Radix Sort

Radix Sort Algorithm

Introduction

Radix Sort is a non-comparative sorting algorithm that sorts data with integer keys by grouping the keys by individual digits, which share the same significant position and value. It is unique among sorting algorithms in that it doesn’t directly compare elements.

Explanation

Radix Sort works by processing each digit of the numbers, starting from the least significant digit (LSD) to the most significant digit (MSD). It uses counting sort or bucket sort as a subroutine to sort the elements based on each digit. The process continues until all digits have been considered, resulting in a sorted array.

JavaScript Implementation

	function radixSort(arr) {
	  const maxNum = Math.max(...arr) * 10;
	  let divisor = 10;
	  while (divisor < maxNum) {
	    let buckets = [...Array(10)].map(() => []);
	    for (let num of arr) {
	      buckets[Math.floor((num % divisor) / (divisor / 10))].push(num);
	    }
	    arr = [].concat(...buckets);
	    divisor *= 10;
	  }
	  return arr;
	}
	// Example: radixSort([170, 45, 75, 90, 802, 24, 2, 66]);

Pros and Cons

• Pros:
  • Fast for sorting data with a known range of integer keys, often outperforming comparison-based sorts.
  • Time complexity can be lower than (O(n \log n)), particularly useful for large arrays.
• Cons:
  • Limited to integer or integer-like data (e.g., strings of equal length).
  • Requires extra space for buckets, making it less memory efficient.

Time Complexity

• Best, Average, and Worst Case: (O(nk)), where (n) is the number of elements and (k) is the number of passes over the data (number of digits in the longest number).

Space Complexity

• (O(n + k)), due to the use of temporary arrays (buckets).

Practical Use Cases

1. Sorting Large Sets of Integer Data:

   • Radix Sort is ideal for scenarios where the data consists of integers or can be transformed into integer-like forms, such as phone numbers, IDs, or dates. It is particularly efficient when dealing with large sets of data.

2. High-Performance Computing:

   • In environments where computational performance is crucial, and data is suitably structured (like large databases or data processing centers), Radix Sort can provide significant performance benefits due to its linear time complexity in many cases.

Conclusion

Radix Sort offers a distinct approach to sorting, eschewing direct comparisons for a digit-by-digit sorting mechanism. This attribute makes it exceptionally efficient for sorting large sets of integer data, though its use is more specialized than more general-purpose sorting algorithms. Its performance advantages make it a valuable tool in the arsenal of sorting algorithms, especially for specific types of data and applications.