1. Alternate Version of STARTING OUT WITH C++ 4th Edition
Chapter 9
Searching and Sorting Arrays
Copyright 2004
Scott/Jones Publishing

2. Topics
9.3 Introduction to Sorting Algorithms
Chapter 9 slide 2

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
Chapter 9 slide 3

4.
Chapter 9 slide 4

5. Bubble Sort Algorithm
Compare 1st two elements and exchange them if they are out of order.
Move down one element and compare 2nd and 3rd elements. Exchange if necessary. Continue until end of array.
Pass through array again, repeating process and exchanging as necessary.
Repeat until a pass is made with no exchanges.
Chapter 9 slide 5

6. Bubble Sort Example Array numlist3 contains 17 23 5 11
Compare values 17 and
23. In correct order, so
no exchange.
Compare values 23 and
11. Not in correct order,
so exchange them. 17 23 5 11
5. Not in correct order,
Chapter 9 slide 6

7. Bubble Sort Example (continued)
After first pass, array numlist3 contains
In order from previous pass
Compare values 17 and
5. Not in correct order,
so exchange them.
23. In correct order, so
no exchange. 17 5 11 23
11. Not in correct order,
Chapter 9 slide 7

8. Bubble Sort Example (continued)
After second pass, array numlist3 contains
Compare values 5 and
11. In correct order, so
no exchange.
Compare values 17 and
23. In correct order, so 5 11 17 23
Compare values 11 and
17. In correct order, so
In order from previous passes
No exchanges, so
array is in order
Chapter 9 slide 8

9. Bubble Sort Tradeoffs Benefit Disadvantage
Easy to understand and implement
Disadvantage
Inefficiency make it slow for large arrays
Chapter 9 slide 9

10. Selection Sort Algorithm
Locate smallest element in array and exchange it with element in position 0.
Locate next smallest element in array and exchange it with element in position 1.
Continue until all elements are in order.
Chapter 9 slide 10

11. Selection Sort Example
Array numlist contains
Smallest element is 2. Exchange 2 with
element in 1st array position (i.e. element 0). 11 2 29 3
Now in order 2 11 29 3
Chapter 9 slide 11

12. Selection Sort – Example (continued)
Next smallest element is 3. Exchange
3 with element in 2nd array position.
Next smallest element is 11. Exchange
11 with element in 3rd array position.
Now in order 2 3 29 11
See pr9-05.cpp
Now in order 2 3 11 29
Chapter 9 slide 12

13. //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]);
Chapter 9 slide 13

14. Analysis of Sort Efficiency or Time Complexity
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)
Chapter 9 slide 14

15. 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
Chapter 9 slide 15

16. 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

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

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

19. 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

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

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

22. 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