Your language already sorts

Think of a teacher lining up a class by height. You don't need to write that routine yourself, because every language has a fast sort built in. It takes about n times log n steps, so even a million numbers sort in well under a second.

In Python it is a list method, in Java it is Arrays.sort, and in C++ it is sort. One line, and the list runs from smallest to largest.

Sorting is one line: in every language, so use it.

JavaScript: sorts as text unless you give it a compare function, so 10 would come before 9.

In code

nums = [7, 2, 9, 4, 1]
nums.sort()
# [1, 2, 4, 7, 9]

Sort [7, 2, 9, 4, 1], then find the 3rd smallest

Before sorting, the 3rd smallest could be anywhere.

Move 1 of 4

In a sorted list, position is rank

Once the class is lined up, the shortest child is first, the second shortest is next, and so on. The same is true of a sorted list: the smallest value sits at position 0, the 2nd smallest at position 1.

So the kth smallest sits at position k − 1. Repeats count once each time they appear: in 2, 2, 5 the 2nd smallest is 2.

After sorting: the kth smallest is just a lookup.

k counts from 1, but positions count from 0.

In code

nums.sort()
return nums[k - 1]