How does a radix sort algorithm work?

A radix sort algorithm works by sorting numbers digit by digit from least significant digit to most significant.

Radix sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by the individual digits which share the same significant position and value. The radix is the base of the number system. For example, for the decimal system, the radix is 10.

The algorithm begins by sorting numbers on the least significant digit. This process is repeated, moving towards the most significant digit. The sorting at each digit is often done using a stable sort algorithm to maintain the relative order of equal sort keys. A stable sort means that if two items have the same key, their order will remain unchanged. This is crucial for radix sort to work correctly.

There are two types of Radix Sort: Most Significant Digit (MSD) and Least Significant Digit (LSD). The LSD starts processing from the least significant digit and moves towards the most significant, stabilising the sort order with each pass. On the other hand, the MSD works the other way around, starting from the most significant digit and moving towards the least significant. It can be used to sort strings of characters, such as words or names.

The efficiency of radix sort depends on the number of digits in the numbers to be sorted. It is a linear time sorting algorithm, which makes it efficient for large lists of numbers. However, it is not as efficient when sorting numbers with a large number of digits.

In summary, radix sort is a unique sorting algorithm that sorts numbers digit by digit, using a stable sort algorithm at each digit. It is efficient for large lists of numbers with a small number of digits.