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Sorting Algorithms

Sorting Algorithms. Selection Sort: Array-Based Lists. List sorted by selecting elements in the list Select elements one at a time Move elements to their proper positions Selection sort operation Find location of the smallest element in unsorted list portion

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Sorting Algorithms

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  1. Sorting Algorithms

  2. Selection Sort: Array-Based Lists • List sorted by selecting elements in the list • Select elements one at a time • Move elements to their proper positions • Selection sort operation • Find location of the smallest element in unsorted list portion • Move it to top of unsorted portion of the list • First time: locate smallest item in the entire list • Second time: locate smallest item in the list starting from the second element in the list, and so on.

  3. List of 8 elements Elements of list during the first iteration Elements of list during the second iteration

  4. Quick Sort 0 1 2 3 4 5 6 7 5 7 11 6 15 9 3 2 Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid]

  5. Quick Sort 0 1 2 3 4 5 6 7 6 7 11 5 15 9 3 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 0 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  6. Quick Sort 0 1 2 3 4 5 6 7 6 7 11 5 15 9 3 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 0 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  7. Quick Sort 0 1 2 3 4 5 6 7 6 7 11 5 15 9 3 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 1 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  8. Quick Sort 0 1 2 3 4 5 6 7 6 5 11 7 15 9 3 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 1 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  9. Quick Sort 0 1 2 3 4 5 6 7 6 5 11 7 15 9 3 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 1 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  10. Quick Sort 0 1 2 3 4 5 6 7 6 5 11 7 15 9 3 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 1 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  11. Quick Sort 0 1 2 3 4 5 6 7 6 5 11 7 15 9 3 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 2 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  12. Quick Sort 0 1 2 3 4 5 6 7 6 5 3 7 15 9 11 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 2 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  13. Quick Sort 0 1 2 3 4 5 6 7 6 5 3 7 15 9 11 2 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 3 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] }

  14. Quick Sort 0 1 2 3 4 5 6 7 6 5 3 2 15 9 11 7 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 3 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } The Last Step for this level is : Swap between List[smallindex] and List[0]

  15. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 n Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid] smallIndex= 3 pivot = List [0]= 6 SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } The Last Step for this level is : Swap between List[smallindex] and List[0]

  16. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 Now We are sure that number 6 is in the rigth place We need to complete the QuickSort 2 5 3 and 15 9 11 7

  17. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 2 5 3 15 9 11 7 Mid= (0 + 2) /2 =1 Swap List[0] and List[mid] Pivot= List[0]= 5 For( n=1; n<=2; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] } Mid= (4 + 7) /2 =5 Swap List[4] and List[mid] Pivot= List[4]= 9 For( n=5; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] }

  18. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 5 2 3 15 9 11 7 Mid= (0 + 2) /2 =1 Swap List[0] and List[mid] Pivot= List[0]= 5 For( n=1; n<=2; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] } Mid= (4 + 7) /2 =5 Swap List[4] and List[mid] Pivot= List[4]= 9 For( n=5; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] }

  19. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 3 2 5 15 9 11 7 Mid= (0 + 2) /2 =1 Swap List[0] and List[mid] Pivot= List[0]= 5 For( n=1; n<=2; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] } Mid= (4 + 7) /2 =5 Swap List[4] and List[mid] Pivot= List[4]= 9 For( n=5; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] }

  20. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 3 2 5 9 15 11 7 Mid= (0 + 2) /2 =1 Swap List[0] and List[mid] Pivot= List[0]= 5 For( n=1; n<=2; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] } Mid= (4 + 7) /2 =5 Swap List[4] and List[mid] Pivot= List[4]= 9 For( n=5; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] }

  21. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 3 2 5 9 7 11 15 Mid= (0 + 2) /2 =1 Swap List[0] and List[mid] Pivot= List[0]= 5 For( n=1; n<=2; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] } Mid= (4 + 7) /2 =5 Swap List[4] and List[mid] Pivot= List[4]= 9 For( n=5; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] }

  22. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 3 2 5 7 9 11 15 Mid= (0 + 2) /2 =1 Swap List[0] and List[mid] Pivot= List[0]= 5 For( n=1; n<=2; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] } Mid= (4 + 7) /2 =5 Swap List[4] and List[mid] Pivot= List[4]= 9 For( n=5; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap List[SamllIndext] with List[n] }

  23. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 3 2 5 7 9 11 15 In this Level we are sure that Number 5 and Number 9 in the right places Now we have the following 4 array 3, 2 and Nothing and 7 and 11 ,15

  24. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 3 2 5 7 9 11 15 0 1 4 6 7 3 2 7 11 15 Mid = (6+7)/2= 6 Swap List[6] and List[mid] Pivot =List[6] For (n=7; n<=7; n++) If(List[n]<pivot) { SmallIndex++; Do the Swap.... } Mid = (0+1)/2= 0 Swap List[0] and List[mid] Pivot =List[0] For (n=1; n<=1; n++) If(List[n]<pivot) { SmallIndex++; Do the Swap.... } Do Nothing

  25. Quick Sort 0 1 2 3 4 5 6 7 2 5 3 6 15 9 11 7 0 1 2 4 5 6 7 3 2 5 7 9 11 15 0 1 4 6 7 2 3 7 11 15 1 7 3 15 0 1 2 3 4 5 6 7 2 3 5 6 7 9 11 15

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