Practice Assignment

(coins.c)

Information

Write a function that, given an amount a money and a number of coins to use, will tell you how many ways that amount can be achieved using different combinations of coins. Here is the prototype for the function:

void calculate_coins(int value, int num_coins);

Here are some example inputs and outputs:

Example 1:

calculate_coins(500, 15); /* Specify amount in cents */

Output:

You can make $5.00 with 5 halves  10 quarters  
You can make $5.00 with 7 halves  5 quarters  2 dimes  1 nickel  
You can make $5.00 with 8 halves  2 quarters  5 dimes  
You can make $5.00 with 8 halves  3 quarters  1 dime  3 nickels  
You can make $5.00 with 9 halves  4 dimes  2 nickels  
You can make $5.00 with 9 halves  1 quarter  5 nickels  
There are 6 possible ways to make $5.00 from 15 coins.

Example 2:

calculate_coins(1234, 35); /* Specify amount in cents */

Output:

You can make $12.34 with 19 halves  11 quarters  1 nickel  4 pennies  
You can make $12.34 with 20 halves  8 quarters  3 dimes  4 pennies  
You can make $12.34 with 21 halves  6 quarters  2 dimes  2 nickels  4 pennies  
You can make $12.34 with 22 halves  3 quarters  5 dimes  1 nickel  4 pennies  
You can make $12.34 with 22 halves  4 quarters  1 dime  4 nickels  4 pennies  
You can make $12.34 with 23 halves  8 dimes  4 pennies  
You can make $12.34 with 23 halves  1 quarter  4 dimes  3 nickels  4 pennies  
You can make $12.34 with 23 halves  2 quarters  6 nickels  4 pennies  
You can make $12.34 with 23 halves  3 quarters  9 pennies  
There are 9 possible ways to make $12.34 from 35 coins.

Example 3:

calculate_coins(1234, 30); /* Specify amount in cents */

Output:

You can make $12.34 with 24 halves  1 quarter  1 nickel  4 pennies  
There is 1 possible way to make $12.34 from 30 coins.

Example 4:

calculate_coins(1000, 15); /* Specify amount in cents */

Output:

It is not possible to make $10.00 from 15 coins.

The name of the file should be coins.c and the command to compile it will look like this:

gcc -O -Werror -Wall -Wextra -ansi -pedantic main.c coins.c -o coins

Approximate number of lines of code: 20.

Notes

You are given the dollar amount in cents (pennies). So, instead of getting the value 8.13 (for 8 dollars and 13 cents), you are given the number 813. It just makes life easier for now.

Hint: You will use nested loops (5 of them). One for each type of coin. Put the largest valued coin in the outer-most loop and have the inner loops decrease in value towards the inner-most loop (which will be the pennies). Do not worry about trying to micro-optimize your code to be really fast and using only logical combinations. If you don't know what that last sentence means, then you're probably not going to do it.

The maximum number of pennies you will be given is 2000 ($20.00) and the maximum number of coins will be 40. You don't have to handle invalid values because the driver is taking care of it for you.

Use the function print_coins to print out your results. (It's included in the partial C file to get you started.) This will ensure that your output is formatted properly. If you don't understand some of the code, don't worry about it. You just need to call it with the number of halves, quarters, dimes, nickels, and pennies. It will do the rest.

The driver (main.c, HTML Text) is not prompting for input. You must specify the input on the command line like this:
```
coins 500 27
```
This will set the amount to $5.00 and the number of coins to 27. These values are passed to your function.

Here is a partial C file to get you started:   HTML    Text
and here are some sample outputs for you to try:
Output for $1.00 and 10 coins   (coins 100 10)
Output for $5.00 and 27 coins   (coins 500 27)
Output for $8.13 and 40 coins   (coins 813 40)

Thought Question: What happens if you accept any amount of money and any number of coins?