This notebook was prepared by Donne Martin. Source and license info is on GitHub.

Solution Notebook

Problem: Implement insertion sort.


  • Is a naive solution sufficient?
    • Yes
  • Are duplicates allowed?
    • Yes
  • Can we assume the input is valid?
    • No
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None -> Exception
  • Empty input -> []
  • One element -> [element]
  • Two or more elements


Wikipedia's animation: alt text

  • For each value index 1 to n - 1
    • Compare with all elements to the left of the current value to determine new insertion point
      • Hold current value in temp variable
      • Shift elements from new insertion point right
      • Insert value in temp variable
      • Break


  • Time: O(n^2) average, worst. O(1) best if input is already sorted
  • Space: O(1) for the iterative solution


  • In-place
  • Stable

Insertion sort works well for very small datasets where most of the input is already sorted.


In [1]:
class InsertionSort(object):

    def sort(self, data):
        if data is None:
            raise TypeError('data cannot be None')
        if len(data) < 2:
            return data
        for r in range(1, len(data)):
            for l in range(r):
                if data[r] < data[l]:
                    temp = data[r]
                    data[l+1:r+1] = data[l:r]
                    data[l] = temp
        return data

Unit Test

In [2]:
import unittest

class TestInsertionSort(unittest.TestCase):

    def test_insertion_sort(self):
        insertion_sort = InsertionSort()

        print('None input')
        self.assertRaises(TypeError, insertion_sort.sort, None)

        print('Empty input')
        self.assertEqual(insertion_sort.sort([]), [])

        print('One element')
        self.assertEqual(insertion_sort.sort([5]), [5])

        print('Two or more elements')
        data = [5, 1, 7, 2, 6, -3, 5, 7, -1]
        self.assertEqual(insertion_sort.sort(data), sorted(data))

        print('Success: test_insertion_sort')

def main():
    test = TestInsertionSort()

if __name__ == '__main__':
In [3]:
%run -i
None input
Empty input
One element
Two or more elements
Success: test_insertion_sort