On-Site Question 2 - SOLUTION

Problem

Write a function that given a target amount of money and a list of possible coin denominations, returns the number of ways to make change for the target amount using the coin denominations

Requirements

Write out your work on paper/pencil, then see if you can code up your solution

Solution

This is a classic interview problem, so classic that you‘ve already seen a very similar problem in the recursion section! Make sure to review that problem first before reading our solution here!

In this solution we will use a bottom-up algorithm.

• As we iterate through each coin, we are adding the ways of making arr[i - coin] to arr[i]
• If we have 2 ways of making 4, and are now iterating on a coin of value 3, there should be 2 ways of making 7.
• We are essentially adding the coin we are iterating on to the number of ways of making arr[i].

def solution(n, coins):
    
    # Set up our array for trakcing results
    arr = [1] + [0] * n
    
    for coin in coins:
        for i in range(coin, n + 1):
            arr[i] += arr[i - coin]
            
    if n == 0:
        return 0
    else:
        return arr[n]

This solution results in O((m)(n)) with m being the number of coins, where we iterate about n operations. This is O(n) space.

Good Job!