Lecture 19 - While Loops

As usual, create two directories for today's class. Create a directory called lecture19 under activities, and a directory called lab19 under labs.

While Loops

For loops work great for when you know exactly how many times you want something to execute. However, it is often times the case that we don't know that critical piece of information. We know when we want to stop, but we don't know how long that process might take.

While loops are essentially a conditional statement that executes while some specific condition continues to hold. This allows us to create a loop that executes for some finite, but undetermined amount of time.

In-class Activity 1

Grade Average

Create a file (using Emacs) called input_average.py in your lecture19 directory. In this file, use a while loop to continually read in positive integers from user input until a -1 value is input by the user.

As the user types in integers, you should use the same accumulator pattern we used in our for loops to compute the total sum of all positive grades entered by the user. You will also need to keep track of how many grades were actually entered.

When you finish your program, go to inquire, and compute your quiz average with your program. Does the total match up with what inquire reports?

Challenge This program could have been written using a for loop, if the user provided you with some additional information to begin with. Create a file called input_average_for.py in your lab19 directory. Write a program that uses a for loop instead. Make sure your input statements are well labeled for all information necessary.

Lab Assignment 19

Babylonian Square Root

As you saw in class today, we can use loops to get decent estimates of slightly complicated mathematical operations, such as log. Another difficult to compute operation is square root. One of the earliest known methods for approximating a square root was in use by the Babylonians in the 5^th century B.C.E.

The method for approximating the square root is very similar to the log example shown in class. To find the square root of n, we start out with s, which is our current approximation for the square root of n. We can iteratively compute a new value:

s′ = (1 / 2)(s + (n / s))

We can continue to perform this computation until our current value s² is close enough to n that the difference is negligible.

Create a file babylonian_roots.py in your lab19 directory. Create a function babylonian_approximation that, when given some positive integer n, returns an approximation of the square root of n.

Make sure you test your program well. How many test cases do you need? Include your test cases in your program file. Comment them appropriately.

Challenge You can use any value of s to get to some approximation. However, choosing a better starting value will cause your code to get better approximations more quickly. If you can figure out how many digits are in n, you can use the following formula to compute a "good" starting value, where d is the number of digits in n: s = 4 × 10 ^{(d - 1) / 2}

Challenge Printing out the values that your test case computes can be helpful, but that only works if you know what the value should be. For our approximation, we can use math.sqrt to compare against. Write a for loop that checks the Babylonian method for all positive integers less that 1000. Your test code should print all integers whose Babylonian root is not close enough to the true square root.

Submission

When you have finished, create a tar file of your lab19 directory. To create a tar file, execute the following commands:

cd ~/cs120/labs
tar czvf lab19.tgz lab19/

To submit your activity, go to cseval.roanoke.edu. You should see an available assignment called Lab Assignment 19. Only one of your pair should submit your activity. Make sure both partners are listed in the header of your files.

Do not forget to email your partner today's files!

Last modified: Tue Oct 8 17:30:36 EDT 2013