Sorting  Sorting Problem:  A list of items:  x1, x2, x3, …., xn  Arranging the list in ascending order  X1 <= X2 <= X3 <= … <= Xn  Or descending order  X1 >= X2 >= X3 >= … >= Xn

Some sorting schemes  One classification of sorting schemes consists of three categories: Selection sorts Exchange sorts Insertion sorts

Selection sort  Basic idea: make number of passes through the list or a part of the list and, on each pass, select one element to be correctly positioned.  Example: on each pass through a sublist, the smallest element in this sublist might be found and then moved to its proper location

Selection sort Original list: Scan the smallest Interchange Continue on sublist

Simple selection sorting algorithm  A list is stored in array x[0],…x[n-1]  For I = 0 to n-1 do the following  // find the smallest in sublist x[i] to x[n-1] Set pos = I Set min = x[pos] For j = i+1 to n-1 do the following  If x[j] < min Set pos = j Set min = x[j] // now interchange the smallest and the beginning of sublist Set x[pos] = x[i] Set x[i] = min

Exchange sort  Selection sort in which some element is selected and them moved to its correct position  Exchange sort interchange pairs of elements that are out of order until eventually no such pairs remain and the list is therefore sorted  Example: bubble sort

Insertion sorts  Based on the same idea as the algorithms for inserting new element into ordered linked list       

algorithm  Array x[0], …, x[n-1]  For I = 0 to n-1 do following Set temp = x[i] Set j = I While temp < x[j-1] do the following  // shift element to the right to open spot  X[j] = x[j-1]  Decrement j by 1 Set x[j] = temp

Evaluation of these sorting schemes  Primary virtue: simplicity  Too inefficient, especially for large lists  More efficient sorting algorithms:  Heap sort – kind of selection sort  Quick sort – kind of exchange sort. One of the most efficient general purpose sorting scheme  Shell sort – kind of insertion sort

Comparison for list of size 500 SortingTypeSorting time(sec) Simple selection selection69 Heap SortSelection18 Bubble sortExchange165 Quick sortExchange6 Linear insertion Insertion66 ShellInsertion11