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

# Solution Notebook¶

## Constraints¶

• Is a naive solution sufficient (ie not stable, not based on a heap)?
• Yes
• Are duplicates allowed?
• Yes
• Can we assume the input is valid?
• No
• Can we assume this fits memory?
• Yes

## Test Cases¶

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

## Algorithm¶

Wikipedia's animation:

We can do this recursively or iteratively. Iteratively will be more efficient as it doesn't require the extra space overhead with the recursive calls.

• For each element
• Check every element to the right to find the min
• If min < current element, swap

Complexity:

• Time: O(n^2) average, worst, best
• Space: O(1) iterative, O(m) recursive where m is the recursion depth (unless tail-call elimination is available, then O(1))
• Note: Tail call elimination is not inherently available in Python, see the following StackOverflow post.

Misc:

• In-place
• Most implementations are not stable, due to swapping of values

Selection sort might be a good option if moving elements is more expensive than comparing them, as it requires at most n-1 swaps.

The finding of a minimum element can be done with a min heap, which would change the worst-case run time to O(n log(n)) and increase the space to O(n). This is called a heap sort.

## Code¶

In [1]:
class SelectionSort(object):

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

def sort_iterative_alt(self, data):
if data is None:
raise TypeError('data cannot be None')
if len(data) < 2:
return data
for i in range(len(data) - 1):
self._swap(data, i, self._find_min_index(data, i))
return data

def sort_recursive(self, data):
if data is None:
raise TypeError('data cannot be None')
if len(data) < 2:
return data
return self._sort_recursive(data, start=0)

def _sort_recursive(self, data, start):
if data is None:
return
if start < len(data) - 1:
swap(data, start, self._find_min_index(data, start))
self._sort_recursive(data, start + 1)
return data

def _find_min_index(self, data, start):
min_index = start
for i in range(start + 1, len(data)):
if data[i] < data[min_index]:
min_index = i
return min_index

def _swap(self, data, i, j):
if i != j:
data[i], data[j] = data[j], data[i]
return data


## Unit Test¶

In [2]:
%%writefile test_selection_sort.py
import unittest

class TestSelectionSort(unittest.TestCase):

def test_selection_sort(self, func):
print('None input')
self.assertRaises(TypeError, func, None)

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

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

print('Two or more elements')
data = [5, 1, 7, 2, 6, -3, 5, 7, -10]
self.assertEqual(func(data), sorted(data))

print('Success: test_selection_sort\n')

def main():
test = TestSelectionSort()
selection_sort = SelectionSort()
test.test_selection_sort(selection_sort.sort)
try:
test.test_selection_sort(selection_sort.sort_recursive)
test.test_selection_sort(selection_sort.sor_iterative_alt)
except NameError:
# Alternate solutions are only defined
# in the solutions file
pass

if __name__ == '__main__':
main()

Overwriting test_selection_sort.py

In [3]:
%run -i test_selection_sort.py

None input
Empty input
One element
Two or more elements
Success: test_selection_sort

None input
Empty input
One element
Two or more elements