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Quick Sort

The Quick Sort algorithm is a popular and efficient sorting technique that employs a divide-and-conquer strategy. It selects a pivot element and partitions the array into two sub-arrays: one with elements less than the pivot and the other with elements greater than or equal to the pivot. Each sub-array is then recursively sorted, leading to an overall sorted array. This in-place sorting algorithm has an average time complexity of O(n log n) and performs well on large data sets. Learn how to implement Quick Sort effectively with step-by-step examples.

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Quick Sort

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  1. Quick Sort

  2. Quick Sort • Divide: • Pick any element p as the pivot, e.g, the first element • Partition the remaining elements into FirstPart,which contains all elements< p SecondPart, which contains all elements ≥ p • Recursively sort the FirstPart and SecondPart • Combine: no work is necessary since sorting is done in place

  3. Partition Recursive call p p p p ≤ x p ≤ x Sorted FirstPart Sorted SecondPart x < p Quick Sort A: pivot FirstPart SecondPart x < p Sorted

  4. Quick Sort Quick-Sort(A, left, right) ifleft ≥ right return else middle ← Partition(A, left, right) Quick-Sort(A, left, middle–1 ) Quick-Sort(A, middle+1, right) end if

  5. p x < p p p ≤ x x < p p ≤ x p Partition A: A: A: p

  6. Partition Example A: 4 8 6 3 5 1 7 2

  7. Partition Example i=0 A: 4 8 6 3 5 1 7 2 j=1

  8. Partition Example i=0 A: 4 8 6 3 5 1 7 2 8 j=1

  9. Partition Example i=0 A: 4 8 6 6 3 5 1 7 2 j=2

  10. i=1 3 8 Partition Example i=0 A: 4 6 3 5 1 7 2 8 3 j=3

  11. i=1 Partition Example A: 4 3 6 8 5 1 7 2 5 j=4

  12. i=1 Partition Example A: 4 3 6 8 5 1 1 7 2 j=5

  13. i=2 1 6 Partition Example A: 4 3 6 8 5 1 7 2 j=5

  14. i=2 Partition Example A: 7 4 3 1 8 5 6 7 2 j=6

  15. i=2 i=3 Partition Example A: 8 2 2 4 3 1 8 5 6 7 2 j=7

  16. i=3 Partition Example A: 4 3 1 2 5 6 7 8 j=8

  17. i=3 Partition Example A: 4 4 3 1 2 5 6 7 8 2

  18. x < 4 4 ≤ x Partition Example pivot in correct position A: 2 4 3 1 5 6 7 8

  19. Partition(A, left, right) • x ← A[left] • i ← left • for j ← left+1 to right • if A[j] < x then • i ← i + 1 • swap(A[i], A[j]) • end if • end for j • swap(A[i], A[left]) • return i n = right – left +1 Time: cn for some constant c Space: constant

  20. 2 3 1 4 5 6 7 8 Quick-Sort(A, 0, 7) Partition A: 4 8 6 3 5 1 7 2

  21. 1 3 2 Quick-Sort(A, 0, 7) , partition Quick-Sort(A, 0, 2) A: 5 6 7 8 4 2 3 1

  22. Quick-Sort(A, 0, 7) Quick-Sort(A, 0, 0) , base case , return 5 6 7 8 4 3 1 2 1

  23. 3 3 Quick-Sort(A, 0, 7) Quick-Sort(A, 1, 1) , base case 5 6 7 8 4 1 2

  24. 1 1 3 3 2 2 Quick-Sort(A, 0, 7) Quick-Sort(A, 0, 2), return Quick-Sort(A, 2, 2),return 5 6 7 8 4

  25. 5 6 7 8 6 7 8 5 1 3 2 Quick-Sort(A, 0, 7) Quick-Sort(A, 4, 7) , partition Quick-Sort(A, 2, 2),return 4

  26. 1 3 2 6 7 8 Quick-Sort(A, 0, 7) Quick-Sort(A, 5, 7) , partition 4 5 6 6 7 8

  27. 1 3 2 Quick-Sort(A, 0, 7) Quick-Sort(A, 6, 7) , partition 4 5 6 7 7 8 8

  28. 1 3 2 Quick-Sort(A, 0, 7) , return , base case Quick-Sort(A, 7, 7) 4 5 6 7 8 8

  29. 1 3 2 Quick-Sort(A, 0, 7) , return Quick-Sort(A, 6, 7) 4 5 6 7 8

  30. 1 3 2 6 7 8 Quick-Sort(A, 0, 7) , return Quick-Sort(A, 5, 7) 4 5

  31. 5 1 3 2 6 7 8 Quick-Sort(A, 0, 7) , return Quick-Sort(A, 4, 7) 4

  32. 5 1 3 2 6 7 8 Quick-Sort(A, 0, 7) , done! Quick-Sort(A, 0, 7) 4

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