Understanding Recursion in Python for Coin Change Problem

Learn how to solve the `coin change` problem using recursion in Python. This guide will help you understand the logic of recursion and the implementation for coin combinations. --- This video is based on the question https://stackoverflow.com/q/67310252/ asked by the user 'Mustafa Tokat' ( https://stackoverflow.com/u/14685566/ ) and on the answer https://stackoverflow.com/a/67311030/ provided by the user 'jweightman' ( https://stackoverflow.com/u/15786199/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions. Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: How can I use recursion function for coin change? Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/licensing The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/by-sa/4.0/ ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/by-sa/4.0/ ) license. If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com. --- Solving the Coin Change Problem Using Recursion in Python When shopping, it's common to come across the need to make change with specific coin denominations. In this guide, we'll explore how to use a recursive function in Python to solve the coin change problem—specifically using coins of values 5 and 7. We'll break down the problem and provide a step-by-step guide to creating a recursive solution that avoids common pitfalls, such as the 'TypeError: 'int' object is not iterable' error encountered in the initial approach. The Problem: Coin Change The goal is to find out different combinations of coins that sum up to a certain amount. For example: For an amount of 24, one possible combination is [5, 5, 7, 7]. For 25, it could be [5, 5, 5, 5, 5]. For 26, it might be [5, 7, 7, 7]. However, the initial attempt faced an error when encountering incompatible argument types during recursion. Understanding Recursive Functions What is Recursion? Recursion is a programming technique where a function calls itself in order to solve a problem. It typically solves complex problems by breaking them down into simpler ones. A recursive function generally includes: Base Case: The simplest instance of the problem, where the function can return a result directly. Recursive Case: The part of the function that breaks the problem down into smaller sub-problems and calls itself to solve those. Example of Recursive and Non-Recursive Functions To illustrate the concept of recursion, consider the following examples that print numbers from 1 to x: Non-Recursive Version: [[See Video to Reveal this Text or Code Snippet]] Recursive Version: [[See Video to Reveal this Text or Code Snippet]] Notice how the recursive version eliminates the explicit loop! Implementing the Coin Change Function Step 1: Define the Base Case For our coin change problem, the base case can be defined as when the amount is zero. The way to make change for 0 is simply by using no coins at all: [[See Video to Reveal this Text or Code Snippet]] Step 2: Define the Recursive Case When the amount is greater than 0, the recursive cases would involve two possibilities: Subtracting a 5 coin from the remaining amount and recursively calling the function. Subtracting a 7 coin from the remaining amount and doing the same. Full Code Implementation Here’s a clean implementation of the recursive coin change function: [[See Video to Reveal this Text or Code Snippet]] Step 3: Running the Function You can use a loop to calculate the coin combinations for amounts from 24 to 1000: [[See Video to Reveal this Text or Code Snippet]] Conclusion Recursion can be a powerful tool when solving problems such as the coin change problem. By correctly defining base and recursive cases and avoiding unnecessary loops, you can arrive at elegant solutions. In this explanation, we moved from understanding the problem to implementing a working solution without running into type errors. Hopefully, this post has provided you with valuable insights into using recursion effectively in Python. Happy coding!