Sorting

1
Sorting

• Sorting Algorithms discussed last time
• Selection Sort
• Bubble Sort
• Insertion Sort

2
Program 5

• Compare the performance of Insertion Sort,
  Bubble Sort and Selection Sort for inputs of
• 100
• 500
• 1000
• 5000
• 10,000
• 50,000
• 100,000
• Do a complete analysis of each algorithm, and
  show the performance in both a table and a chart.

3
Sorting

• Sorting Algorithms for today
• Shell Sort
• Merge Sort
• Quick Sort

4
Sorting

• Shell Sort
• Applies insertion sort to each of several
  interleaving subfiles of a given file
• On each pass through the file, the subfiles in
  queston are formed by stepping through the file
  with an increment

procedure ShellSort(a0, a1, , an-1) for
increment n/2 down to 1, decrementing by
n/2 for i increment to n temp ai for
j i j gt increment j j - increment
if temp lt aj - increment then aj
aj-increment else break aj temp

5
Sorting

• Merge Sort
• Recursive algorithm
• Merges two sorted lists in linear time with the
  procedure Merge()

procedure Merge(An, TmpArrayn, Lpos, Rpos,
RightEnd) Leftend Rpos 1 TmpPos
Lpos NumElements RightEnd Lpos 1 while
(Lpos lt LeftEnd Rpos lt RightEnd) if
ALpos lt ARpos TmpArrayTmpPos
ALpos else TmpArrayTmpPos
ARpos while (Lpos lt LeftEnd)
TmpArrayTmpPos ALpos while (Rpos
lt RightEnd) TmpArrayTmpPos
ARpos for(i 0 i lt NumElements i,
RightEnd--) ARightEnd TmpArrayRightEnd
6
Sorting

• Merge Sort

procedure MergeSort(An) MSort(A,
TmpArray, 0, n-1) procedure MSort(An,
TmpArrayn, Left, Right) if (Left lt
Right) Center (Left Right) / 2 MSort(A,
TmpArray, Left, Center) MSort(A, TmpArray,
Center 1, Right) Merge(A, TmpArray, Left,
Center1, Right)
7
Sorting

• Quick Sort
• Fastest known sorting algorithm

procedure QuickSort(An) QSort(A, 0,
n-1) procedure Median(An, Left, Right)
Center (Left Right) / 2 if (ALeft gt
ACenter) Swap(ALeft, ACenter) if
(ALeft gt ARight) Swap(ALeft,
ARight) if (ACenter gt ARight) Swap(ACent
er, ARight) Swap (ACenter,
ARight-1) Return ARight-1
8
Sorting

• Quick Sort

procedure QSort(A, 0, n-1) If (Left Cutoff lt
Right) Pivot Median(A, Left, Right) i
Left j Right 1 for( ) while(ai lt
Pivot) while(a--j gt Pivot) if (i lt j)
swap(Ai,Aj) else break swap(Ai
, ARight-1) Qsort(A, Left, i-1) Qsort(A,
i1, Right) else InsertionSort(ALeft,
Right-Left1)