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

如果插入的键具有可比性但不像int型,则可能重写它们上的比较操作符(即<=变成>,>变成<=)。否则,您可以重写heapq。heapq模块中的_siftup(最后都是Python代码)。

其他回答

你可以使用

import heapq
listForTree = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]    
heapq.heapify(listForTree)             # for a min heap
heapq._heapify_max(listForTree)        # for a maxheap!!

如果你想要弹出元素,使用:

heapq.heappop(minheap)      # pop from minheap
heapq._heappop_max(maxheap) # pop from maxheap

如果你想用max heap得到最大的K元素,你可以做下面的技巧:

nums= [3,2,1,5,6,4]
k = 2  #k being the kth largest element you want to get
heapq.heapify(nums) 
temp = heapq.nlargest(k, nums)
return temp[-1]

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"

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()

这是一个基于heapq的简单MaxHeap实现。虽然它只适用于数值。

import heapq
from typing import List


class MaxHeap:
    def __init__(self):
        self.data = []

    def top(self):
        return -self.data[0]

    def push(self, val):
        heapq.heappush(self.data, -val)

    def pop(self):
        return -heapq.heappop(self.data)

用法:

max_heap = MaxHeap()
max_heap.push(3)
max_heap.push(5)
max_heap.push(1)
print(max_heap.top())  # 5