# Selection Sort

## Dec. 29 2019

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
``````