堆排序
M
A
R
S
A
P
"""
This is a pure Python implementation of the heap sort algorithm.
For doctests run following command:
python -m doctest -v heap_sort.py
or
python3 -m doctest -v heap_sort.py
For manual testing run:
python heap_sort.py
"""
def heapify(unsorted, index, heap_size):
largest = index
left_index = 2 * index + 1
right_index = 2 * index + 2
if left_index < heap_size and unsorted[left_index] > unsorted[largest]:
largest = left_index
if right_index < heap_size and unsorted[right_index] > unsorted[largest]:
largest = right_index
if largest != index:
unsorted[largest], unsorted[index] = unsorted[index], unsorted[largest]
heapify(unsorted, largest, heap_size)
def heap_sort(unsorted):
"""
Pure implementation of the heap sort algorithm in Python
:param collection: some mutable ordered collection with heterogeneous
comparable items inside
:return: the same collection ordered by ascending
Examples:
>>> heap_sort([0, 5, 3, 2, 2])
[0, 2, 2, 3, 5]
>>> heap_sort([])
[]
>>> heap_sort([-2, -5, -45])
[-45, -5, -2]
"""
n = len(unsorted)
for i in range(n // 2 - 1, -1, -1):
heapify(unsorted, i, n)
for i in range(n - 1, 0, -1):
unsorted[0], unsorted[i] = unsorted[i], unsorted[0]
heapify(unsorted, 0, i)
return unsorted
if __name__ == "__main__":
user_input = input("Enter numbers separated by a comma:\n").strip()
unsorted = [int(item) for item in user_input.split(",")]
print(heap_sort(unsorted))
关于此算法
问题陈述
给定一个包含 n 个元素的无序数组，编写一个函数对数组进行排序。
方法
- 从输入数据构建一个最大堆。
- 此时，最大项存储在堆的根节点处。用堆的最后一个项替换它，然后将堆的大小减少 1。最后，对树的根节点进行堆化。
- 当堆的大小大于 1 时，重复上述步骤。
时间复杂度
O(n log n) 最坏情况性能
O(n log n)（不同的键）或 O(n)（相等的键）最佳情况性能
O(n log n) 平均性能
空间复杂度
O(1) 最坏情况辅助空间
示例
Input data: 4, 10, 3, 5, 1
4(0)
/ \
10(1) 3(2)
/ \
5(3) 1(4)
The numbers in bracket represent the indices in the array
representation of data.
Applying heapify procedure to index 1:
4(0)
/ \
10(1) 3(2)
/ \
5(3) 1(4)
Applying heapify procedure to index 0:
10(0)
/ \
5(1) 3(2)
/ \
4(3) 1(4)
The heapify procedure calls itself recursively to build heap
in top down manner.
