Fast and Efficient: Radix Sort Without Comparisons

Unleashing the Power of Radix Sort

In the world of computer science, sorting algorithms play a vital role in organizing data efficiently. Among the numerous sorting techniques, radix sort stands out as a unique and powerful method that doesn’t rely on comparisons. In this tutorial, we’ll delve into the inner workings of radix sort, explore its advantages, and learn how to implement it using JavaScript.

The Radix Sort Advantage

Unlike popular sorting algorithms like merge sort and quicksort, radix sort doesn’t compare items to determine their order. Instead, it groups items into buckets based on their component digits or letters. This approach makes radix sort ideal for sorting data sets containing integers, words, or other sequences that can be ordered based on their individual components.

How Radix Sort Works

The radix sort algorithm starts by grouping items into buckets according to their least significant digit. It then collapses the items in the buckets into a new data set, sorted based on the digit at the start position. This process is repeated for each digit in each item until the data set is fully sorted.

Radix Sort in Action

Let’s take a look at an example to illustrate how radix sort works its magic. Suppose we have a data set containing the following integers: [48, 12, 3705, 620]. Using radix sort, we can sort this data set without comparing items. Here’s a step-by-step breakdown of the process:

1. Group items into buckets based on their least significant digit (ones place).
2. Collapse the items in the buckets into a new data set, sorted based on the ones place digit.
3. Repeat steps 1-2 for each digit in each item until the data set is fully sorted.

Implementing Radix Sort in JavaScript

To implement radix sort in JavaScript, we’ll need to create a few helper functions to make the process seamless. Let’s define these functions first:

• asInteger(): A utility function that takes a number as its argument, removes the decimal portion, and returns the absolute representation.
• digitAtPosition(): A function that takes a number and a zero-based position as its arguments and returns the digit at that position.
• digitsCount(): A function that takes a number as its argument and returns the number of significant digits it has.
• maxDigitsCount(): A function that takes an array of numbers and returns the maximum number of significant digits among them.

With these helper functions in place, we can now implement the radixSort() function. Here’s the implementation:
“`javascript
function radixSort(arr) {
const maxDigits = maxDigitsCount(arr);
let buckets = Array.from({ length: 10 }, () => []);

for (let k = 0; k < maxDigits; k++) {
for (let i = 0; i < arr.length; i++) {
const digit = digitAtPosition(arr[i], k);
buckets[digit].push(arr[i]);
}

arr = [].concat(...buckets);
buckets = Array.from({ length: 10 }, () => []);

}

return arr;
}
“`
Sorting in Alphabetical Order

Radix sort isn’t limited to sorting integers. We can modify the algorithm to sort a list of words in alphabetical order. Here’s an updated implementation:
“`javascript
function radixSortAlphabetical(arr) {
const maxLength = Math.max(…arr.map((str) => str.length));
const characters = ‘abcdefghijklmnopqrstuvwxyz_’;

for (let k = maxLength – 1; k >= 0; k–) {
const buckets = {};

for (let i = 0; i < arr.length; i++) {
  const char = arr[i][k] || '_';
  if (!buckets[char]) buckets[char] = [];
  buckets[char].push(arr[i]);
}

arr = [].concat(...Object.values(buckets));

}

return arr;
}
“`
Conclusion

Radix sort is a powerful sorting algorithm that offers a unique approach to organizing data. By grouping items into buckets based on their component digits or letters, radix sort can sort data sets efficiently without comparisons. While it has its limitations, radix sort can be improved to scale beyond most of its inherent limitations. With this tutorial, you should now have a solid understanding of how radix sort works and how to implement it in JavaScript.