Selection Sort is an in-place sorting algorithm that succeeds in sorting smaller arrays of values, but suffers with larger arrays.

How It Works?

Selection Sort works in-place, meaning it doesn't require a separate array for storing the sorted values. Instead we perform a series of swaps, finding lowest value (usually indicated by index j) to index i. Index i moves from left to right, shrinking the array at each pass.

Implementation

Below is a more traditional implementation where only one swap occurs, if and only if, a value is found to be smaller than nums[i]:

def traditionalSelectionSort(nums: list) -> list:
  for i in range(len(nums) - 1):
    minIndex = i

    for j in range(i, len(nums)):
      if nums[j] < nums[minIndex]:
        minIndex = j

    if minIndex != i:
      nums[i], nums[minIndex] = nums[minIndex], nums[i]

  return nums

print(selectionSort([3, 8, 2, 5, 7, 4]))
# => [2, 3, 4, 5, 7, 8]

Below is a modified version of implementation that will swap every value (nums[j]) less than nums[i]. I prefer this approach since it's more condensed and swapping values in an array is a constant operation (e.g. O(1)):

def modifiedSelectionSort(nums: list) -> list:
  for i in range(len(nums) - 1):    # i = receiving min value
    for j in range(i, len(nums)):   # j = searches for min values
      if nums[j] < nums[i]:         # swap with values < nums[i]
        nums[i], nums[j] = nums[j], nums[i]

  return nums

print(selectionSort([3, 8, 2, 5, 7, 4]))
# => [2, 3, 4, 5, 7, 8]

Visual Representation

Analysis

Selection Sort is similar to Insertion Sort (except for when comparing best-case performances, in which Insertion Sort is better).

Time:
  Worst:   O(n^2)
  Best:    O(n^2)
  Average: O(n^2)

Space: O(1) - swapping in place

Further Reading

Selection Sort - Wikipedia article on Selection Sort.