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Quicksort Algorithm

Quicksort Algorithm. Given an array of n elements (e.g., integers): If array only contains one element, return Else pick one element to use as pivot. Partition elements into two sub-arrays: Elements less than or equal to pivot Elements greater than pivot Quicksort two sub-arrays

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Quicksort Algorithm

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  1. Quicksort Algorithm Given an array of n elements (e.g., integers): • If array only contains one element, return • Else • pick one element to use as pivot. • Partition elements into two sub-arrays: • Elements less than or equal to pivot • Elements greater than pivot • Quicksort two sub-arrays • Return results

  2. Example We are given array of n integers to sort: 40 20 10 80 60 50 7 30 100

  3. Pick Pivot Element There are a number of ways to pick the pivot element. In this example, we will use the first element in the array: 40 20 10 80 60 50 7 30 100

  4. Partitioning Array Given a pivot, partition the elements of the array such that the resulting array consists of: • One sub-array that contains elements >= pivot • Another sub-array that contains elements < pivot The sub-arrays are stored in the original data array. Partitioning loops through, swapping elements below/above pivot.

  5. 40 20 10 80 60 50 7 30 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  6. While data[too_big_index] <= data[pivot] • ++too_big_index 40 20 10 80 60 50 7 30 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  7. While data[too_big_index] <= data[pivot] • ++too_big_index 40 20 10 80 60 50 7 30 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  8. While data[too_big_index] <= data[pivot] • ++too_big_index 40 20 10 80 60 50 7 30 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  9. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index 40 20 10 80 60 50 7 30 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  10. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index 40 20 10 80 60 50 7 30 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  11. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] 40 20 10 80 60 50 7 30 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  12. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] 40 20 10 30 60 50 7 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  13. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 60 50 7 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  14. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 60 50 7 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  15. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 60 50 7 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  16. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 60 50 7 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  17. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 60 50 7 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  18. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 60 50 7 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  19. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  20. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  21. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  22. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  23. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  24. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  25. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  26. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  27. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  28. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. • Swap data[too_small_index] and data[pivot_index] 40 20 10 30 7 50 60 80 100 pivot_index = 0 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  29. While data[too_big_index] <= data[pivot] • ++too_big_index • While data[too_small_index] > data[pivot] • --too_small_index • If too_big_index < too_small_index • swap data[too_big_index] and data[too_small_index] • While too_small_index > too_big_index, go to 1. • Swap data[too_small_index] and data[pivot_index] 7 20 10 30 40 50 60 80 100 pivot_index = 4 [0] [1] [2] [3] [4] [5] [6] [7] [8] too_big_index too_small_index

  30. Partition Result 7 20 10 30 40 50 60 80 100 [0] [1] [2] [3] [4] [5] [6] [7] [8] <= data[pivot] > data[pivot]

  31. Recursion: Quicksort Sub-arrays 7 20 10 30 40 50 60 80 100 [0] [1] [2] [3] [4] [5] [6] [7] [8] <= data[pivot] > data[pivot]

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