Explain the radix sort algorithm.

Explain the radix sort algorithm.

Radix sort is a non-comparative sorting algorithm that sorts data by processing individual digits or groups of digits from the least significant digit to the most significant digit. It is based on the idea of distributing the elements into different buckets or queues based on the value of the current digit being considered.

The radix sort algorithm starts by considering the least significant digit of each element in the input array. It then distributes the elements into 10 different buckets (0 to 9) based on the value of this digit. After distributing all the elements, it collects them back into a single array in the order of the buckets. This process is repeated for each subsequent digit, moving from the least significant to the most significant, until all digits have been considered.

The key idea behind radix sort is that by sorting the elements based on each digit individually, it can eventually sort the entire array. This is because the relative order of elements with the same digit value is preserved during each iteration.

Radix sort can be implemented using either the least significant digit (LSD) or the most significant digit (MSD) approach. In the LSD approach, the algorithm starts with the least significant digit and moves towards the most significant digit. In the MSD approach, the algorithm starts with the most significant digit and moves towards the least significant digit.

The time complexity of radix sort depends on the number of digits in the input elements and the number of elements to be sorted. It has a time complexity of O(d * (n + k)), where d is the number of digits, n is the number of elements, and k is the range of values for each digit (usually 10 for decimal numbers). Radix sort is often considered efficient for large datasets with a relatively small range of values.

Overall, radix sort is a stable sorting algorithm that can efficiently sort data by considering individual digits or groups of digits. It is particularly useful for sorting integers or fixed-length strings.