Coin Change Problem | Algorithmic Solutions

Introduction

The coin change problem is a classic algorithmic problem that involves determining the number of unique ways to make change for a given amount of money. This problem has a wide range of applications, from vending machines to financial systems.

Skills Graph

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Coin Change

Problem

Given a set of coins of different denominations and a total amount of money n, determine the total number of unique ways to make change for n cents. The coins provided have denominations less than n cents.

Requirements

To solve this problem, the following requirements must be met:

The coins must reach exactly n cents.
An infinite number of coins can be assumed to make n cents.
The combination(s) of coins that represent the minimum do not need to be reported.
The coin denominations are not given in sorted order.
The solution must fit in memory.

Example Usage

The following examples demonstrate the usage of the coin change problem:

coins: None or n: None -> Exception
coins: [] or n: 0 -> 0
coins: [1, 2, 3], n: 5 -> 5

Summary

The coin change problem is a fundamental algorithmic problem that involves determining the total number of unique ways to make change for a given amount of money. By meeting the requirements outlined above, a solution can be developed to solve this problem.

Optimal Coin Change Solution