1. Chapter 9: Searching, Sorting, and Algorithm Analysis
Starting Out with C++ Early Objects
Ninth Edition
by Tony Gaddis, Judy Walters, and Godfrey Muganda

2. Topics
9.3 Introduction to Sorting Algorithms 9.4 Sorting an Array of Objects 9.5 Sorting Vectors

3. 9.3 Introduction to Sorting Algorithms
Sort: arrange values into an order
Alphabetical
Ascending numeric
Descending numeric
Two algorithms considered here
Bubble sort
Selection sort
Insertion sort

4. Selection Sort Algorithm
Locate the smallest element in the array and exchange it with the element in position 0.
Locate the next smallest element in the array and exchange it with element in position 1.
Continue until all of the elements are in order.
See pr9-05.cpp

5. Selection Sort Example
Array numlist contains
The smallest element is 2. Exchange 2 with the element at subscript 0. 11 2 29 3
Now in order 2 11 29 3

6. Selection Sort Example, Continued2 11 29 3
The next smallest element is 3. Exchange 3 with the element at subscript 1. The next smallest element is 11. Exchange 11 with the element at subscript 2. 2 3 29 11 2 3 11 29

7. //Select sort puts elements in a in ascending order, by
Chapter 9 slide 1212
//Select sort puts elements in a in ascending order, by
//repeatedly finding minimum element and swapping it with
//first element in “unsorted part” of array
void selectSort (ArrayType a; int n) {
int mindex;
for (int i = 0; i < n-1; i++)
mindex = i;
//find index of min element in unsorted subarray
for (int j = i+1; j < n-1; j++)
if (a[j] < a[mindex])
mindex = j; }
//swap 1st unsorted element with minimum element
swap (a[mindex], a[i]);

8. Analysis of Sort Efficiency or Time Complexity
Chapter 9 slide 1313
Analysis of Sort
Notice: N elements  N-1 passes
In EACH iteration, found smallest element in unsorted part of list and put it in its correct place
on each pass, 1 element put in its proper place
Efficiency or Time Complexity
1ST Pass: N-1 comparisons
2nd Pass: N-2 comparisons …
(N-1)st Pass: 1 comparison
(N-1) + (N-2) + …+ 1 = N (N-1) = N2-N = O (N2)

9. Selection Sort Tradeoffs
Chapter 9 slide 1414
Selection Sort Tradeoffs
Benefit
Easy to understand
Uses FindMax or FindMin algorithm from CMPS1044
Disadvantage
There are better ways to sort, esp. if you know something about your data

10. 9.4 Sorting an Array of Objects
As with searching, arrays to be sorted can contain objects or structures
The key field determines how the structures or objects will be ordered
When exchanging the contents of array elements, entire structures or objects must be exchanged, not just the key fields in the structures or objects
See pr9-06.cpp

11. Insertion Sort
Good when data is random, great when data is already somewhat ordered….
Algorithm:
Consider first element is in sorted part of list
for the next element in unsorted part of list
put it into its proper place relative to the sorted part of the list
Chapter 9 slide 16

12. Example
initial start end 1st pass
start end
2nd pass
sorted
unsorted
Chapter 9 slide 17

13. Example
start end
4th pass
sorted
unsorted
start end
3rd pass
Chapter 9 slide 18

14. void insertSort (ArrayType a; int n) { bool found; int j;
//Insert sort puts elements in ascending order by repeatedly
//putting 1st element in unsorted subarray into proper position of sorted array
void insertSort (ArrayType a; int n) {
bool found;
int j;
//put each element in unsorted subarray in proper position
for (int i=1; i < n; i++)
//find proper place for a[i] relative to a[0]..a[i]
found = false;
j = i;
while ((j > i) && !found)
//swap and decrement j
if a[j] < a[j-1]
swap (a[j], a[j-1]);
j= j-1; }
else
found = true;
} //end while
} //end for
} //end insertSort

15. Best Case Analysis- Data Ordered
Pass # comparisons … N = (N-1) * 1 = N-1 = O(N)
Chapter 9 slide 20

16. Worst Case Analysis
Pass # comparisons … N-1 N (N-2) + (N-1) = O (N2)
Chapter 9 slide 21

17. Efficiency Sorting is a COMMON operation
to ignore efficiency of sort is to ignore efficiency of program
Level of efficiency measured by # of comparisons (dominant operation)
# of comparisons is a function of n
Chapter 9 slide 22

18. 9.5 Sorting Vectors
Sorting algorithms can be applied to vectors as well as to arrays
You need slight modifications to functions to use vector arguments
vector <type> & used in prototype
There is no need to indicate the vector size, as functions can use the vector’s size member function
See pr9-07.cpp

19. Other Resources on Sorting
Sorting Algorithms Animations
HTML5 Canvas Demo: Sorting Algorithms

20. Chapter 9: Searching, Sorting, and Algorithm Analysis
Starting Out with C++ Early Objects
Ninth Edition
by Tony Gaddis, Judy Walters, and Godfrey Muganda