Ford-Fulkerson Algorithm Finally Does Something Useful: Solves Your Splitwise Debts Like a Math Wizard

A developer has provided a comprehensive explanation of the Ford-Fulkerson algorithm, a maximum flow algorithm, by applying it to Splitwise's "Simplify Debts" feature. The algorithm, often found in textbooks and interviews, was previously unclear to the developer, but by using a real-world example, they were able to understand its application. Splitwise's feature aims to simplify debts among users by finding the cleanest way to settle money, without preserving original transactions or sequences. The algorithm models money as flow, using nodes and edges to represent people and transactions. The developer explains key concepts, such as the source and sink, which represent all debts and credits, and reverse edges, which allow for undoing previous payments. The algorithm ensures that the maximum possible amount of money reaches the sink without violating constraints, achieving system-level optimality. This explanation provides context and clarity on the algorithm's application in real-world scenarios, such as debt simplification, and highlights its significance in the industry.