arr[(i-1)/2]返回父节点。
Arr[(2*i)+1]返回左子节点。
Arr[(2*i)+2]返回右子节点。
最大堆上的操作：
- getMax() ：它返回最大堆的根元素。此操作的时间复杂度为O(1) 。
- extractMax() ：从 MaxHeap 中移除最大元素。此操作的时间复杂度为O(Log n)，因为此操作需要在移除 root 后维护堆属性(通过调用 heapify())。
- insert() ：插入新键需要O(Log n)时间。我们在树的末尾添加一个新键。如果新键小于它的父键，那么我们不需要做任何事情。否则，我们需要向上遍历以修复违反的堆属性。
注意：在下面的实现中，我们从索引 1 开始索引以简化实现。
# Python3 implementation of Max Heap
import sys
class MaxHeap:
def __init__(self, maxsize):
self.maxsize = maxsize
self.size = 0
self.Heap = [0] * (self.maxsize + 1)
self.Heap[0] = sys.maxsize
self.FRONT = 1
# Function to return the position of
# parent for the node currently
# at pos
def parent(self, pos):
return pos // 2
# Function to return the position of
# the left child for the node currently
# at pos
def leftChild(self, pos):
return 2 * pos
# Function to return the position of
# the right child for the node currently
# at pos
def rightChild(self, pos):
return (2 * pos) + 1
# Function that returns true if the passed
# node is a leaf node
def isLeaf(self, pos):
if pos >= (self.size//2) and pos <= self.size:
return True
return False
# Function to swap two nodes of the heap
def swap(self, fpos, spos):
self.Heap[fpos], self.Heap[spos] = (self.Heap[spos],
self.Heap[fpos])
# Function to heapify the node at pos
def maxHeapify(self, pos):
# If the node is a non-leaf node and smaller
# than any of its child
if not self.isLeaf(pos):
if (self.Heap[pos] < self.Heap[self.leftChild(pos)] or
self.Heap[pos] < self.Heap[self.rightChild(pos)]):
# Swap with the left child and heapify
# the left child
if (self.Heap[self.leftChild(pos)] >
self.Heap[self.rightChild(pos)]):
self.swap(pos, self.leftChild(pos))
self.maxHeapify(self.leftChild(pos))
# Swap with the right child and heapify
# the right child
else:
self.swap(pos, self.rightChild(pos))
self.maxHeapify(self.rightChild(pos))
# Function to insert a node into the heap
def insert(self, element):
if self.size >= self.maxsize:
return
self.size += 1
self.Heap[self.size] = element
current = self.size
while (self.Heap[current] >
self.Heap[self.parent(current)]):
self.swap(current, self.parent(current))
current = self.parent(current)
# Function to print the contents of the heap
def Print(self):
for i in range(1, (self.size // 2) + 1):
print(" PARENT : " + str(self.Heap[i]) +
" LEFT CHILD : " + str(self.Heap[2 * i]) +
" RIGHT CHILD : " + str(self.Heap[2 * i + 1]))
# Function to remove and return the maximum
# element from the heap
def extractMax(self):
popped = self.Heap[self.FRONT]
self.Heap[self.FRONT] = self.Heap[self.size]
self.size -= 1
self.maxHeapify(self.FRONT)
return popped
# Driver Code
if __name__ == "__main__":
print('The maxHeap is ')
maxHeap = MaxHeap(15)
maxHeap.insert(5)
maxHeap.insert(3)
maxHeap.insert(17)
maxHeap.insert(10)
maxHeap.insert(84)
maxHeap.insert(19)
maxHeap.insert(6)
maxHeap.insert(22)
maxHeap.insert(9)
maxHeap.Print()
print("The Max val is " + str(maxHeap.extractMax()))
输出 ：
The maxHeap is
PARENT : 84 LEFT CHILD : 22 RIGHT CHILD : 19
PARENT : 22 LEFT CHILD : 17 RIGHT CHILD : 10
PARENT : 19 LEFT CHILD : 5 RIGHT CHILD : 6
PARENT : 17 LEFT CHILD : 3 RIGHT CHILD : 9
The Max val is 84
使用库函数：
我们使用 heapq 类在Python实现堆。默认情况下，Min Heap 由此类实现。但是我们将每个值乘以 -1，以便我们可以将其用作 MaxHeap。
# Python3 program to demonstrate working of heapq
from heapq import heappop, heappush, heapify
# Creating empty heap
heap = []
heapify(heap)
# Adding items to the heap using heappush
# function by multiplying them with -1
heappush(heap, -1 * 10)
heappush(heap, -1 * 30)
heappush(heap, -1 * 20)
heappush(heap, -1 * 400)
# printing the value of maximum element
print("Head value of heap : "+str(-1 * heap[0]))
# printing the elements of the heap
print("The heap elements : ")
for i in heap:
print(-1 * i, end = ' ')
print("\n")
element = heappop(heap)
# printing the elements of the heap
print("The heap elements : ")
for i in heap:
print(-1 * i, end = ' ')
输出 ：
Head value of heap : 400
The heap elements :
400 30 20 10
The heap elements :
30 10 20
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