Today I Learned: Number of Ways to Make Coin Changes

Problem Statement

Given an array of unique positive integers representing coin denominations and a single positive integer n representing a target amount of money, implement a function that returns the number of ways to make change for that target amount.

Sample Input & Output

n = 6
denominations = [1, 5]

Sample Output

2 # 1x coin 5 + 5x coin 1 and 6 x coin 1

Code #1

def number_of_ways_to_make_changes(n, denominations):
    ways = [0] * (n + 1)
    ways[0] = 1

    for denom in denominations:
        for amount in range(1, n + 1):
            if amount >= denom:
                ways[amount] += ways[amount - denom]

    return ways[n]

Notes

• Assumption: if n is 0, means there is 0 coin combination available.

Credits

• Algoexpert for the problem statement.
• Ibrahim Rifath for the cover image (https://unsplash.com/photos/OApHds2yEGQ).