Comparison vs Non-Comparison Sorting Algorithms

Sorting algorithms can be broadly classified into two categories based on how they sort elements:

Comparison-Based Sorting Algorithms

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.

Non-Comparison-Based Sorting Algorithms

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.

Key Differences

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.

Conclusion

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.