堆:一种完全二叉树,有最大堆和最小堆两种。
最大堆:根总是最大值,最小的值存储在叶节点中,
最小堆:每个非叶子节点的两个孩子的值都比它大。
堆的操作:
插入新的值,依然保证堆的最大堆或者最小堆的结构。
删除一个值。
堆的表示:使用数组表示堆。
parent = int(i-1)/2
left = 2i +1
right = 2i+2
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(len(self._items)):
self._items[i] = value
def __iter__(self):
for item in self._items:
yield item
"""heap 实现"""
class Maxheap(object):
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')
# 开始加入,先把值放在最后一位,最后一位就是_count
self._elements[self._count] = value
self._count += 1
self._siftup(self._count - 1) # 定义_siftup函数,传入的值是添加元素的位置
def _siftup(self, ndx): # 递归交换,直到满足最大堆的特性。
if ndx > 0:
parent = int((ndx - 1 / 2))
if self._elements[ndx] > self._elements[parent]: # 如果他的值大于父亲就交换
self._elements[ndx], self._elements[parent] = self._elements[parent], self._elements[ndx]
self._siftup(parent) # 递归
def extract(self):
if self._count <= 0:
raise Exception('empty')
value = self._elements[0]
self._count -= 1
self._elements[0] = self._elements[self._count]
self._siftdown(0)
return value
def _siftdown(self, ndx):
left = 2 * ndx + 1
right = 2 * ndx + 2
largest = ndx
if (left < self._count and self._elements[left] >= self._elements[largest] and self._elements[left] >=
self._elements[right]):
largest = left
elif right < self._count and self._elements[right] >= self._elements[largest]:
largest = right
if largest != ndx:
self._elements[ndx], self._elements[largest] = self._elements[largest], self._elements[ndx]
self._siftdown(largest)
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()