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 << 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))])