Algorithms Analysis Practice Test

The Big-O complexity of the selection sort algorithm is O(n^2). This classification arises from how the algorithm operates during its execution.

Selection sort works by dividing the input list into two parts: a sorted section and an unsorted section. Initially, the sorted section is empty, and the unsorted section contains all the elements. The algorithm repeatedly selects the smallest element from the unsorted section and moves it to the end of the sorted section.

To find the smallest element, the algorithm examines each element in the unsorted section. In the worst case, during the first iteration, it checks n elements, in the second iteration n-1 elements, and continues this pattern until there is only one element left to sort. The number of comparisons needed to sort an array of n elements can be expressed as:

(n-1) + (n-2) + ... + 1 + 0 = n(n-1)/2

This summation yields a quadratic expression, which simplifies to O(n^2). Therefore, the selection sort algorithm has a time complexity of O(n^2), reflecting the fact that it involves a nested loop structure where one loop runs n times and the inner loop runs increasingly fewer times down to 1.

Thus,