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Sorting Algorithms 1
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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.
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3 List of 8 elements Elements of list during the first iteration Elements of list during the second iteration
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Quick Sort 5711615932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid]
![Quick Sort Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid]](http://images.slideplayer.com/15/4774146/slides/slide_4.jpg "Quick Sort Mid = (0 + 7) /2 = 3 Swap between List[0] and List[mid]")
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Quick Sort 6711515932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 0
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 0](http://images.slideplayer.com/15/4774146/slides/slide_5.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 0")
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Quick Sort 6711515932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 0
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 0](http://images.slideplayer.com/15/4774146/slides/slide_6.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 0")
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Quick Sort 6711515932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1](http://images.slideplayer.com/15/4774146/slides/slide_7.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1")
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Quick Sort 6511715932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1](http://images.slideplayer.com/15/4774146/slides/slide_8.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1")
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Quick Sort 6511715932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1](http://images.slideplayer.com/15/4774146/slides/slide_9.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1")
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Quick Sort 6511715932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1](http://images.slideplayer.com/15/4774146/slides/slide_10.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 1")
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Quick Sort 6511715932 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 2
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 2](http://images.slideplayer.com/15/4774146/slides/slide_11.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 2")
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Quick Sort 6537159112 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 2
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 2](http://images.slideplayer.com/15/4774146/slides/slide_12.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 2")
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Quick Sort 6537159112 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3](http://images.slideplayer.com/15/4774146/slides/slide_13.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3")
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Quick Sort 6532159117 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3 The Last Step for this level is : Swap between List[smallindex] and List[0]
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3 The Last Step for this level is : Swap between List[smallindex] and List[0]](http://images.slideplayer.com/15/4774146/slides/slide_14.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3 The Last Step for this level is : Swap between List[smallindex] and List[0]")
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Quick Sort 2536159117 0 1 2 3 4 5 6 7 Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3 The Last Step for this level is : Swap between List[smallindex] and List[0]
![Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3 The Last Step for this level is : Swap between List[smallindex] and List[0]](http://images.slideplayer.com/15/4774146/slides/slide_15.jpg "Quick Sort Mid = (0 + 7) /2 = 3 pivot = List [0]= 6 Swap between List[0] and List[mid] SmallIndex=0 for (n= 1 ; n<=7; n++) If(List[n] < pivot) { SmallIndex++; Swap between List[SmallIndex] and List [n] } n smallIndex= 3 The Last Step for this level is : Swap between List[smallindex] and List[0]")
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Quick Sort 2536159117 0 1 2 3 4 5 6 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
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Quick Sort 2536159117 0 1 2 3 4 5 6 7 253159117 0 1 2 4 5 6 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] }
![Quick Sort 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] }](http://images.slideplayer.com/15/4774146/slides/slide_17.jpg "Quick Sort 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] }")
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Quick Sort 2536159117 523159117 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] } 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
![Quick Sort 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] }](http://images.slideplayer.com/15/4774146/slides/slide_18.jpg "Quick Sort 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] }")
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Quick Sort 2536159117 325159117 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] } 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
![Quick Sort 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] }](http://images.slideplayer.com/15/4774146/slides/slide_19.jpg "Quick Sort 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] }")
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Quick Sort 2536159117 325915117 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] } 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
![Quick Sort 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] }](http://images.slideplayer.com/15/4774146/slides/slide_20.jpg "Quick Sort 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] }")
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Quick Sort 2536159117 32597 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] } 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
![Quick Sort 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] }](http://images.slideplayer.com/15/4774146/slides/slide_21.jpg "Quick Sort 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] }")
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Quick Sort 2536159117 32579 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] } 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
![Quick Sort 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] }](http://images.slideplayer.com/15/4774146/slides/slide_22.jpg "Quick Sort 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] }")
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Quick Sort 2536159117 32579 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 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
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Quick Sort 2536159117 32579 15 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.... } 3271115 0 1 4 6 7 Do Nothing 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.... } 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
![Quick Sort 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....](http://images.slideplayer.com/15/4774146/slides/slide_24.jpg "} Do Nothing 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.... }")
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Quick Sort 2536159117 32579 15 2371115 0 1 4 6 7 315 1 7 2356791115 0 1 2 3 4 5 6 7 0 1 2 4 5 6 7
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