Solving the Coin Change Problem: Avoiding Unintended Changes in Python Dictionaries

Learn how to efficiently tackle the coin change problem in Python, addressing common pitfalls like unintended dictionary changes using dynamic programming. --- This video is based on the question https://stackoverflow.com/q/68149114/ asked by the user 'random' ( https://stackoverflow.com/u/12984137/ ) and on the answer https://stackoverflow.com/a/68150207/ provided by the user 'trincot' ( https://stackoverflow.com/u/5459839/ ) 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: Unintended changes in dictionary's content when solving the coin change problem 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: Avoiding Unintended Changes in Python Dictionaries The coin change problem is a classic challenge in algorithm design, often encountered in coding interviews and competitive programming. The task is straightforward: given a list of coin denominations and a target sum, find all the possible combinations to form that sum using those coins with the option to use each coin multiple times. For example, with a target sum of 4 and coins [1, 2, 3], the combinations would include [1,1,1,1], [1,1,2], [2,2], [1,3], and more. However, a common issue arises when trying to implement a solution using recursive strategies with dynamic programming. In particular, unintended changes can occur in the contents of dictionaries, leading to incorrect results. Let’s dive deeper into how to solve this problem effectively. Understanding the Problem In the provided code snippet, an attempt was made to keep track of combinations using a dictionary called memo. This is designed to store previously computed combinations for specific target sums, which enhances efficiency. However, certain mistakes can lead to mutations in the stored lists, resulting in faulty outputs. The Issue with Mutability In Python, lists are mutable objects. When a list is appended or modified in a way that refers to another list, it can lead to unexpected behavior: Example of Mutation: When you use i.append(num), if i refers to a list that’s already in memo, this will alter the entry in memo as well. Thus, multiple combinations will reflect unexpected changes in their values. The Incorrect Output When testing the code with the function call: [[See Video to Reveal this Text or Code Snippet]] You might get incorrect results like: [[See Video to Reveal this Text or Code Snippet]] This reflects that the memo dictionary contains entries that should not be showing previously known values in a mutated state. Steps to Correct the Approach To achieve a proper solution, we need to focus on the following changes: 1. Properly Constructing New Lists Instead of mutating an existing list, create a new list when adding a coin. The updated line of code should read: [[See Video to Reveal this Text or Code Snippet]] This way, each combination created is independent of others already stored in memo. 2. Base Case Correction Instead of returning [[0]], which unnecessarily adds zero to each combination, return an empty list indicating there’s one way to create a sum of zero: [[See Video to Reveal this Text or Code Snippet]] 3. Dynamic Calculation of Remainders Instead of keeping a separate remainder variable, directly compute the value during the recursive call: [[See Video to Reveal this Text or Code Snippet]] This eliminates the risk of unintended cumulative changes. 4. Exclude Permutations If you need combinations without permutations, you should maintain a sense of order when considering coins: [[See Video to Reveal this Text or Code Snippet]] This requires adjustments to your recursive calls and allows you to specify which coins can still be used. Final Solution By implementing the corrections listed above, here's a complete solution to the coin change problem: [[See Video to Reveal this Text or Code Snippet]] When you test this refined function with: [[See Video to Reveal this Text or Code Snippet]] You should receive the accurate outputs expected! Conclusion The coin change problem is an excellent example of how subtle mistakes in handling mutable objects can lead to major discrepancies in outputs. By applying careful pointers to copy lists and efficiently utilizing dynamic programming techniques, one can solve this problem effectively. Happy codin