概述

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,tail)
        self.pop(tail)
        return val

    def decrease_key(self,key):
        """将i处的值减少到key，伪码如下：
        HEAP-DECREASE-KEY(A,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))])

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