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插入排序

M
A
R
S
A
P
以及 5 位其他贡献者
"""
A pure Python implementation of the insertion sort algorithm

This algorithm sorts a collection by comparing adjacent elements.
When it finds that order is not respected, it moves the element compared
backward until the order is correct.  It then goes back directly to the
element's initial position resuming forward comparison.

For doctests run following command:
python3 -m doctest -v insertion_sort.py

For manual testing run:
python3 insertion_sort.py
"""

from collections.abc import MutableSequence
from typing import Any, Protocol, TypeVar


class Comparable(Protocol):
    def __lt__(self, other: Any, /) -> bool: ...


T = TypeVar("T", bound=Comparable)


def insertion_sort(collection: MutableSequence[T]) -> MutableSequence[T]:
    """A pure Python implementation of the insertion sort algorithm

    :param collection: some mutable ordered collection with heterogeneous
    comparable items inside
    :return: the same collection ordered by ascending

    Examples:
    >>> insertion_sort([0, 5, 3, 2, 2])
    [0, 2, 2, 3, 5]
    >>> insertion_sort([]) == sorted([])
    True
    >>> insertion_sort([-2, -5, -45]) == sorted([-2, -5, -45])
    True
    >>> insertion_sort(['d', 'a', 'b', 'e', 'c']) == sorted(['d', 'a', 'b', 'e', 'c'])
    True
    >>> import random
    >>> collection = random.sample(range(-50, 50), 100)
    >>> insertion_sort(collection) == sorted(collection)
    True
    >>> import string
    >>> collection = random.choices(string.ascii_letters + string.digits, k=100)
    >>> insertion_sort(collection) == sorted(collection)
    True
    """

    for insert_index in range(1, len(collection)):
        insert_value = collection[insert_index]
        while insert_index > 0 and insert_value < collection[insert_index - 1]:
            collection[insert_index] = collection[insert_index - 1]
            insert_index -= 1
        collection[insert_index] = insert_value
    return collection


if __name__ == "__main__":
    from doctest import testmod

    testmod()

    user_input = input("Enter numbers separated by a comma:\n").strip()
    unsorted = [int(item) for item in user_input.split(",")]
    print(f"{insertion_sort(unsorted) = }")
关于此算法

问题陈述

给定一个包含 n 个元素的数组,编写一个函数,将该数组按升序排序。

方法

  • 定义一个“键”索引,该索引左侧的子数组已排序。
  • 将“键”初始化为 1,即数组的第二个元素(因为第二个元素左侧只有一个元素,可以视为包含一个元素的已排序数组)。
  • 如果位置 (key - 1) 处的元素的值小于位置 (key) 处的元素的值;则递增“键”。
  • 否则,将已排序子数组中大于位置“键”处元素的值的元素移动到其当前位置的前面一位。将位置“键”处元素的值放到新创建的空位中。

时间复杂度

  • О(n^2) 次比较,О(n^2) 次交换 - 最坏情况

  • O(n) 次比较,O(1) 次交换 - 最佳情况

空间复杂度

O(1) - (无需额外空间,排序在原地进行)

示例


12, 11, 13, 5, 6

Let us loop for i = 1 (second element of the array) to 4 (Size of input array)

i = 1.
Since 11 is smaller than 12, move 12 and insert 11 before 12
11, 12, 13, 5, 6

i = 2.
13 will remain at its position as all elements in sorted subarray are smaller than 13
11, 12, 13, 5, 6

i = 3.
5 will move to the beginning,
and all other elements from 11 to 13 will move one position ahead of their current position.
5, 11, 12, 13, 6

i = 4.
6 will move to position after 5,
and elements from 11 to 13 will move one position ahead of their current position.
5, 6, 11, 12, 13  -- sorted array

视频解释

解释插入排序算法的 CS50 视频