# -*- 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 << 1) + 1;     @classmethod     def right(cls, i):         """右儿子下标"""         return (i << 1) + 2; 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 < heap_size and A[l] < A[i]:             least = l         else:             least = i         if r < heap_size and A[r] < A[least]:             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] < 1         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 <= val, "new key is larger than current 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))])