Chapter 5: Sorting Algorithms
Introduction to Sorting
Sorting is one of the most fundamental operations in computer science. It involves arranging data in a particular order (ascending or descending). Many algorithms and data structures rely on sorted data for efficiency. Understanding different sorting algorithms and their trade-offs is crucial for choosing the right one for your use case.
This comprehensive chapter covers the 8 most popular and widely-used sorting algorithms, each with different characteristics, complexity trade-offs, and optimal use cases. From simple comparison-based sorts to advanced hybrid algorithms, you'll learn when and how to apply each algorithm effectively.
The algorithms are organized by their approach:
- Comparison-Based: Bubble Sort, Selection Sort, Insertion Sort, Quick Sort, Merge Sort, Heap Sort
- Non-Comparison-Based: Radix Sort
- Hybrid: Tim Sort
Sorting Algorithms
1. Bubble Sort
A simple comparison-based sorting algorithm that repeatedly steps through the list and swaps adjacent elements if they are in the wrong order.
- Time Complexity: O(n²) worst/average, O(n) best
- Space Complexity: O(1)
- Best For: Educational purposes, small datasets
- Type: Comparison-Based
2. Quick Sort
A divide-and-conquer algorithm that picks a pivot element and partitions the array around the pivot, with excellent average-case performance.
- Time Complexity: O(n log n) average, O(n²) worst
- Space Complexity: O(log n)
- Best For: General-purpose sorting, large datasets
- Type: Comparison-Based
3. Selection Sort
A simple in-place comparison-based sorting algorithm that repeatedly finds the minimum element and places it at the beginning.
- Time Complexity: O(n²)
- Space Complexity: O(1)
- Best For: Small datasets, minimizing swaps
- Type: Comparison-Based
4. Insertion Sort
An efficient sorting algorithm for small datasets and nearly sorted arrays, building the sorted array one element at a time.
- Time Complexity: O(n²) worst/average, O(n) best
- Space Complexity: O(1)
- Best For: Small arrays, nearly sorted data
- Type: Comparison-Based
5. Merge Sort
A divide-and-conquer algorithm that divides the array into two halves, sorts them recursively, and merges the sorted halves.
- Time Complexity: O(n log n)
- Space Complexity: O(n)
- Best For: Stable sorting, guaranteed O(n log n)
- Type: Comparison-Based
6. Heap Sort
An in-place sorting algorithm that uses a binary heap data structure to sort elements, providing guaranteed O(n log n) performance.
- Time Complexity: O(n log n)
- Space Complexity: O(1)
- Best For: In-place sorting with guaranteed performance
- Type: Comparison-Based
7. Radix Sort
A non-comparison-based sorting algorithm that sorts numbers by processing individual digits, potentially achieving O(n) performance.
- Time Complexity: O(d × n) where d is number of digits
- Space Complexity: O(n + k)
- Best For: Integers, fixed-length keys
- Type: Non-Comparison-Based
8. Tim Sort
A hybrid stable sorting algorithm derived from merge sort and insertion sort, designed for real-world data with excellent performance.
- Time Complexity: O(n log n) worst, O(n) best
- Space Complexity: O(n)
- Best For: General-purpose, partially sorted data
- Type: Hybrid
Algorithm Comparison
Here's a comprehensive comparison of all 8 sorting algorithms to help you choose the right one for your use case.
| Algorithm | Best Case | Average Case | Worst Case | Space | Stable |
|---|---|---|---|---|---|
| Bubble Sort | O(n) | O(n²) | O(n²) | O(1) | Yes |
| Quick Sort | O(n log n) | O(n log n) | O(n²) | O(log n) | No |
| Selection Sort | O(n²) | O(n²) | O(n²) | O(1) | No |
| Insertion Sort | O(n) | O(n²) | O(n²) | O(1) | Yes |
| Merge Sort | O(n log n) | O(n log n) | O(n log n) | O(n) | Yes |
| Heap Sort | O(n log n) | O(n log n) | O(n log n) | O(1) | No |
| Radix Sort | O(d × n) | O(d × n) | O(d × n) | O(n + k) | Yes |
| Tim Sort | O(n) | O(n log n) | O(n log n) | O(n) | Yes |
Algorithm Selection Guide
For Small Datasets (< 50 elements):
- Use Insertion Sort - Simple and efficient
For General-Purpose Sorting:
- Use Quick Sort - Fast average case
- Use Tim Sort - Excellent for real-world data
- Use Merge Sort - Guaranteed O(n log n)
When Stability is Required:
- Use Merge Sort - Stable and efficient
- Use Insertion Sort - For small arrays
- Use Tim Sort - Default in many languages
When In-Place Sorting is Required:
- Use Heap Sort - Guaranteed O(n log n) in-place
- Use Quick Sort - Fast average case
For Special Cases:
- Integers with limited range: Radix Sort
- Nearly sorted data: Insertion Sort or Tim Sort
- Educational purposes: Bubble Sort or Selection Sort
What's Next?
Now that you understand sorting algorithms, explore related topics:
- Chapter 6: Searching Algorithms - Binary search requires sorted data
- Chapter 3: Recursion & Divide-and-Conquer - Used in merge sort and quick sort
- Chapter 4: Trees - Heap sort uses binary heaps