Python包含了用于min-堆的heapq模块,但我需要一个max堆。在Python中我应该使用什么来实现最大堆?


当前回答

我还需要使用max-heap,我处理的是整数,所以我只是包装了我需要的heap中的两个方法,如下所示:

import heapq


def heappush(heap, item):
    return heapq.heappush(heap, -item)


def heappop(heap):
    return -heapq.heappop(heap)

然后,我只是分别用heappush()和heappop()替换了我的heapq.heappush()和heappop()调用。

其他回答

解决方案是当你在堆中存储你的值时对其求反,或者像这样反转你的对象比较:

import heapq

class MaxHeapObj(object):
  def __init__(self, val): self.val = val
  def __lt__(self, other): return self.val > other.val
  def __eq__(self, other): return self.val == other.val
  def __str__(self): return str(self.val)

max-heap的例子:

maxh = []
heapq.heappush(maxh, MaxHeapObj(x))
x = maxh[0].val  # fetch max value
x = heapq.heappop(maxh).val  # pop max value

但是您必须记住包装和打开您的值,这需要知道您正在处理的是最小堆还是最大堆。

MinHeap, MaxHeap类

为MinHeap和MaxHeap对象添加类可以简化代码:

class MinHeap(object):
  def __init__(self): self.h = []
  def heappush(self, x): heapq.heappush(self.h, x)
  def heappop(self): return heapq.heappop(self.h)
  def __getitem__(self, i): return self.h[i]
  def __len__(self): return len(self.h)

class MaxHeap(MinHeap):
  def heappush(self, x): heapq.heappush(self.h, MaxHeapObj(x))
  def heappop(self): return heapq.heappop(self.h).val
  def __getitem__(self, i): return self.h[i].val

使用示例:

minh = MinHeap()
maxh = MaxHeap()
# add some values
minh.heappush(12)
maxh.heappush(12)
minh.heappush(4)
maxh.heappush(4)
# fetch "top" values
print(minh[0], maxh[0])  # "4 12"
# fetch and remove "top" values
print(minh.heappop(), maxh.heappop())  # "4 12"

我创建了一个堆包装器,它将值颠倒以创建max-heap,还为min-heap创建了一个包装器类,以使库更像oop。这是要点。有三个班级;Heap(抽象类),HeapMin和HeapMax。

方法:

isempty() -> bool; obvious
getroot() -> int; returns min/max
push() -> None; equivalent to heapq.heappush
pop() -> int; equivalent to heapq.heappop
view_min()/view_max() -> int; alias for getroot()
pushpop() -> int; equivalent to heapq.pushpop

我创建了一个名为heap_class的包,它实现了最大堆,还将各种堆函数包装到一个与列表兼容的环境中。

>>> from heap_class import Heap
>>> h = Heap([3, 1, 9, 20], max=True)
>>> h.pop()
20
>>> h.peek()  # same as h[0]
9
>>> h.push(17)  # or h.append(17)
>>> h[0]  # same as h.peek()
17
>>> h[1]  # inefficient, but works
9

从最大堆中获得最小堆。

>>> y = reversed(h)
>>> y.peek()
1
>>> y  # repr is inefficient, but correct
Heap([1, 3, 9, 17], max=False)
>>> 9 in y
True
>>> y.raw()  # underlying heap structure
[1, 3, 17, 9]

正如其他人所提到的,在max堆中处理字符串和复杂对象在heapq中是相当困难的,因为它们不同 否定的形式。heap_class实现简单:

>>> h = Heap(('aa', 4), ('aa', 5), ('zz', 2), ('zz', 1), max=True)
>>> h.pop()
('zz', 2)

支持自定义键,并与后续的推/追加和弹出一起工作:

>>> vals = [('Adam', 'Smith'), ('Zeta', 'Jones')]
>>> h = Heap(vals, key=lambda name: name[1])
>>> h.peek()  # Jones comes before Smith
('Zeta', 'Jones')
>>> h.push(('Aaron', 'Allen'))
>>> h.peek()
('Aaron', 'Allen')

(实现是建立在heapq函数上的,所以它都是用C语言或C语言包装的,除了Python中max heap上的heappush和heapreplace)

arr = [3,4,5,1,2,3,0,7,8,90,67,31,2,5,567]
# max-heap sort will lead the array to assending order
def maxheap(arr,p):
    
    for i in range(len(arr)-p):
        if i > 0:
            child = i
            parent = (i+1)//2 - 1
            
            while arr[child]> arr[parent] and child !=0:
                arr[child], arr[parent] = arr[parent], arr[child]
                child = parent
                parent = (parent+1)//2 -1
                
    
def heapsort(arr):
    for i in range(len(arr)):
        maxheap(arr,i)
        arr[0], arr[len(arr)-i-1]=arr[len(arr)-i-1],arr[0]
        
    return arr
        

print(heapsort(arr))

试试这个

扩展int类并重写__lt__是一种方法。

import queue
class MyInt(int):
    def __lt__(self, other):
        return self > other

def main():
    q = queue.PriorityQueue()
    q.put(MyInt(10))
    q.put(MyInt(5))
    q.put(MyInt(1))
    while not q.empty():
        print (q.get())


if __name__ == "__main__":
    main()