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Sorting Algorithm Focusing on Large Datasets with Large Number Range

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Sorted Algorithm Using Divide-and-Conquer Strategy Based on the Number of Bits in a Given Number
Sorted Algorithm Using Divide-and-Conquer Strategy Based on the Number of Bits in a Given Number

Sorting Algorithm Focusing on Large Datasets with Large Number Range

Radix Sort is a sorting algorithm that is particularly effective for large datasets with many digits. In this article, we'll walk through an example of Radix Sort being applied to the array [170, 45, 75, 90, 802, 24, 2, 66].

The Radix Sort Process

Radix Sort distributes elements into buckets based on each digit's value, unlike Merge Sort or Quick Sort. Here's how it works:

  1. Find the largest element: In our example, the largest element is 802.
  2. Sort the elements based on the unit place digits: Using a stable sorting technique like counting sort, we sort the array as follows: [170, 45, 75, 90, 2, 24, 66, 802].
  3. Sort the elements based on the tens place digits: We then sort the array based on the tens place digits: [802, 2, 24, 45, 66, 170, 75, 90].
  4. Sort the elements based on the hundreds place digits: (No specific sorted array is provided in the text for this step.)
  5. Repeat the process for the remaining significant digits: We continue this process for the thousands place digits and so on, until all digits have been sorted.
  6. Combine the sorted arrays: After each digit has been sorted, we combine the sorted arrays to get the final sorted array. In our example, the final sorted array is [2, 24, 45, 66, 75, 90, 170, 802].

Radix Sort's Efficiency and Complexity

Radix Sort is often faster than other comparison-based sorting algorithms like quicksort or merge sort for large datasets, especially when the keys have many digits. However, it's important to note that in practical implementations, Radix Sort is not as efficient for small datasets due to its time complexity growing linearly with the number of digits.

The time complexity of Radix Sort is O(d * (n + b)), where d is the number of digits, n is the number of elements, and b is the base of the number system being used. Radix Sort has a space complexity of O(n + b), due to the need to create buckets for each digit value and to copy the elements back to the original array after each digit has been sorted.

Counting Sort Within Radix Sort

Kartik uses Counting Sort within his Radix Sort implementation for illustration. Counting Sort efficiently sorts digits by counting frequencies without comparisons, which differs from algorithms like Merge Sort or Quick Sort, which are comparison-based, divide-and-conquer sorts that recursively split and merge or partition elements based on comparisons.

The Final Sorted Array

In the final sorted array using Radix Sort, the elements are in ascending order. For the given array [170, 45, 75, 90, 802, 24, 2, 66], the sorted array based on the hundreds place digits is [2, 24, 45, 66, 75, 90, 170, 802].

In conclusion, Radix Sort is a linear sorting algorithm for fixed length digit counts that can efficiently handle large datasets with many digits. Its unique approach of distributing elements into buckets based on each digit's value sets it apart from other comparison-based sorting algorithms.

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