How does the radix sort algorithm sort numbers?

Radix sort algorithm sorts numbers by processing individual digits, starting from the least significant digit to the most significant one.

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 works by distributing the numbers into buckets according to their radix. It starts from the least significant digit (rightmost digit) and moves towards the most significant digit (leftmost digit). For each digit, the numbers are collected from the buckets, which preserves the order of the previous step. This process is repeated for each digit until all digits have been processed.

There are two types of Radix Sort: Most Significant Digit (MSD) and Least Significant Digit (LSD). The LSD radix sort is the most common and it starts from the least significant digit and moves towards the most significant. It uses a stable sort algorithm, like counting sort or bucket sort, to sort digits at each stage. On the other hand, the MSD radix sort starts from the most significant digit and moves towards the least significant. It uses a recursive sort to sort the digits.

The time complexity of Radix Sort is O(nk), where n is the number of elements and k is the number of digits in the maximum number. This makes it very efficient for large data sets. However, it has a space complexity of O(n + k), which means it requires additional space to perform the sorting.

In summary, Radix Sort is a unique sorting algorithm that sorts numbers digit by digit from least significant to most significant. It is efficient for large data sets, but requires additional space to perform the sorting.