冒泡排序
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from typing import Any
def bubble_sort_iterative(collection: list[Any]) -> list[Any]:
"""Pure implementation of bubble sort algorithm in Python
:param collection: some mutable ordered collection with heterogeneous
comparable items inside
:return: the same collection ordered by ascending
Examples:
>>> bubble_sort_iterative([0, 5, 2, 3, 2])
[0, 2, 2, 3, 5]
>>> bubble_sort_iterative([])
[]
>>> bubble_sort_iterative([-2, -45, -5])
[-45, -5, -2]
>>> bubble_sort_iterative([-23, 0, 6, -4, 34])
[-23, -4, 0, 6, 34]
>>> bubble_sort_iterative([0, 5, 2, 3, 2]) == sorted([0, 5, 2, 3, 2])
True
>>> bubble_sort_iterative([]) == sorted([])
True
>>> bubble_sort_iterative([-2, -45, -5]) == sorted([-2, -45, -5])
True
>>> bubble_sort_iterative([-23, 0, 6, -4, 34]) == sorted([-23, 0, 6, -4, 34])
True
>>> bubble_sort_iterative(['d', 'a', 'b', 'e']) == sorted(['d', 'a', 'b', 'e'])
True
>>> bubble_sort_iterative(['z', 'a', 'y', 'b', 'x', 'c'])
['a', 'b', 'c', 'x', 'y', 'z']
>>> bubble_sort_iterative([1.1, 3.3, 5.5, 7.7, 2.2, 4.4, 6.6])
[1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7]
>>> bubble_sort_iterative([1, 3.3, 5, 7.7, 2, 4.4, 6])
[1, 2, 3.3, 4.4, 5, 6, 7.7]
>>> import random
>>> collection_arg = random.sample(range(-50, 50), 100)
>>> bubble_sort_iterative(collection_arg) == sorted(collection_arg)
True
>>> import string
>>> collection_arg = random.choices(string.ascii_letters + string.digits, k=100)
>>> bubble_sort_iterative(collection_arg) == sorted(collection_arg)
True
"""
length = len(collection)
for i in reversed(range(length)):
swapped = False
for j in range(i):
if collection[j] > collection[j + 1]:
swapped = True
collection[j], collection[j + 1] = collection[j + 1], collection[j]
if not swapped:
break # Stop iteration if the collection is sorted.
return collection
def bubble_sort_recursive(collection: list[Any]) -> list[Any]:
"""It is similar iterative bubble sort but recursive.
:param collection: mutable ordered sequence of elements
:return: the same list in ascending order
Examples:
>>> bubble_sort_recursive([0, 5, 2, 3, 2])
[0, 2, 2, 3, 5]
>>> bubble_sort_iterative([])
[]
>>> bubble_sort_recursive([-2, -45, -5])
[-45, -5, -2]
>>> bubble_sort_recursive([-23, 0, 6, -4, 34])
[-23, -4, 0, 6, 34]
>>> bubble_sort_recursive([0, 5, 2, 3, 2]) == sorted([0, 5, 2, 3, 2])
True
>>> bubble_sort_recursive([]) == sorted([])
True
>>> bubble_sort_recursive([-2, -45, -5]) == sorted([-2, -45, -5])
True
>>> bubble_sort_recursive([-23, 0, 6, -4, 34]) == sorted([-23, 0, 6, -4, 34])
True
>>> bubble_sort_recursive(['d', 'a', 'b', 'e']) == sorted(['d', 'a', 'b', 'e'])
True
>>> bubble_sort_recursive(['z', 'a', 'y', 'b', 'x', 'c'])
['a', 'b', 'c', 'x', 'y', 'z']
>>> bubble_sort_recursive([1.1, 3.3, 5.5, 7.7, 2.2, 4.4, 6.6])
[1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7]
>>> bubble_sort_recursive([1, 3.3, 5, 7.7, 2, 4.4, 6])
[1, 2, 3.3, 4.4, 5, 6, 7.7]
>>> import random
>>> collection_arg = random.sample(range(-50, 50), 100)
>>> bubble_sort_recursive(collection_arg) == sorted(collection_arg)
True
>>> import string
>>> collection_arg = random.choices(string.ascii_letters + string.digits, k=100)
>>> bubble_sort_recursive(collection_arg) == sorted(collection_arg)
True
"""
length = len(collection)
swapped = False
for i in range(length - 1):
if collection[i] > collection[i + 1]:
collection[i], collection[i + 1] = collection[i + 1], collection[i]
swapped = True
return collection if not swapped else bubble_sort_recursive(collection)
if __name__ == "__main__":
import doctest
from random import sample
from timeit import timeit
doctest.testmod()
# Benchmark: Iterative seems slightly faster than recursive.
num_runs = 10_000
unsorted = sample(range(-50, 50), 100)
timer_iterative = timeit(
"bubble_sort_iterative(unsorted[:])", globals=globals(), number=num_runs
)
print("\nIterative bubble sort:")
print(*bubble_sort_iterative(unsorted), sep=",")
print(f"Processing time (iterative): {timer_iterative:.5f}s for {num_runs:,} runs")
unsorted = sample(range(-50, 50), 100)
timer_recursive = timeit(
"bubble_sort_recursive(unsorted[:])", globals=globals(), number=num_runs
)
print("\nRecursive bubble sort:")
print(*bubble_sort_recursive(unsorted), sep=",")
print(f"Processing time (recursive): {timer_recursive:.5f}s for {num_runs:,} runs")
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
- 选择数组的第一个元素。
- 将其与下一个元素进行比较。
- 如果它大于下一个元素，则交换它们。
- 否则什么也不做。
- 对数组的每个索引重复此操作。
- 重复上述过程 n 次。
时间复杂度
O(n^2) 最坏情况性能
O(n) 最佳情况性能
O(n^2) 平均性能
空间复杂度
O(1) 最坏情况
创始人姓名
- 术语“冒泡排序”首次由 Iverson, K 于 1962 年使用。
示例
arr[] = {10, 80, 40, 30}
Indexes: 0 1 2 3
1. Index = 0, Number = 10
2. 10 < 80, do nothing and continue
3. Index = 1, Number = 80
4. 80 > 40, swap 80 and 40
5. The array now is {10, 40, 80, 30}
6. Index = 2, Number = 80
7. 80 > 30, swap 80 and 30
8. The array now is {10, 40, 30, 80}
Repeat the Above Steps again
arr[] = {10, 40, 30, 80}
Indexes: 0 1 2 3
1. Index = 0, Number = 10
2. 10 < 40, do nothing and continue
3. Index = 1, Number = 40
4. 40 > 30, swap 40 and 30
5. The array now is {10, 30, 40, 80}
6. Index = 2, Number = 40
7. 40 < 80, do nothing
8. The array now is {10, 30, 40, 80}
Repeat the Above Steps again
arr[] = {10, 30, 40, 80}
Indexes: 0 1 2 3
1. Index = 0, Number = 10
2. 10 < 30, do nothing and continue
3. Index = 1, Number = 30
4. 30 < 40, do nothing and continue
5. Index = 2, Number = 40
6. 40 < 80, do nothing
Since there are no swaps in above steps, it means the array is sorted and we can stop here.
视频讲解
其他
冒泡排序也称为下沉排序。
