复制代码 代码如下:
# -*- coding: utf-8 -*-class heap(object):
    @classmethod
    def parent(cls, i):
        父结点下标
        return int((i - 1) >> 1);
    @classmethod
    def left(cls, i):
        左儿子下标
        return (i
    @classmethod
    def right(cls, i):
        右儿子下标
        return (i
class minpriorityqueue(list, heap):
    @classmethod
    def min_heapify(cls, a, i, heap_size):
        最小堆化a[i]为根的子树
        l, r = cls.left(i), cls.right(i)
        if l             least = l
        else:
            least = i
        if r             least = r
        if least != i:
            a[i], a[least] = a[least], a[i]
            cls.min_heapify(a, least, heap_size)
    def minimum(self):
        返回最小元素，伪码如下：
        heap-minimum(a)
        1  return a[1]
        t(n) = o(1)
return self[0]
    def extract_min(self):
        去除并返回最小元素，伪码如下：
        heap-extract-min(a)
        1  if heap-size[a]         2    then error heap underflow
        3  min ← a[1]
        4  a[1] ← a[heap-size[a]] // 尾元素放到第一位
        5  heap-size[a] ← heap-size[a] - 1 // 减小heap-size[a]
        6  min-heapify(a, 1) // 保持最小堆性质
        7  return min
        t(n) = θ(lgn)
heap_size = len(self)
        assert heap_size > 0, heap underflow
        val = self[0]
        tail = heap_size - 1
        self[0] = self[tail]
        self.min_heapify(self, 0, tail)
        self.pop(tail)
        return val
    def decrease_key(self, i, key):
        将i处的值减少到key，伪码如下：
        heap-decrease-key(a, i, key)
        1  if key > a[i]
        2    then error new key is larger than current key
        3  a[i] ← key
        4  while i > 1 and a[parent(i)] > a[i] // 不是根结点且父结点更大时
        5    do exchange a[i] ↔ a[parent(i)] // 交换两元素
        6       i ← parent(i) // 指向父结点位置
        t(n) = θ(lgn)
val = self[i]
        assert key         self[i] = key
        parent = self.parent
        while i > 0 and self[parent(i)] > self[i]:
            self[i], self[parent(i)] = self[parent(i)], self[i]
            i = parent(i)
    def insert(self, key):
        将key插入a，伪码如下：
        min-heap-insert(a, key)
        1  heap-size[a] ← heap-size[a] + 1 // 对元素个数增加
        2  a[heap-size[a]] ← +∞ // 初始新增加元素为+∞
        3  heap-decrease-key(a, heap-size[a], key) // 将新增元素减少到key
        t(n) = θ(lgn)
self.append(float('inf'))
        self.decrease_key(len(self) - 1, key)
if __name__ == '__main__':
    import random
    keys = range(10)
    random.shuffle(keys)
    print(keys)
    queue = minpriorityqueue() # 插入方式建最小堆
    for i in keys:
        queue.insert(i)
    print(queue)
    print('*' * 30)
    for i in range(len(queue)):
        val = i % 3
        if val == 0:
            val = queue.extract_min() # 去除并返回最小元素
        elif val == 1:
            val = queue.minimum() # 返回最小元素
        else:
            val = queue[1] - 10
            queue.decrease_key(1, val) # queue[1]减少10
        print(queue, val)
    print([queue.extract_min() for i in range(len(queue))])