"""
堆是一种完全二叉树，有最大堆和最小堆两种。
最大堆：对于每个非叶子结点V，V的值都比它的两个孩子结点大，称为最大堆特性(heap order property),
最大堆里面的根总是储存最大值，最小值储存在叶子结点。
最小堆：和最大堆相反，每个非叶子结点V，它的两个孩子的值都比V的值大。
"""
# 实现最大堆
# 首先实现一个数组
class Array(object):
def __init__(self, size=32):
self._size = size
self._items = [None] * size
def __getitem__(self, index):
return self._items[index]
def __setitem__(self, index, value):
self._items[index] = value
def __len__(self):
return self._size
def clear(self, value = None):
for i in range(self._size):
self._items[i] = value
def __iter__(self):
for item in self._items:
yield item
# 用数组来实现堆。
# 因为堆是完全二叉树，舍某结点的下标为i，
# 它的父结点为 int((i-1)/2),左孩子结点为2*i + 1， 右孩子结点为2*i +2， 超出下标表示没有孩子结点
class MaxHeap(object):
"""dmaxsizetring for MaxHeap"""
def __init__(self, maxsize = None):
self.maxsize = maxsize
self._elements = Array(maxsize)
self._count = 0
def __len__(self):
return self._count
def add(self, value):
if self._count>=self.maxsize:
raise Exception("Full")
self._elements[self._count] = value
self._count += 1
self._siftup(self._count-1) # 因为第一个结点是从0开始的，最后一个结点是结点个数减一
'''
partent = int((n-1)/2)
self._elements[n] = value
while self._elements[n] > self._elements[partent]:
self._elements[n], self._elements[partent] = self._elements[partent], self._elements[n]
'''
def _siftup(self, ndx): # 递归交换，知道满足最大堆特性
if ndx > 0:
parent = int((ndx-1)/2)
if self._elements[ndx] > self._elements[parent]:
self._elements[ndx], self._elements[parent] = self._elements[parent], self._elements[ndx]
self._siftup(parent)
def extract(self): # 拿掉堆的最大值
if self._count <= 0:
raise Exception('empty')
value = self._elements[0]
self._elements[0] = self._elements[self._count-1] # 把最后一个结点赋值给根结点 然后进行siftdown 操作
self._count -= 1
self._siftdown(0)
return value
def _siftdown(self, ndx):
left = ndx * 2 + 1
right = ndx * 2 +2
largest = ndx
# 保证下标不越界， 左孩子大于该结点， 而且左孩子大于右孩子
if (left < self._count and
self._elements[left] >= self._elements[largest] and
self._elements[left] >= self._elements[right]):
largest = left # 把最大的下标赋值给left 孩子
elif (right < self._count and
self._elements[right] >= self._elements[largest] and
self._elements[right] >= self._elements[left]):
largest = right
if largest != ndx:
self._elements[ndx], self._elements[largest] = self._elements[largest], self._elements[ndx]
self._siftdown(largest)
# 堆堆倒叙排序
def heapsort_reverse(array):
length = len(array)
maxheap = MaxHeap(length)
l = []
for i in range(length):
maxheap.add(i)
for i in range(length):
l.append(maxheap.extract())
return l
def test_max_heap():
import random
n = 5
h = MaxHeap(n)
for i in range(n):
h.add(i)
for i in reversed(range(n)):
assert i == h.extract()
l = list(range(10))
random.shuffle(l)
assert heapsort_reverse(l) == sorted(l, reverse=True)
