Cash

Getting Started

Open VS Code.

Start by clicking inside your terminal window, then execute cd by itself. You should find that its “prompt” resembles the below.

$

Click inside of that terminal window and then execute

wget https://cdn.cs50.net/2021/fall/psets/1/cash.zip

followed by Enter in order to download a ZIP called cash.zip in your codespace. Take care not to overlook the space between wget and the following URL, or any other character for that matter!

Now execute

unzip cash.zip

to create a folder called cash. You no longer need the ZIP file, so you can execute

rm cash.zip

and respond with “y” followed by Enter at the prompt to remove the ZIP file you downloaded.

Now type

cd cash

followed by Enter to move yourself into (i.e., open) that directory. Your prompt should now resemble the below.

cash/ $

If all was successful, you should execute

ls

and see a file named cash.c. Executing code cash.c should open the file where you will type your code for this problem set. If not, retrace your steps and see if you can determine where you went wrong!

Greedy Algorithms

US coins

When making change, odds are you want to minimize the number of coins you’re dispensing for each customer, lest you run out (or annoy the customer!). Fortunately, computer science has given cashiers everywhere ways to minimize numbers of coins due: greedy algorithms.

According to the National Institute of Standards and Technology (NIST), a greedy algorithm is one “that always takes the best immediate, or local, solution while finding an answer. Greedy algorithms find the overall, or globally, optimal solution for some optimization problems, but may find less-than-optimal solutions for some instances of other problems.”

What’s all that mean? Well, suppose that a cashier owes a customer some change and in that cashier’s drawer are quarters (25¢), dimes (10¢), nickels (5¢), and pennies (1¢). The problem to be solved is to decide which coins and how many of each to hand to the customer. Think of a “greedy” cashier as one who wants to take the biggest bite out of this problem as possible with each coin they take out of the drawer. For instance, if some customer is owed 41¢, the biggest first (i.e., best immediate, or local) bite that can be taken is 25¢. (That bite is “best” inasmuch as it gets us closer to 0¢ faster than any other coin would.) Note that a bite of this size would whittle what was a 41¢ problem down to a 16¢ problem, since 41 - 25 = 16. That is, the remainder is a similar but smaller problem. Needless to say, another 25¢ bite would be too big (assuming the cashier prefers not to lose money), and so our greedy cashier would move on to a bite of size 10¢, leaving him or her with a 6¢ problem. At that point, greed calls for one 5¢ bite followed by one 1¢ bite, at which point the problem is solved. The customer receives one quarter, one dime, one nickel, and one penny: four coins in total.

It turns out that this greedy approach (i.e., algorithm) is not only locally optimal but also globally so for America’s currency (and also the European Union’s). That is, so long as a cashier has enough of each coin, this largest-to-smallest approach will yield the fewest coins possible. How few? Well, you tell us!

Implementation Details

In cash.c, we’ve implemented most (but not all!) of a program that prompts the user for the number of cents that a customer is owed and then prints the smallest number of coins with which that change can be made. Indeed, main is already implemented for you. But notice how main calls several functions that aren’t yet implemented! One of those functions, get_cents, takes no arguments (as indicated by void) and returns an int. The rest of the functions all take one argument, an int, and also return an int. All of them currently return 0 so that the code will compile. But you’ll want to replace every TODO and return 0; with your own code. Specifically, complete the implementation of those functions as follows:

  • Implement get_cents in such a way that the function prompts the user for a number of cents using get_int and then returns that number as an int. If the user inputs a negative int, your code should prompt the user again. (But you don’t need to worry about the user inputting, e.g., a string, as get_int will take care of that for you.) Odds are you’ll find a do while loop of help, as in mario.c!
  • Implement calculate_quarters in such a way that the function calculates (and returns as an int) how many quarters a customer should be given if they’re owed some number of cents. For instance, if cents is 25, then calculate_quarters should return 1. If cents is 26 or 49 (or anything in between, then calculate_quarters should also return 1. If cents is 50 or 74 (or anything in between), then calculate_quarters should return 2. And so forth.
  • Implement calculate_dimes in such a way that the function calculates the same for dimes.
  • Implement calculate_nickels in such a way that the function calculates the same for nickels.
  • Implement calculate_pennies in such a way that the function calculates the same for pennies.

Note that, unlike functions that only have side effects, functions that return a value should do so explicitly with return! Take care not to modify the distribution code itself, only replace the given TODOs and the subsequent return value!
Note too that, recalling the idea of abstraction, each of your calculate functions should accept any value of cents , not just those values that the greedy algorithm might suggest. If cents is 85, for example, calculate_dimes should return 8.

Hint
  • Recall that there are several sample programs in Week 1’s Source Code that illustrate how functions can return a value. You might find discount1.c and discount2.c insightful.

Your program should behave per the examples below.

$ ./cash
Change owed: 41
4
$ ./cash
Change owed: -41
Change owed: foo
Change owed: 41
4

How to Test Your Code

For this program, try testing your code manually–it’s good practice:

  • If you input -1, does your program prompts you again?
  • If you input 0, does your program output 0?
  • If you input 1, does your program output 1 (i.e., one penny)?
  • If you input 4, does your program output 4 (i.e., four pennies)?
  • If you input 5, does your program output 1 (i.e., one nickel)?
  • If you input 24, does your program output 6 (i.e., two dimes and four pennies)?
  • If you input 25, does your program output 1 (i.e., one quarter)?
  • If you input 26, does your program output 2 (i.e., one quarter and one penny)?
  • If you input 99, does your program output 9 (i.e., three quarters, two dimes, and four pennies)?

You can also execute the below to evaluate the correctness of your code using check50. But be sure to compile and test it yourself as well!

check50 cs50/problems/2022/x/cash

And execute the below to evaluate the style of your code using style50.

style50 cash.c

How to Submit

In your terminal, execute the below to submit your work.

submit50 cs50/problems/2022/x/cash