# -*- coding: utf-8 -*-
class Heap(object):
@classmethod
def parent(cls, i):
""" Parent subscript """
return int((i - 1) >> 1);
@classmethod
def left(cls, i):
""" Left son subscript """
return (i << 1) + 1;
@classmethod
def right(cls, i):
""" Right son subscript """
return (i << 1) + 2;
class MaxPriorityQueue(list, Heap):
@classmethod
def max_heapify(cls, A, i, heap_size):
""" Most of the A[i] Is the subtree of the root """
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):
""" Returns the maximum element. The pseudo-code is as follows:
HEAP-MAXIMUM(S)
1 return A[1]
T(n) = O(1)
"""
return self[0]
def extract_max(self):
""" Remove and return the maximum element. The pseudo-code is as follows:
HEAP-EXTRACT-MAX(A)
1 if heap-size[A] < 1
2 then error "heap underflow"
3 max please A[1]
4 A[1] please A[heap-size[A]] //The tail element comes first
5 heap-size[A] please heap-size[A] - 1 //Reduce heap - size [A]
6 MAX-HEAPIFY(A, 1) //Keep the maximum number of properties
7 return max
T(n) = Theta. (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):
""" will i The value at PI increases to PI key , the pseudo-code is as follows:
HEAP-INCREASE-KEY(A, i, key)
1 if key < A[i]
2 the error "new key is smaller than current key"
3 A[i] please key
4 while i > 1 and A[PARENT(i)] < A[i] //It's not the root and the parent is smaller
5 do exchange A[i] ↔ A[PARENT(i)] //Swap two elements
6 i please PARENT(i) //Point to the parent location
T(n) = Theta. (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):
""" will key insert A , the pseudo-code is as follows:
MAX-HEAP-INSERT(A, key)
1 heap-size[A] please heap-size[A] + 1 //Increase the number of elements
2 A[heap-size[A]] please - up //The initial addition is minus infinity
3 HEAP-INCREASE-KEY(A, heap-size[A], key) //Increases the new element to key
T(n) = Theta. (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() # Insert mode to build maximum heap
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() # Remove and return the largest element
elif val == 1:
val = queue.maximum() # Returns the maximum element
else:
val = queue[1] + 10
queue.increase_key(1, val) # queue[1] increase 10
print(queue, val)
print([queue.extract_max() for i in range(len(queue))])