University of Wisconsin-Madison

Homework Assignment #8 : Due Friday 12/3 Before Lecture

The purpose of this assignment is to explore the intuitive sorting algorithms and their complexity.

Part 1: Operations

Consider the following scripts; assume each is run independently.

A) For each of the scripts, how many times will a statement in the (largest) innermost loop execute? (that is, what will be the value of the counter variable when the script terminates?)

B) What is the order of magnitude for the number of operations in each algorithm as a function of the variable N? Remember that when calculating the order of magnitude, one disregards all constant factors. Hint: If an algorithm runs in an amount of time completely independent of the size of N, then that algorithm is O(1).

C) Imagine that you must choose between two different algorithms, A and B, that perform the same task (i.e., the solve the same problem). Algorithm A executes 3 * N * N instructions; algorithm B executes 243000*N instructions. For what values of N is Algorithm A faster? For what values of N is Algorithm B faster? As N gets larger, which Algorithm is the better choice?

Part 2: Sorting

A) Use an in-place selection sort on the following three lists. Show the contents of each list at the end of each iteration of the outermost loop (where the variable i is increased).

i) 573, 839, 102, 550, 593, 996, 678, 111, 264, 266

ii) 95, 36, 683, 92784, 73856, 3811, 392, 38, 258, 399

iii) 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100

B) Given the items in List i), how many times will the inner loop be executed during a given iteration of the outer loop? Fill in the following table.

C) Use an insertion sort (such as the one shown above) on the following lists. Show the contents of the list at the end of each iteration of the outermost loop.

i) 573, 839, 102, 550, 593, 996, 678, 111, 264, 266

ii) 95, 36, 683, 92784, 73856, 3811, 392, 38, 258, 399

iii) 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100

D) Imagine that the numbers in the lists above are high scores; associated with each high score list is another list called "Names". The contents of the Names list is initially Alice, Bob, Charles, Doug, Ethan, Frank, George, Harriot, Ian, Janice. When this Names list is associated with the high score list from part i), then Alice has the score 573, Bob has the score 839, and so forth.

Imagine that each of the sorting algorithms (whether selection or insertion) is modified to shuffle the elements of the Names list at the same time as the elements of the High Scores list; that is, when a score that was initially at position i of the High Scores list is moved to position k, then the Name that was previoiusly at position i of the Names list should be moved to position k in the Names list as well.

What will be the final order of the Names list when the sorting algorithm runs over the List in example i)?

Turning in Your Work

You may either turn in a written version of your homework before lecture on Friday or upload a copy to Folder Homework 8 through Learn@UW.