heapq内置模块位于./Anaconda3/Lib/heapq.py，提供基于堆的优先排序算法
堆的逻辑结构就是完全二叉树，并且二叉树中父节点的值小于等于该节点的所有子节点的值。这种实现可以使用 heap[k] <= heap[2k+1] 并且 heap[k] <= heap[2k+2] （其中 k 为索引，从 0 开始计数）的形式体现，对于堆来说，最小元素即为根元素 heap[0]。
1.初始化
可以通过 list 对 heap 进行初始化，或者通过 api 中的 heapify 将已知的 list 转化为 heap 对象。
2. heapq.py中提供的函数方法
heapq.heappush(heap, item)
heapq.heappop(heap)：返回 root 节点，即 heap 中最小的元素。
heapq.heapreplace(heap,item): python3中heappushpop的更高效版。
heapq.heappushpop(heap, item)：向 heap 中加入 item 元素，并返回 heap 中最小元素。
heapq.heapify(x)：Transform list into a heap, in-place, in O(len(x)) time
heapq.merge(*iterables, key=None, reverse=False)
heapq.nlargest(n, iterable, key=None)：返回可枚举对象中的 n 个最大值，并返回一个结果集 list，key 为对该结果集的操作。
heapq.nsmallest(n, iterable, key=None)：同上相反
heapq._heappop_max(heap): Maxheap version of a heappop
heapq._heapreplace_max(heap,item)：Maxheap version of a heappop followed by a heappush.
heapq._heapify_max(x)：Transform list into a maxheap, in-place, in O(len(x)) time
heapq._siftdown(heap,startpos,pos)： Follow the path to the root, moving parents down until finding a place
heapq._siftup(heap,pos)：Bubble up the smaller child until hitting a leaf
heapq._siftdown_max(heap,startpos,pos)：Maxheap variant of _siftdown
heapq._siftup_max(heap,pos)：Maxheap variant of _siftup
3. 举例
1 import heapq
2 def heapsort(iterable):
3 h = []
4 for i in iterable:
5 heapq.heappush(h, i)
6 return [heapq.heappop(h) for i in range(len(h))]
7
8 # method 1: sort to list
9 s = [3, 5, 1, 2, 4, 6, 0, 1]
10 print(heapsort(s))
11 '''
12 [0, 1, 1, 2, 3, 4, 5, 6]
13 '''
14
15 # method 2: use key to find price_min
16 portfolio = [{'name': 'IBM', 'shares': 100, 'price': 91.1},
17 {'name': 'AAPL', 'shares': 50, 'price': 543.22},
18 {'name': 'FB', 'shares': 200, 'price': 21.09},
19 {'name': 'HPQ', 'shares': 35, 'price': 31.75},
20 {'name': 'YHOO', 'shares': 45, 'price': 16.35},
21 {'name': 'ACME', 'shares': 75, 'price': 115.65}]
22 cheap = heapq.nsmallest(1, portfolio, key=lambda s:s['price'])
23 print(cheap)
24 '''
25 [{'name': 'YHOO', 'shares': 45, 'price': 16.35}]
26 '''
27
28 # method 3: use while to push min element
29 def heapilize_list(x):
30 n = len(x)
31 # 获取存在子节点的节点 index 列表，并对每个节点单元进行最小堆处理
32 for i in reversed(range(n // 2)):
33 raiseup_node(x, i)
34
35 def put_down_node(heap, startpos, pos):
36 current_item = heap[pos]
37 # 判断单元中最小子节点与父节点的大小
38 while pos > startpos:
39 parent_pos = (pos - 1) >> 1
40 parent_item = heap[parent_pos]
41 if current_item < parent_item:
42 heap[pos] = parent_item
43 pos = parent_pos
44 continue
45 break
46 heap[pos] = current_item
47
48 def raiseup_node(heap, pos):
49 heap_len = len(heap)
50 start_pos = pos
51 current_item = heap[pos]
52 left_child_pos = pos * 2 + 1
53 while left_child_pos < heap_len:
54 right_child_pos = left_child_pos + 1
55 # 将这个单元中的最小子节点元素与父节点元素进行位置调换
56 if right_child_pos < heap_len and not heap[left_child_pos] < heap[right_child_pos]:
57 left_child_pos = right_child_pos
58 heap[pos] = heap[left_child_pos]
59 pos = left_child_pos
60 left_child_pos = pos * 2 + 1
61 heap[pos] = current_item
62 put_down_node(heap, start_pos, pos)
63
64 p = [4, 6, 2, 10, 1]
65 heapilize_list(p)
66 print(p)
67 '''
68 [1, 4, 2, 10, 6]
69 '''
未完待续
问题1：
1 def heapify(x):
2 for i in reversed(range(n//2)):
3 _siftup(x, i)
n//2是什么意思？