Radix Sort

Radix Sort is a non-comparative sorting algorithm that sorts integers by processing individual digits. Unlike comparison-based algorithms (like Quick Sort or Merge Sort), Radix Sort groups numbers by their individual digits.

Key Concepts

• Digit Positioning: Radix Sort processes digits from the least significant digit (LSD) to the most significant digit (MSD).
• Stable Sorting: It maintains the relative order of records with equal keys.
• Counting Sort as a Subroutine: Radix Sort often uses Counting Sort for sorting digits, ensuring stable sorting at each digit level.

Steps of Radix Sort

• Determine the Maximum Number of Digits: Find the maximum number in the array to understand the number of digits.
• Sorting by Each Digit: Use Counting Sort to sort based on each digit’s place value
  • Initialize Buckets: create an array of buckets for each digit from 0 to the radix minus one (e.g., for decimal numbers, you need 10 buckets).
  • Distribute the Numbers: start with the LSD and move towards the MSD. distribute each number into the corresponding bucket based on the current digit
  • Collect Numbers: collect numbers from the buckets and update the list in the new order
• Repeat for Each Digit Position: Continue the process for each digit until all positions are sorted.

Big O notation

If we take

• n is the number of elements
• k is the number of digits in the largest number

the time complexity for Radix sort will be O(n×k) and the space complexity will be O(n+k)

Advantages

• Efficiency: Linear time complexity O(n×k) when k is the number of digits.
• Predictable Performance: Performs consistently regardless of the input data’s initial order.

Disadvantages

• Limited Scope: Primarily useful for integers or fixed-length strings.
• Memory Usage: Requires additional memory for the Counting Sort process.