Problem: Pennies

Implement a program that calculates the sum of getting a doubled amount of money each day for a month, per the below.

This course’s philosophy on academic honesty is best stated as "be reasonable." The course recognizes that interactions with classmates and others can facilitate mastery of the course’s material. However, there remains a line between enlisting the help of another and submitting the work of another. This policy characterizes both sides of that line.

The essence of all work that you submit to this course must be your own. Collaboration on problems is not permitted (unless explicitly stated otherwise) except to the extent that you may ask classmates and others for help so long as that help does not reduce to another doing your work for you. Generally speaking, when asking for help, you may show your code or writing to others, but you may not view theirs, so long as you and they respect this policy’s other constraints. Collaboration on quizzes and tests is not permitted at all. Collaboration on the final project is permitted to the extent prescribed by its specification.

Below are rules of thumb that (inexhaustively) characterize acts that the course considers reasonable and not reasonable. If in doubt as to whether some act is reasonable, do not commit it until you solicit and receive approval in writing from your instructor. If a violation of this policy is suspected and confirmed, your instructor reserves the right to impose local sanctions on top of any disciplinary outcome that may include an unsatisfactory or failing grade for work submitted or for the course itself.

If ever given the choice between $10,000,000 or a month’s worth of pennies, whereby you receive a penny the first day, two pennies the second, four pennies the third, and so forth…​ take the pennies^[1].

Anyhow, why the pennies? Exponentiation. Those pennies add up Consider how many pennies you’d receive on the 31st day alone, not to mention on the days leading up to it:

Put more succinctly, that’s 1 × 2³⁰. Convert those pennies to dollars (by dividing by 100) and you get, what, over $10,000,000? On just that day? Crazy.

What if you were given more than one penny on that first day? Or the month were February, in which case you’d get shortchanged a few million? (Best to take the pennies in January, March, May, July, August, October, or December^[2].) Let’s find out.

Implement, in a file called pennies.c, a program that first asks the user how many days there are in the month and then asks the user how many pennies he or she will receive on the first day of that month. The program should then calculate the amount that the user will have received in total by the end of the month (not just on the last day) if that amount is doubled on every day but the first, expressed not as pennies but as dollars and cents. If the user does not type in 28, 29, 30, or 31 for the number of days in the month, the program should prompt the user to retry. If the user does not input a positive integer for the first day’s number of pennies, the program should prompt the user to retry.

For instance, your program might behave as follows, whereby underlined text represents some user’s input.

Notice how this output suggests that the program should indeed re-prompt the user if he or she fails to cooperate with these rules (as by inputting too many days).

How to begin? Well, as before, create a new file inside of your ~/chapter1/pennies directory (remember how?) and name it pennies.c. Then, fill the file with some "boilerplate" code like the below:

Save the file and, just to be safe, try compiling it with

in your terminal window, just to make sure you didn’t make any syntactical mistakes, in which case you’ll see errors that will need to be fixed! Then dive back into your code.

Odds are you’ll want a couple of loops, one with which to prompt (and potentially re-prompt) the user for a number of days, and another with which to prompt (and potentially re-prompt) the user for a number of first-day pennies. How to get both those numbers? Perhaps the CS50 Library offers some options? You may also find functions in the math.h header file that can help when working on this problem. Have a look at the CS50 Programmer’s Manual to see which functions those might be. Be sure, if you use any of those functions, to place this line of code near the top of your pennies.c file:

Of course, if you store the user’s amount due in an int (which is only 32 bits), the total will be bounded by (2³¹ - 1) pennies. (Why 2³¹ and not 2³²? And why 1 less than 2³¹?) Best, then, to store your total in a long long, so that the user benefits from 64 bits. (Don’t worry if users' totals overflow 64 bits and even go negative; consider it punishment for greed!)

Do take care to format the user’s total as dollars and cents (to just 2 decimal places), prefixed with a dollar sign, just as we did in the output above. You do not need to insert commas after every 3 digits to the left of the decimal, as you might normally do.

So that we can automate some tests of your code, we ask that your program’s last line of output be the amount owed to a user, followed by \n. The rest of your program’s personality we leave entirely to you!

And if you’d like to play with the staff’s own implementation of pennies in CS50 IDE, you may execute the below.