Sorting algorithms can be broadly classified into two categories based on how they sort elements:
In comparison-based algorithms, elements are compared with each other to determine their order. Examples include Quick Sort, Merge Sort, Heap Sort, Bubble Sort, Selection Sort, and Insertion Sort.
These algorithms do not compare elements directly. Instead, they leverage the properties of keys, often integers, to sort in linear or near-linear time. Examples include Counting Sort, Radix Sort, and Bucket Sort.
Feature | Comparison-Based Sorting | Non-Comparison-Based Sorting |
---|---|---|
Approach | Compare elements pairwise. | Use key properties, counting, or distribution. |
Time Complexity | Best O(n log n), worst O(n²). | Often O(n), depends on input constraints. |
Applicability | General purpose, any comparable data. | Mostly integer keys or mapped values. |
Space Complexity | Can be in-place (O(1)) | Extra space required (O(n)). |
Stability | Varies (stable or unstable) | Usually stable. |
Examples | Quick Sort, Merge Sort, Heap Sort, etc. | Counting Sort, Radix Sort, Bucket Sort. |
Comparison-based sorting algorithms are versatile and widely applicable, making them suitable for a broad range of problems. However, non-comparison sorting algorithms provide faster, often linear-time sorting when conditions (like integer keys) permit. Choosing between them depends on the data, constraints, and performance needs.