Challenge: The Coin Change Problem

Problem statement

Given an infinite number of $quarters$ (25 cents), $dimes$ (10 cents), $nickels$ (5 cents), and $pennies$ (1 cent), write code to calculate the number of ways to represent n $cents$.

Input

The inputs are the values of the coins available to represent the cents with (the denominations) and the number of cents.

Output

The output is the number of ways that the given number of cents can be represented.

Sample input

int amount = 10;
int denoms = [25,10,5,1]

Sample output

4

Coding exercise

Take a close look and design a step-by-step algorithm before jumping to the implementation. This problem is designed for your practice, so try to solve it on your own first. If you get stuck, you can always refer to the hint and solution provided in the code tab. Good Luck!