1. “Human Sorting” It’s a “Problem Solving” game:
Students are divided into teams.
Each team works on the given problem independently and look for the best solution that they can come up with.
Each team presents its solution to the other teams. .
CS331 D. & A. of Algorithms

2. Problem: Given a list of n numbers, sort them in
non-increasing (descending) order
Game: For each team
Sort your team (e.g. 2 rows each) in descending order by using the assigned sorting algorithms
(either Selection Sort, Bubble Sort, Merge Sort, or Quick Sort).
The output should have the tallest person on the front seat (seat #1), the second tallest person on the second seat (seat #2), and so on.
(2) How many comparisons are needed in your solution?
n – number of persons in your team .
CS331 D. & A. of Algorithms

3. One way (Algorithm) to do it
Repeat the process of finding the tallest person in your team. Called “Selection Sort”
1 st time: find the tallest person in your team, put him on the front seat,
take this person off the team. (n-1 comparisons)
2 nd time: find the tallest person in your remaining team, put him on the 2 nd seat, take this person off the team. (n-2 comparisons) …
n-1 th time: find the tallest person in your remaining team, put him on the n-1 th seat, take this person off the team. (1 comparisons)
n th time: just one person left, put him on the last seat. (0 comparison)  
total # of comparisons: (n–1) + (n-2) + … = n(n-1)/2 .
CS331 D. & A. of Algorithms

4. Another way (Algorithm) to do it
Repeat the process of bubbling the the tallest person in your team up the row. Called “Bubble Sort”
1 st time: bubble up the tallest person in your team, have him on the front seat,
take this person off the team. (n-1 comparisons)
2 nd time: bubble up the tallest person in your remaining team, have him on the
2nd seat, take this person off the team. (n-2 comparisons) …
n-1 th time: bubble up the tallest person in your remaining team, put him on the
n-1 th seat, take this person off the team. (1 comparisons)
n th time: just one person left, put him on the last seat. (0 comparison)  
total # of comparisons: (n–1) + (n-2) + … = n(n-1)/2 .
CS331 D. & A. of Algorithms

5. List List#1 List#2 Called “Merge Sort”
Another way (Algorithm) to sort your team
“Divide-and-Conquer Method”
List List#1 List#2
n elements n/2 elements n/2 elements
You can repeat this process
repeatedly until their sizes
are small enough.
Then sort it directly.
Called “Merge Sort”
Number of comparisons required is in the order of n  log2n
Sort List#1 Sort List#2
Sorted list of list#1 Sorted list of list#2
(n/2 elements) (n/2 elements)
Sorted list of the original list (n elements)
Merge them .
CS331 D. & A. of Algorithms

6. List Pivot List#1 List#2 Called “Quick Sort”
Another way (Algorithm) to sort your team
“Divide-and-Conquer Method”
List Pivot List#1 List#2
n elements larger List Smaller List
You can repeat this process
repeatedly until their sizes
are small enough.
Then sort it directly.
Called “Quick Sort”
Number of comparisons required is in the order of n2
Sort List#1 Sort List#2
Sorted list of list#1 Pivot Sorted list of list#2
Sorted list of the original list (n elements) .
CS331 D. & A. of Algorithms