Selection Sort Algorithm

The selection sort algorithm sorts an array by repeatedly finding the minimum element (if sorting in ascending order) from the unsorted part of the array and putting it at the end of the sorted part of the array. The algorithm maintains two subarrays in a given array:

1. A subarray of already sorted elements.
2. A subarray of elements that remain to be sorted.

At the start of the algorithm, the first subarray is empty. In each pass through the outer loop of the selection sort, the minimum element from the unsorted subarray is selected and moved to the end of the sorted subarray.

Pseudocode

procedure selection_sort(array : list of sortable items, n : length of list)
    i ← 0
    while i < n - 1
        min_index ← i
        j ← i + 1
        while j < n
            if array[j] < array[min_index]
                min_index ← j
            end if
            j ← j + 1
        end while
        swap array[i] and array[min_index]
        i ← i + 1
    end while
end procedure

Example

The following example illustrates how an array changes after each pass through the outer loop of the selection sort algorithm.

Complexity

Time Complexity: O(n²)

Space Complexity: O(1)

The primary advantage of selection sort is that it never makes more than O(n) swaps, which can be useful if the array elements are large and copying them is a costly operation.