Sorting (Concepts and Techniques) Data Structure

This presentation dives deep into the world of advanced sorting algorithms, crafted specifically for students aiming to strengthen their algorithmic knowledge. Moving beyond the basics, this slide deck explores the theory, implementation, and real-world implications of sorting techniques

1. Sorting

2. What is Sorting? Rearranging elements into order (ascending/descending). Types: Basic Sorting → Bubble, Selection, Insertion Advanced Sorting → Merge, Quick, Heap, Shell, Counting, Radix, Bucket

3. Why Sorting? Faster searching (binary search needs sorted data). Organizes data for easy use. Used in databases File systems Competitive programming.

4. Sorting Algorithms

5. Bubble Sort Compare adjacent elements, swap if needed. Complexity: Best O(n), Worst O(n²), Stable. Pseudocode:

6. Selection Sort Select smallest element & put it at correct position. Complexity: Always O(n²), Not Stable. Pseudocode:

7. Insertion Sort Insert each element into correct place in sorted part. Complexity: Best O(n), Worst O(n²), Stable. Pseudocode:

8. Merge Sort Divide → Sort → Merge. Complexity: O(n log n), Stable. Pseudocode:

9. Quick Sort Choose pivot → Partition → Recursively sort. Complexity: Avg O(n log n), Worst O(n²), Not Stable. Pseudocode:

10. Heap Sort Build max heap → Extract max repeatedly. Complexity: O(n log n), Not Stable. Pseudocode: ( 2 3 7 1 8 5 6 )

11. Shell Sort Gap-based insertion sort. . Complexity: O(n log n) to O(n²), Not Stable. Pseudocode:

12. Counting Sort Count occurrences → Place accordingly . Complexity: O( n+k ), Stable . Pseudocode:

13. Radix Sort Sort digits one by one using stable sort. Complexity: O( nk ), Stable . Pseudocode:

14. Bucket Sort Divide into buckets → Sort buckets → Merge. Complexity: Best O(n+k), Worst O(n²), Stability depends. Pseudocode:

15. Stable Bubble Merge Counting Radix Unstable Selection Quick Heap Shell Comparison-based Bubble Merge Quick Heap Non-comparison-based Counting Radix Bucket

16. Algorithm Best Avg Worst Space Stable Bubble O(n) O(n²) O(n²) O(1) ✅ Selection O(n²) O(n²) O(n²) O(1) ❌ Insertion O(n) O(n²) O(n²) O(1) ✅ Merge O(n log n) O(n log n) O(n log n) O(n) ✅ Quick O(n log n) O(n log n) O(n²) O(n log n) ❌ Heap O(n log n) O(n log n) O(n log n) O(1) ❌ Shell O(n log n) O(n^1.5) O(n²) O(1) ❌ Counting O( n+k ) O( n+k ) O( n+k ) O( n+k ) ✅ Radix O( nk ) O( nk ) O( nk ) O( n+k ) ✅ Bucket O( n+k ) O( n+k ) O(n²) O( n+k ) Depends