PHP Implementation of Radix Sort Algorithm and Its Time Complexity Analysis

Radix Sort Algorithm Implementation Steps and Time Complexity Analysis in PHP

Radix Sort is a common sorting algorithm with a linear time complexity of O(n). It works by comparing digits and distributing elements to achieve sorting, and is particularly suitable for sorting positive integers. In this article, we will introduce the implementation steps of the Radix Sort algorithm in PHP and analyze its time complexity.

Basic Principle of Radix Sort

The basic idea behind Radix Sort is to distribute all the elements to a limited number of buckets, then collect the elements from the buckets in order, and finally achieve sorting through multiple rounds of distribution and collection.

Implementation Steps

The implementation of Radix Sort can be broken down into the following steps:

• Initialize Bucket Array: Create a two-dimensional array representing the buckets, where each bucket is a one-dimensional array. The number of buckets depends on the maximum number of digits of the elements to be sorted.
• Find the Maximum Number of Digits: Traverse the array to find the largest element and determine the number of digits it has.
• Distribute and Collect by Digits: Starting from the least significant digit, extract each element’s corresponding digit, and distribute the element to the corresponding bucket. Then, collect the elements from the buckets in order.
• Repeat the Distribution Process: Continue distributing and collecting for each digit until all digits have been processed.
• Complete the Sorting: After multiple rounds of distribution and collection, the array becomes sorted.

PHP Implementation Code

<span class="fun">function radixSort(array $arr): array {</span>

Time Complexity Analysis

The time complexity of Radix Sort depends on the number of digits (d) in the elements to be sorted and the number of buckets (k). Its complexity is O(d * (n + k)). In the worst case, where the number of digits equals the number of buckets (d = k), the time complexity becomes O(2 * n). However, the actual performance of Radix Sort is closely related to the characteristics of the data being sorted, especially when the data size is large, and its space complexity must also be considered.

Conclusion

This article has introduced the implementation process of Radix Sort in PHP and analyzed its time complexity. Although Radix Sort offers near-linear time complexity, its space complexity is relatively high, and additional processing is required when handling negative numbers. As such, it is best suited for environments with moderate data sizes and sufficient memory. In practical development, the choice of sorting algorithm can be made based on the specific needs of the data to improve performance.