heapq 模块提供了堆算法。heapq是一种子节点和父节点排序的树形数据结构。这个模块提供heap[k] <= heap[2*k+1] and heap[k] <= heap[2*k+2]。为了比较不存在的元素被人为是无限大的。heap最小的元素总是[0]。

打印 heapq 类型

import math import randomfrom cStringIO import StringIOdef show_tree(tree, total_width=36, fill=' '): output = StringIO() last_row = -1 for i, n in enumerate(tree): if i: row = int(math.floor(math.log(i+1, 2))) else: row = 0 if row != last_row: output.write('\n') columns = 2**row col_width = int(math.floor((total_width * 1.0) / columns)) output.write(str(n).center(col_width, fill)) last_row = row print output.getvalue() print '-' * total_width print returndata = random.sample(range(1,8), 7)print 'data: ', datashow_tree(data)

打印结果

data: [3, 2, 6, 5, 4, 7, 1] 3 2 6 5 4 7 1 -------------------------heapq.heappush(heap, item)

push一个元素到heap里, 修改上面的代码

heap = []data = random.sample(range(1,8), 7)print 'data: ', datafor i in data: print 'add %3d:' % i heapq.heappush(heap, i) show_tree(heap)

打印结果

data: [6, 1, 5, 4, 3, 7, 2]add 6: 6 ------------------------------------add 1: 1 6 ------------------------------------add 5: 1 6 5 ------------------------------------add 4: 1 4 5 6------------------------------------add 3: 1 3 5 6 4------------------------------------add 7: 1 3 5 6 4 7------------------------------------add 2: 1 3 2 6 4 7 5------------------------------------

根据结果可以了解，子节点的元素大于父节点元素。而兄弟节点则不会排序。

heapq.heapify(list)

将list类型转化为heap, 在线性时间内, 重新排列列表。

print 'data: ', dataheapq.heapify(data)print 'data: ', datashow_tree(data)

打印结果

data: [2, 7, 4, 3, 6, 5, 1]data: [1, 3, 2, 7, 6, 5, 4] 1 3 2 7 6 5 4 ------------------------------------heapq.heappop(heap)

删除并返回堆中最小的元素, 通过heapify() 和heappop()来排序。

data = random.sample(range(1, 8), 7)print 'data: ', dataheapq.heapify(data)show_tree(data)heap = []while data: i = heapq.heappop(data) print 'pop %3d:' % i show_tree(data) heap.append(i)print 'heap: ', heap

打印结果

data: [4, 1, 3, 7, 5, 6, 2] 1 4 2 7 5 6 3------------------------------------pop 1: 2 4 3 7 5 6------------------------------------pop 2: 3 4 6 7 5------------------------------------pop 3: 4 5 6 7------------------------------------pop 4: 5 7 6------------------------------------pop 5: 6 7------------------------------------pop 6: 7------------------------------------pop 7:------------------------------------heap: [1, 2, 3, 4, 5, 6, 7]

可以看到已排好序的heap。

heapq.heapreplace(iterable, n)

删除现有元素并将其替换为一个新值。

data = random.sample(range(1, 8), 7)print 'data: ', dataheapq.heapify(data)show_tree(data)for n in [8, 9, 10]: smallest = heapq.heapreplace(data, n) print 'replace %2d with %2d:' % (smallest, n) show_tree(data)

打印结果

data: [7, 5, 4, 2, 6, 3, 1] 1 2 3 5 6 7 4------------------------------------replace 1 with 8: 2 5 3 8 6 7 4------------------------------------replace 2 with 9: 3 5 4 8 6 7 9------------------------------------replace 3 with 10: 4 5 7 8 6 10 9------------------------------------

heapq.nlargest(n, iterable) 和 heapq.nsmallest(n, iterable)

返回列表中的n个最大值和最小值

data = range(1,6)l = heapq.nlargest(3, data)print l # [5, 4, 3]s = heapq.nsmallest(3, data)print s # [1, 2, 3]

PS：一个计算题
构建元素个数为 K=5 的最小堆代码实例:

#!/usr/bin/env python # -*- encoding: utf-8 -*- # Author: kentzhan # import heapq import random heap = [] heapq.heapify(heap) for i in range(15): item = random.randint(10, 100) print "comeing ", item, if len(heap) >= 5: top_item = heap[0] # smallest in heap if top_item < item: # min heap top_item = heapq.heappop(heap) print "pop", top_item, heapq.heappush(heap, item) print "push", item, else: heapq.heappush(heap, item) print "push", item, pass print heap pass print heap print "sort" heap.sort() print heap

结果: