Quick sort-Data Structure
- 1. QUICK SORT
- 2. This sorting algorithm uses the idea of divide and conquer. It finds the element called pivot which divides the array into two halves in such a way that elements in the left half are smaller than pivot and elements in the right half are greater than pivot. QUICK SORT
- 3. Three steps Find pivot that divides the array into two halves. Quick sort the left half. Quick sort the right half. QUICK SORT
- 4. Example Consider an array having 6 elements 5 2 6 1 3 4 Arrange the elements in ascending order using quick sort algorithm
- 5. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array
- 6. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array Left
- 7. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array Left Initially pointing to the First element of the array
- 8. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array Left Initially pointing to the First element of the array Right
- 9. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array Left Initially pointing to the First element of the array Right Initially pointing to the Last element of the array
- 10. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array Left Initially pointing to the First element of the array Right Initially pointing to the Last element of the array Pivot
- 11. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array Left Initially pointing to the First element of the array Right Initially pointing to the Last element of the array Pivot Initially pointing to the First element
- 12. 0 1 2 3 4 5 5 2 6 1 3 4 Array index Array element This is our unsorted array Left Initially pointing to the First element of the array Right Initially pointing to the Last element of the array Pivot Initially pointing to the First element We will quick sort this array
- 13. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot
- 14. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Remember this rule:
- 15. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Remember this rule: All element to the RIGHT of pivot be GREATER than pivot.
- 16. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Remember this rule: All element to the RIGHT of pivot be GREATER than pivot. All element to the LEFT of pivot be SMALLER than pivot.
- 17. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot As the pivot is pointing at left
- 18. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot As the pivot is pointing at left So we will start from right
- 19. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot As the pivot is pointing at left So we will start from rightAnd move towards left
- 20. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Pivot = 5 Right =4
- 21. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Pivot = 5 Right =4 Is Pivot < Right ( 5 < 4)
- 22. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Pivot = 5 Right =4 NO Is Pivot < Right ( 5 < 4)
- 23. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Pivot = 5 Right =4 So we swap pivot and right NO Is Pivot < Right ( 5 < 4)
- 24. 0 1 2 3 4 5 5 2 6 1 3 4 Left Right Pivot Pivot = 5 Right =4 So we swap pivot and right NO Is Pivot < Right ( 5 < 4)
- 25. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Right =4 So we swap pivot and right NO Is Pivot < Right ( 5 < 4)
- 26. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =4 Is Pivot < Left Now move pivot to right
- 27. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =4 Is Pivot < Left NO So we swap pivot to the right
- 28. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Now the pivot is pointing at right
- 29. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Now the pivot is pointing at right So we will start from left
- 30. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Now the pivot is pointing at right So we will start from left And move towards right
- 31. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =4 Is Pivot > Left ( 5 > 4)
- 32. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =4 Is Pivot > Left YES ( 5 > 4)
- 33. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =4 Is Pivot > Left YES ( 5 > 4) So we move left one position towards right
- 34. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =2 Is Pivot > Left ( 5 > 2)
- 35. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =2 Is Pivot > Left ( 5 > 2) YES
- 36. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =2 Is Pivot > Left ( 5 > 2) YES So we move left one position towards right
- 37. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =6 Is Pivot > Left ( 5 > 6)
- 38. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =6 Is Pivot > Left ( 5 > 6) NO
- 39. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =6 Is Pivot > Left ( 5 > 6) NO So we swap pivot and left
- 40. 0 1 2 3 4 5 4 2 6 1 3 5 Left Right Pivot Pivot = 5 Left =6 Is Pivot > Left ( 5 > 6) NO So we swap pivot and left
- 41. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Left =6 Is Pivot > Left ( 5 > 6) NO So we swap pivot and left
- 42. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Left =6 Is Pivot > Left ( 5 > 6) NO So we swap pivot and left And move the pivot to left
- 43. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot
- 44. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Now the pivot is pointing at left
- 45. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Now the pivot is pointing at left So we will start from right
- 46. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Now the pivot is pointing at left So we will start from right And move towards left
- 47. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Right =6 Is Pivot < Right ( 5 < 6)
- 48. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Right =6 Is Pivot < Right ( 5 < 6) YES
- 49. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Right =6 Is Pivot < Right ( 5 < 6) YES So we move right one position towards left
- 50. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Right =3 Is Pivot < Right ( 5 < 3)
- 51. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Right =3 Is Pivot < Right ( 5 < 3) NO
- 52. 0 1 2 3 4 5 4 2 5 1 3 6 Left Right Pivot Pivot = 5 Right =3 Is Pivot < Right ( 5 < 3) NO So we swap pivot and right
- 53. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Pivot = 5 Right =3 Is Pivot < Right ( 5 < 3) NO So we swap pivot and right
- 54. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Pivot = 5 Right =3 Is Pivot > Right ( 5 > 3) NO So we swap pivot and right And move the pivot to right
- 55. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Pivot = 5 Left =3 Is Pivot > Left ( 5 > 3)
- 56. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Pivot = 5 Left =3YES Is Pivot > Left ( 5 > 3)
- 57. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Pivot = 5 Left =3 Is Pivot > Left ( 5 > 3) So we move left one position towards right YES
- 58. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Pivot = 5 Left = 1 Is Pivot > Left ( 5 > 1)
- 59. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot
- 60. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Now both left and right are pointing at the same element of the array
- 61. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Now both left and right are pointing at the same element of the array This time 5 is the pivot and it is at the sorted position 4 5
- 62. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Now both left and right are pointing at the same element of the array This time 5 is the pivot and it is at the sorted position 4 5 Elements left of pivot are smaller
- 63. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Now both left and right are pointing at the same element of the array This time 5 is the pivot and it is at the sorted position 4 5 Elements left of pivot are smaller Elements right of pivot are greater
- 64. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Now both left and right are pointing at the same element of the array This time 5 is the pivot and it is at the sorted position 4 5 Elements left of pivot are smaller Elements right of pivot are greater So pivot has divided the array into two sub array
- 65. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Now both left and right are pointing at the same element of the array This time 5 is the pivot and it is at the sorted position 4 5 Elements left of pivot are smaller Elements right of pivot are greater Left sub array Right sub array So pivot has divided the array into two sub array
- 66. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Now both left and right are pointing at the same element of the array This time 5 is the pivot and it is at the sorted position 4 5 Elements left of pivot are smaller Elements right of pivot are greater Left sub array Right sub array So pivot has divided the array into two sub array We will now quick sort the left sub array
- 67. 0 1 2 3 4 5 4 2 3 1 5 6 Left Right Pivot Pivot = 4 Left =1 Is Pivot < Left ( 4 < 1)
- 68. 0 1 2 3 4 5 4 2 3 1 5 6 Pivot Pivot = 4 Left =1 Is Pivot < Left ( 4 < 1) NO Left Right
- 69. 0 1 2 3 4 5 4 2 3 1 5 6 Pivot Pivot = 4 Left =1 Is Pivot < Left ( 4 < 1) NO So we swap pivot and right Left Right
- 70. 0 1 2 3 4 5 1 2 3 4 5 6 Pivot Pivot = 4 Left =1 Is Pivot < Left ( 4 < 1) NO So we swap pivot and right Left Right
- 71. 0 1 2 3 4 5 1 2 3 4 5 6 Left Right Pivot Pivot = 4 Left =1 Is Pivot < Left ( 4 < 1) NO So we swap pivot and right Now move the pivot to right
- 72. 0 1 2 3 4 5 1 2 3 4 5 6 Pivot Pivot = 4 Left =1 Is Pivot < Left ( 4 < 1) NO So we swap pivot and right Left Right
- 73. 0 1 2 3 4 5 1 2 3 4 5 6 The Array is Sorted