![Example step by step
Input Array: [10, 80, 30, 90, 40, 50, 70]
Choose Pivot: 50.
Partition: Rearrange elements around pivot.
Result: [10, 30, 40, 50, 90, 80, 70].
Recursive Steps: Repeat for subarrays [10, 30, 40] and [90, 80, 70].](https://image.slidesharecdn.com/jyothi22d21a0547daa-241117172347-cb33c0f8/85/jyothi-22D21A0547-DAA-pptx-in-DAA-computer-6-320.jpg)
jyothi(22D21A0547)DAA.pptx in DAA computer
- 1. Quick sort
- 2. Introduction to Quick sort Definition: Quick Sort is a divide-and-conquer sorting algorithm that rearranges elements in a list based on a pivot. Popular for its efficiency in average-case scenarios. History: Invented by Tony Hoare in 1960. Based on the idea of partitioning and recursion
- 3. Why Quick sort Advantages: Efficient: Performs faster than many other sorting algorithms for large datasets. In-Place: Requires minimal extra memory. Adaptability: Works well with arrays and linked lists. Applications: Used in system libraries like Python’s sorted() and Java’s Arrays.sort() for primitives.
- 4. Key features Partitioning: Divides the array into smaller segments around a pivot. Recursion: Solves smaller subproblems until the array is sorted. Dynamic: Adaptable to random datasets but relies on good pivot selection.
- 5. How to Quick sort work Choose a Pivot: Select an element (e.g., first, last, random, or median). Partition: Rearrange the array: All elements smaller than pivot Left. → All elements larger than pivot Right. → Recursively Sort: Apply Quick Sort to the left and right partitions.
- 6. Example step by step Input Array: [10, 80, 30, 90, 40, 50, 70] Choose Pivot: 50. Partition: Rearrange elements around pivot. Result: [10, 30, 40, 50, 90, 80, 70]. Recursive Steps: Repeat for subarrays [10, 30, 40] and [90, 80, 70].
- 7. Pivot selection techniques First Element: Simple but risks poor performance for sorted arrays. Last Element: Similar risk to the first element. Random Element: Reduces chances of worst-case scenarios. Median-of-Three: Selects the median of the first, middle, and last elements for better balance.
- 8. Time complexity analysis Case Explanation Time Complexity Best Case Balanced partitions Recursive depth log(n). → O(n log n) Average Case Random data, balanced partitions on average. O(n log n) Worst Case Pivot divides array into 1 and (n-1).O(n²) Key Insight: Good pivot selection minimizes chances of worst-case performance.
- 9. Space complexity Recursive Stack: Depth of recursion depends on partitioning. Best case: O(log n) (balanced recursion). Worst case: O(n) (unbalanced recursion). In-Place Sorting: No additional memory required beyond recursion stack.
- 10. Advantages and Disadvantages Advantages: Faster than other O(n log n) algorithms like merge sort for small datasets. Minimal memory overhead. Highly efficient for randomly distributed data. Disadvantages: Poor pivot selection can lead to O(n²) performance. Recursion may cause stack overflow for large datasets.
- 11. Conclusion Key Takeaways: Quick Sort is a powerful sorting algorithm combining speed and simplicity. Pivot selection is critical for efficiency. Ideal for general-purpose use but consider alternatives for specialized cases. Closing Thought: Mastering Quick Sort provides a foundation for understanding more complex algorithms.
- 12. Thank you P .Jyothi 22D21A0547 CSE-A