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https://github.com/adrianhenry15/cs50-cash

HarvardX CS50's Introduction To Computer Science
https://github.com/adrianhenry15/cs50-cash

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HarvardX CS50's Introduction To Computer Science

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# HarvardX CS50's Introduction To Computer Science



## Week 1 Problem Set: Cash



### Greedy Algorithms






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 `TODO`s 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.



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 This Program

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)?



### Getting Started



1. Make sure you have a compiler for C programs. Some popular compilers include GCC, Clang, and Microsoft Visual C++.

2. Clone the repo.

3. `cd` into the respective directory.

4. Compile the code `gcc -o cash cash.c`.

5. Start the program `./cash`