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#!/usr/bin/env python
# -*- coding:utf-8 -*-
from math import *
import copy
class Heap(object):
"""最大二叉堆实现"""
def __init__(self, *arg):
super(Heap, self).__init__()
self.__array = list(arg)
self.length = len(arg)
self.height = int(log(self.length))
self.__build_heap()
@classmethod
def make_heap(cls, li):
return Heap(*li)
def __build_heap(self):
for x in reversed(xrange(0, self.length / 2)):
self.loop_heapify(x)
def heapify(self, parent):
"""
基本思路是从一个元素开始，如果这个元素不符合最大堆的规定，那么就把其子节点的元素，提升到父节点上面。
注意这是一个递归的过程，只有在满足最大堆的条件或者到达堆的叶节点的时候才会退出.
注意：heapify方法的条件是他的子节点都是最大堆，使用的时候要注意这一点。
"""
largest = parent
left = parent * 2 + 1
right = parent * 2 + 2
# 这个地方使用left和right比较，是为了防止到了叶节点的时候会出现数组越界。
if left < self.length and self.__array[parent] < self.__array[left]:
largest = left
if right < self.length and self.__array[largest] < self.__array[right]:
largest = right
# 保证在父元素就是最大值的时候不要移动元素
if largest != parent:
self.__array[largest], self.__array[parent] = self.__array[parent], self.__array[largest]
self.heapify(largest)
def loop_heapify(self, parent):
"""
while true break是一个比较方便的把递归转换成循环的方法，因为在while的时候不用判断任何条件，判断都在break里面，避免了在while
中设置复杂的条件
"""
while True:
largest = parent
left = parent * 2 + 1
right = parent * 2 + 2
# 这个地方使用left和right比较，是为了防止到了叶节点的时候会出现数组越界。
if left < self.length and self.__array[parent] < self.__array[left]:
largest = left
if right < self.length and self.__array[largest] < self.__array[right]:
largest = right
# 保证在父元素就是最大值的时候不要移动元素
if largest != parent:
self.__array[largest], self.__array[parent] = self.__array[parent], self.__array[largest]
parent = largest
else:
break
def __left(self, parent):
return parent * 2 + 1
def __right(self, parent):
return parent * 2 + 2
def __wide_walk_through(self, func, start=0):
for x in xrange(start, self.length):
func(self.__array[x])
def __deep_walk_through(self, func, start=0):
if start >= self.length:
func(start)
left = start * 2 + 1
right = start * 2 + 2
self.__deep_walk_through(func, left)
self.__deep_walk_through(func, right)
def __str__(self):
title = "Heap Length: %s\n" % self.length
content_list = [title]
self.__wide_walk_through(lambda s: content_list.append(str(s)))
return '\t'.join(content_list)
def __len__(self):
return self.length
def __getitem__(self, index):
return self.__array[index]
def append(self, value):
self.__array.append(value)
insert_index = self.length
while True:
parent = (insert_index - 1) / 2
# 这儿需要判断使得parent不会越界
if parent >= 0 and self.__array[insert_index] > self.__array[parent]:
self.__array[parent], self.__array[insert_index] = self.__array[insert_index], self.__array[parent]
insert_index = parent
else:
break
self.length += 1
def append_with_one_assign(self, value):
"""
添加了一项优化，就是在移动节点的时候不要交换值，而是仅仅移动父节点，在最后空出来的节点上面插入值.
这样的好处是仅需要赋值一次。减低了算法中的常数项。
"""
self.__array.append(value)
insert_index = self.length
while True:
parent = (insert_index - 1) / 2
# 这儿需要判断使得parent不会越界
if parent >= 0 and value > self.__array[parent]:
self.__array[insert_index] = self.__array[parent]
insert_index = parent
else:
break
self.__array[insert_index] = value
self.length += 1
def __setitem__(self, index, value):
self.__array[index] = value
def __copy__(self):
newone = type(self)(*self.__array)
newone.__dict__.update(self.__dict__)
return newone
def __deepcopy__(self):
newone = type(self)(*self.__array)
newone.__dict__.update(self.__dict__)
for x in self.__dict__:
newone.__dict__[x] = copy.deepcopy(self.__dict__[x])
return newone
@classmethod
def heap_sort(cls, list):
new_heap = Heap(*list)
result = new_heap.__array
i = len(result) - 1
while True:
result[0], result[i] = result[i], result[0]
new_heap.length -= 1
i -= 1
if i is 2:
break
new_heap.loop_heapify(0)
return result
def pop(self, index=-1):
node = self.__array.pop(index)
self.length -= 1
"""这里也可以使用比较复杂的逻辑支持移动一个元素(O(lgn))，但是调用这个方法比较方便
复杂度:O(n)
"""
self.__build_heap()
return node
def pop_max(self):
"""
这个方法仅仅支持pop首元素，因此可以直接调用loop_heapify。上面的不可以
复杂度:O(lgn)
"""
max_node = self.__array[0]
self.length -= 1
if self.length > 0:
self.__array[0] = self.__array.pop()
self.loop_heapify(0)
return max_node
class MaxQueue(object):
"""使用堆实现最大优先堆"""
class Node(object):
"""优先队列里面的节点"""
def __init__(self, key, obj):
super(MaxQueue.Node, self).__init__()
self.key = key
self.obj = obj
def __str__(self):
return "".join(["Key: ", str(self.key), "\tObject:", str(self.obj)])
def __cmp__(self, other):
if self.key < other.key:
return -1
elif self.key > other.key:
return 1
else:
return 0
def __init__(self, kargs):
super(MaxQueue, self).__init__()
values = [MaxQueue.Node(kargs[obj], obj) for obj in kargs]
self.__heap = Heap(*values)
self.length = self.__heap.length
def max(self):
return self.__heap[0].obj
def pop_max(self):
self.length -= 1
if self.length < 0:
return None
return self.__heap.pop_max()
def __setitem__(self, key, value):
node = MaxQueue.Node(key, value)
self.__heap.append_with_one_assign(node)
def __str__(self):
return str(self.__heap)
class FifoQueue(object):
"""先进先出队列使用优先队列实现，基本思路是给键设一个递减的数字"""
def __init__(self, *arg):
super(FifoQueue, self).__init__()
self.__min_key = 0
result = []
for value in arg:
result.append((value, self.__min_key))
self.__min_key -= 1
self.__max_queue = MaxQueue(dict(result))
self.length = self.__max_queue.length
def __str__(self):
return str(self.__max_queue)
def pop(self):
return self.__max_queue.pop_max()
def append(self):
self.__min_key -= 1
self.__max_queue[self.__min_key] = value
def main():
queue = FifoQueue(16, 4, 10, 14, 7, 9, 3, 2, 8, 1)
print queue
for x in xrange(0, queue.length):
print queue.pop()
if __name__ == '__main__':
main()