Radix Sort Algorithm

Radix Sort Algorithm

Radix Sort is a non-comparative sorting algorithm that sorts numbers by processing individual digits. It is particularly useful when sorting large sets of integers and can perform better than other conventional comparison-based sorting algorithms in certain scenarios. In this article, we will explore how Radix Sort works, its process, key concepts, and provide detailed examples, performance complexities, advantages, and disadvantages.

How Radix Sort Works

The Process

The Radix Sort algorithm processes integers digit by digit, starting from the least significant digit (LSD) to the most significant digit (MSD). It employs a stable sorting algorithm (like Counting Sort) as a subroutine to sort numbers based on each digit. Here’s the basic step-by-step process:

1. Find the maximum number to determine the number of digits.
2. For each digit (starting from the least significant to the most significant), perform the following:
   1. Apply Counting Sort (or another stable sort) by that digit.

Key Concepts

• Stable Sort: A sorting algorithm retains the relative order of equal elements.
• Least Significant Digit (LSD): The digit furthest to the right in a number.
• Most Significant Digit (MSD): The digit furthest to the left in a number.

Radix Sort Example

Let’s consider an example with the following list of numbers: [170, 45, 75, 90, 802, 24, 2, 66].

            
            // Example of Radix Sort

            function countingSort(array, place) {
                const output = new Array(array.length);
                const count = new Array(10).fill(0);

                // Count occurrences
                for (let i = 0; i < array.length; i++) {
                    const index = Math.floor(array[i] / place) % 10;
                    count[index]++;
                }

                // Modify count to be positions
                for (let i = 1; i < 10; i++) {
                    count[i] += count[i - 1];
                }

                // Build the output array
                for (let i = array.length - 1; i >= 0; i--) {
                    const index = Math.floor(array[i] / place) % 10;
                    output[count[index] - 1] = array[i];
                    count[index]--;
                }

                // Copy the output array to original array
                for (let i = 0; i < array.length; i++) {
                    array[i] = output[i];
                }
            }

            function radixSort(array) {
                const max = Math.max(...array);
                for (let place = 1; Math.floor(max / place) > 0; place *= 10) {
                    countingSort(array, place);
                }
            }

            let input = [170, 45, 75, 90, 802, 24, 2, 66];
            radixSort(input);
            console.log(input); // Output: [2, 24, 45, 66, 75, 90, 170, 802]
            
        

The above code demonstrates the Radix Sort algorithm using JavaScript to sort the array step by step.

Radix Sort Complexity

Time Complexity

The time complexity of Radix Sort can be summarized as follows:

Here, n is the number of elements in the array, d is the number of digits in the largest number, and k represents the range of the input values.

Space Complexity

The space complexity of Radix Sort is O(n + k), mainly due to the output array used in the counting sort.

Advantages of Radix Sort

• Efficient for large datasets: Performs well with large numbers of elements, especially when the range of data is small.
• Stable sorting: Retains the relative order of equal elements, which is important for certain applications.
• Non-comparative: Does not rely on comparisons, thus can outperform traditional sorting algorithms in specific cases.

Disadvantages of Radix Sort

• Auxiliary space needed: Requires additional space proportional to the size of the digits.
• Limited to non-negative integers: Standard implementations primarily address non-negative integers, though adaptations exist for negative numbers.
• Not in-place: Requires extra space for the output, making it unsuitable for scenarios where memory conservation is critical.

Conclusion

In conclusion, Radix Sort is a powerful and efficient sorting algorithm that operates on the principle of arranging numbers based on their individual digits. While it has its advantages and disadvantages, it is particularly suitable for scenarios where traditional comparison-based sorting algorithms may not be as efficient. Understanding Radix Sort can broaden a programmer’s toolkit for data sorting strategies.

FAQ

1. What types of data can Radix Sort sort?

Radix Sort can primarily sort non-negative integers but can be adapted to work with other types of data, such as strings or floating-point numbers.

2. Is Radix Sort stable?

Yes, Radix Sort is a stable sorting algorithm, which means it preserves the relative order of records with equal keys.

3. How does Radix Sort compare to other sorting algorithms?

Radix Sort can be more efficient than comparison-based sorting algorithms (like Quick Sort or Merge Sort) especially when dealing with large datasets with a known range of data values.

4. Can Radix Sort be used for negative numbers?

Standard Radix Sort does not handle negative numbers well. However, with adaptations using two passes (one for positive and one for negative), it can be implemented for negative integers.

5. What is the best scenario to use Radix Sort?

Radix Sort excels in scenarios with large datasets of integers or strings where the number of digits or characters is relatively small compared to the number of elements.