INFSCI 0015 Data Structures Lecture 13: Sorting

1
INFSCI 0015 - Data StructuresLecture 13 Sorting

• Peter Brusilovsky
• http//www2.sis.pitt.edu/peterb/0015-011/

2
Outline

• Solution for 5.1
• About Sorting
• Insertion Sort
• Selection Sort
• Bubble Sort
• One-Array Solution for 5.1

3
Problem 5.1 Partition Array

• include ltstdio.hgt
• define N 10 / dimension of the array /
• void readarray(int ar, int n)
• void partition_array(int ar, int n)
• void printarray(int ar, int n)
• int odd(int a)
• int even(int a)
• main()
• int testarrayN / elements from ar0 to
  arN-1 /
• readarray(testarray, N)
• printf("Before partitioning, numbers are ")
• printarray(testarray, N)
• partition_array(testarray, N)
• printf("After partitioning, numbers are ")
• printarray(testarray, N)

4
Problem 5.1 Partition Array
1
2
3
4
5
6
7
1
3
5
7
2
4
6
5
Problem 5.1 Partition Array
1
3
5
7
2
4
6
1
3
5
7
2
4
6
6
Problem 5.1 Partition Array

• void readarray(int ar, int n_of_elements)
• int i
• for (i 0 i lt n_of_elements i)
• printf("dgt ", i)
• scanf("d", ari)
• return
• void printarray(int ar, int n_of_elements)
• int i
• for (i 0 i lt n_of_elements i)
• printf ("d ", ari)
• printf("\n")
• return
• int odd(int a)
• return(a 2)

7
Problem 5.1 Partition Array

• void partition_array(int ar, int n)
• int i, j, k
• int oddarN, evenarN
• j k 0
• for (i 0 i lt n i)
• if (odd(ari))
• oddarj ari j
• else
• evenark ari k
• / copying odd array /
• for(i 0 i lt j i)
• ari oddari
• / copying even array /
• for(i 0 i lt k i)
• arji evenari
• return

8
Sort Classification
9
Sort Stability

• Does it keep the same order for data with equal
  keys?

10
Straight Insertion Sort

• Array is divided sorted / unsorted
• At each step an element from unsorted part is
  inserted in its place in sorted part

11
(No Transcript)
12
GF Driver for Sort Exploration

• int main ( void )
• int i
• int ary MAX_ARY_SIZE 89, 72, 3, 15, 21,
  57, 61, 44, 19, 98, 5, 77, 39, 59, 61
• printf( "Unsorted array " )
• for ( i 0 i lt MAX_ARY_SIZE i )
• printf( "3d", ary i )
• insertionSort ( ary, MAX_ARY_SIZE - 1) / call
  of some sort /
• printf( "\nSorted array " )
• for ( i 0 i lt MAX_ARY_SIZE i )
• printf( "3d", ary i )
• printf( "\n" )
• return 0

13
Insertion Sort Code

• void insertionSort (int list , int last )
• int current / index for outer loop /
• int hold / here well store the element to be
  inserted /
• int walker / index for inner moving loop /
• for ( current 1 current lt last current )
  
• hold listcurrent / element to be
  inserted /
• / moving array elements up to free space /
• for (walker current - 1
• walker gt 0 hold lt listwalker
  walker--)
• listwalker 1 listwalker
• / inserting the element into its right
  place /
• list walker 1 hold
• / for current /
• return

14
Complexity for insertion sorts

• Complexity for straight insertion
• 12n-1
• n2/2 ? O(n2 )
• Complexity for Shell sort
• O(n1.25 )

15
Selection Sort (MinSort)

• Array is divided sorted / unsorted
• At each step we find min element in the unsorted
  part and swap it with the first

16
Figure 11-9
17
Selection Sort (Min) Code

• void selectionSort (int list , int last )
• int current
• int smallest
• int holdData
• int walker
• for ( current 0 current lt last current )
• / Finding smallest element in the unsorted
  part /
• smallest current
• for (walker current 1 walker lt last
  walker)
• if ( list walker lt list smallest )
• smallest walker
• / Smallest selected exchange with current /
• holdData list current
• listcurrent list smallest
• listsmallest holdData
• / for current /
• return

18
Complexity for selection sorts

• Complexity for straight selection
• 12n-1
• n2/2 ? O(n2 )
• Complexity for heap sort
• O(nlog2n)

19
Bubble Sort

• Array is divided sorted / unsorted
• At each step the smallest element is bubbled up
  to the sorted sublist

20
(No Transcript)
21
Bubble Sort Code

• void bubbleSort (int list , int last)
• int current int sorted
• int walker int temp
• / Each iteration is one sort pass /
• for(current 0, sorted 0 current lt last
  !sorted current)
• for(walker last, sorted 1 walker gt current
  walker--)
• if ( list walker lt list walker - 1 )
• / Any exchange means list is not sorted /
• sorted 0
• temp listwalker
• listwalker listwalker - 1
• listwalker - 1 temp
• / if /
• return

22
Complexity for exchange sorts

• Complexity for bubble sort
• O(n2 )
• Complexity for quick sort
• O(nlog2n)

23
External Sorts Merging Files
24
Using exchange approach for 5.1

• / Partition Array /
• void partition_array(int ar, int n)
• int i, sw, swaps 1
• while(swaps gt 0)
• swaps 0 / initializing number of swaps /
• for (i 1 i lt n i)
• if (odd(ari) even(ari-1))
• sw ari-1
• ari-1 ari
• ari sw
• swaps
• return