Problem: Pennies
Questions? Feel free to head to CS50 on Reddit, CS50 on StackExchange, or the CS50 Facebook group.
Objectives
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Use algorithms to solve problems.
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See firsthand the power of exponentiation.
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Explore some of the other header files available to you.
Recommended Reading
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Pages 1 – 7, 9, and 10 of http://www.howstuffworks.com/c.htm.
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Chapters 1 – 5, 9, and 11 – 17 of Absolute Beginner’s Guide to C.
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Chapters 1 – 6 of Programming in C.
Academic Honesty
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 problem sets is not permitted 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 to others, but you may not view theirs, so long as you and they respect this policy’s other constraints. Collaboration on the course’s test and quiz is not permitted at all. Collaboration on the course’s 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 the course’s heads. Acts considered not reasonable by the course are handled harshly. If the course refers some matter for disciplinary action and the outcome is punitive, the course reserves the right to impose local sanctions on top of that outcome that may include an unsatisfactory or failing grade for work submitted or for the course itself. The course ordinarily recommends exclusion (i.e., required withdrawal) from the course itself.
If you commit some act that is not reasonable but bring it to the attention of the course’s heads within 72 hours, the course may impose local sanctions that may include an unsatisfactory or failing grade for work submitted, but the course will not refer the matter for further disciplinary action except in cases of repeated acts.
Reasonable
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Communicating with classmates about problem sets' problems in English (or some other spoken language).
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Discussing the course’s material with others in order to understand it better.
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Helping a classmate identify a bug in his or her code at office hours, elsewhere, or even online, as by viewing, compiling, or running his or her code, even on your own computer.
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Incorporating a few lines of code that you find online or elsewhere into your own code, provided that those lines are not themselves solutions to assigned problems and that you cite the lines' origins.
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Reviewing past semesters' quizzes and solutions thereto.
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Sending or showing code that you’ve written to someone, possibly a classmate, so that he or she might help you identify and fix a bug.
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Sharing a few lines of your own code online so that others might help you identify and fix a bug.
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Turning to the course’s heads for help or receiving help from the course’s heads during the quiz or test.
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Turning to the web or elsewhere for instruction beyond the course’s own, for references, and for solutions to technical difficulties, but not for outright solutions to problem set’s problems or your own final project.
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Whiteboarding solutions to problem sets with others using diagrams or pseudocode but not actual code.
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Working with (and even paying) a tutor to help you with the course, provided the tutor does not do your work for you.
Not Reasonable
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Accessing a solution to some problem prior to (re-)submitting your own.
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Asking a classmate to see his or her solution to a problem set’s problem before (re-)submitting your own.
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Decompiling, deobfuscating, or disassembling the staff’s solutions to problem sets.
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Failing to cite (as with comments) the origins of code or techniques that you discover outside of the course’s own lessons and integrate into your own work, even while respecting this policy’s other constraints.
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Giving or showing to a classmate a solution to a problem set’s problem when it is he or she, and not you, who is struggling to solve it.
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Looking at another individual’s work during the test or quiz.
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Paying or offering to pay an individual for work that you may submit as (part of) your own.
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Providing or making available solutions to problem sets to individuals who might take this course in the future.
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Searching for or soliciting outright solutions to problem sets online or elsewhere.
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Splitting a problem set’s workload with another individual and combining your work.
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Submitting (after possibly modifying) the work of another individual beyond the few lines allowed herein.
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Submitting the same or similar work to this course that you have submitted or will submit to another.
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Submitting work to this course that you intend to use outside of the course (e.g., for a job) without prior approval from the course’s heads.
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Turning to humans (besides the course’s heads) for help or receiving help from humans (besides the course’s heads) during the quiz or test.
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Viewing another’s solution to a problem set’s problem and basing your own solution on it.
Assessment
Your work on this problem set will be evaluated along four axes primarily.
- Scope
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To what extent does your code implement the features required by our specification?
- Correctness
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To what extent is your code consistent with our specifications and free of bugs?
- Design
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To what extent is your code written well (i.e., clearly, efficiently, elegantly, and/or logically)?
- Style
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To what extent is your code readable (i.e., commented and indented with variables aptly named)?
To obtain a passing grade in this course, all students must ordinarily submit all assigned problems unless granted an exception in writing by the instructor.
Double or Nothing
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:
1 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
× 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
× 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 1073741824
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.
~/workspace/chapter1 $ ./pennies
Days in month: 32
Days in month: 31
Pennies on first day: 1
$21474836.47
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 ~/workspace/chapter1
directory (remember how?) and name it pennies.c
. Then, fill the file with some "boilerplate" code like the below:
#include <cs50.h>
#include <stdio.h>
int main(void)
{
}
Save the file and, just to be safe, try compiling it with
make pennies
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 Reference50 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:
#include <math.h>
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!
To test the correctness of your program, you may execute the below at the terminal window.
check50 1617.chapter1.pennies pennies.c
And if you’d like to play with the staff’s own implementation of pennies
in CS50 IDE, you may execute the below.
~cs50/chapter1/pennies
How to Submit
Step 1 of 3
Recall that, in the Scratch problem, you signed up for a GitHub account.
If you haven’t already, visit cs50.me, log in with that same GitHub account, and click Authorize application. If you’ve forgotten your GitHub account’s password, reset it first.
Once you’ve logged in and authorized, you can immediately log out. Logging in once simply ensures that you can submit code via submit50
, per step 2 of 3!
Step 2 of 3
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To submit
pennies
, executecd ~/workspace/chapter1/ submit50 2016/ap/pennies
inputting your GitHub username and GitHub password as prompted.
If you run into any trouble, email sysadmins@cs50.harvard.edu!
You may resubmit any problem as many times as you’d like.
Step 3 of 3
Submit this form!
Your submission should be graded within a few weeks, at which point your score will appear at cs50.me!
This was Pennies.