Solving the Coin Change Problem with Memoization in Python

Learn how to efficiently solve the `Coin Change Problem` using memoization in Python, with clear explanations and practical examples. --- This video is based on the question https://stackoverflow.com/q/63992253/ asked by the user 'shubhamprashar' ( https://stackoverflow.com/u/14304456/ ) and on the answer https://stackoverflow.com/a/63993950/ provided by the user 'Stef' ( https://stackoverflow.com/u/3080723/ ) 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: Coin Change problem using Memoization (Amazon interview question) 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. --- Tackling the Coin Change Problem Using Memoization The Coin Change problem is a classic challenge that often appears in coding interviews, such as those conducted by Amazon. At its core, the problem requires you to determine the minimum number of coins needed to make up a given target amount using a specified set of coin denominations. This problem can become complex, especially when you're trying to find the most efficient solution. In this post, we will explore an effective approach to this problem using memoization, a technique that helps us avoid redundant calculations. The Problem Statement Given a target amount and a list of coin denominations, you need to find the minimum number of coins required to achieve that target. For instance, if your target is 74 and you have coins of denominations 1, 5, 10, and 25, you want to discover the fewest coins you can combine to reach the total amount. The Memoization Solution The joy of solving the Coin Change problem using memoization lies in its efficiency. The standard recursive approach can lead to extensive recalculations, which can slow down your program. Here is the function that employs memoization for our problem: [[See Video to Reveal this Text or Code Snippet]] Setting Up Your Parameters To successfully run this function, you first need to initialize the parameters: Target Amount: The amount you want to achieve, e.g., 74. Coin Denominations: A list of coins, like [1, 5, 10, 25]. Known Results: An array initialized to zeros, which holds previously calculated results. This is crucial for the memoization to work. Here's how you would call the function: [[See Video to Reveal this Text or Code Snippet]] Why Initialize known_results with Zeros? You might wonder why we initialize known_results with zeros of length target + 1. Why not just start with an empty list? Using an empty list would result in an error when the algorithm tries to access an index that doesn’t exist: With known_results = [], you cannot access any index from 0 to target. For example, trying a[3] = 1 would throw an IndexError. With known_results = [0] * (target + 1), you're creating a list that predefines the required size. This ensures that all indices are accessible, which avoids runtime errors and unnecessary complexity in handling results. Conclusion Starting with an appropriately sized array for known_results not only prevents errors but enhances the performance of your algorithm. Utilizing memoization for the Coin Change problem effectively reduces computation time significantly by caching results, allowing for rapid access when needed. In summary, memoization simplifies the coding and execution aspect of the Coin Change problem, making it a highly efficient method of achieving your desired solution. Happy coding!