The Algorithms logo
The Algorithms
AboutDonate
"""
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
"""


def insertion_sort(collection: list) -> list:
    """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, insert_value in enumerate(collection[1:]):
        temp_index = insert_index
        while insert_index >= 0 and insert_value < collection[insert_index]:
            collection[insert_index + 1] = collection[insert_index]
            insert_index -= 1
        if insert_index != temp_index:
            collection[insert_index + 1] = 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) = }")

Insertion Sort

M
A
E
R
s
S
L
K
and 31 more contributors

Problem Statement

Given an array of n elements, write a function to sort the array in increasing order.

Approach

  • Define a "key" index, the subarray to the left of which is sorted.
  • Initiate "key" as 1, ie. the second element of array(as there is only one element to left of the second element, which can be considered as sorted array with one element).
  • If value of element at (key - 1) position is less than value of element at (key) position; increment "key".
  • Else move elements of sorted subarray that are greater than value of element at "key" to one position ahead of their current position. Put the value of element at "key" in the newly created void.

Time Complexity

  • О(n^2) comparisons, О(n^2) swaps -- Worst Case

  • O(n) comparisons, O(1) swaps -- Best Case

Space Complexity

O(1) -- (No extra space needed, sorting done in place)

Example


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

Code Implementation Links

Video Explanation

A CS50 video explaining the Insertion Search Algorithm