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 MaxPriorityQueue(list, Heap):
@classmethod
def max_heapify(cls, A, i, heap_size):
"""最大堆化A[i]为根的子树"""
l, r = cls.left(i), cls.right(i)
if l < heap_size and A[l] > A[i]:
largest = l
else:
largest = i
if r < heap_size and A[r] > A[largest]:
largest = r
if largest != i:
A[i], A[largest] = A[largest], A[i]
cls.max_heapify(A, largest, heap_size)
def maximum(self):
"""返回最大元素，伪码如下：
HEAP-MAXIMUM(S)
1 return A[1]
T(n) = O(1)
"""
return self[0]
def extract_max(self):
"""去除并返回最大元素，伪码如下：
HEAP-EXTRACT-MAX(A)
1 if heap-size[A] < 1
2 then error "heap underflow"
3 max ← 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 MAX-HEAPIFY(A, 1) // 保持最大堆性质
7 return max
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.max_heapify(self, 0, tail)
self.pop(tail)
return val
def increase_key(self, i, key):
"""将i处的值增加到key，伪码如下：
HEAP-INCREASE-KEY(A, i, key)
1 if key < A[i]
2 the error "new key is smaller 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小时
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 smaller 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：
MAX-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-INCREASE-KEY(A, heap-size[A], key) // 将新增元素增加到key
T(n) = θ(lgn)
"""
self.append(float('-inf'))
self.increase_key(len(self) - 1, key)
if __name__ == '__main__':
import random
keys = range(10)
random.shuffle(keys)
print(keys)
queue = MaxPriorityQueue() # 插入方式建最大堆
for i in keys:
queue.insert(i)
print(queue)
print('*' * 30)
for i in range(len(keys)):
val = i % 3
if val == 0:
val = queue.extract_max() # 去除并返回最大元素
elif val == 1:
val = queue.maximum() # 返回最大元素
else:
val = queue[1] + 10
queue.increase_key(1, val) # queue[1]增加10
print(queue, val)
print([queue.extract_max() for i in range(len(queue))])
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