gen-explain-maximum-flow-as-you-would-to-a-capable-student-in-3-3256

Explain maximum flow as you would to a capable student, in 3-4 sentences.

Maximum flow is about finding the greatest amount of "stuff" (like water, data, or traffic) you can push from a source to a destination through a network with capacity limits on each connection. Think of it like a pipe system where each pipe can only handle so much flow—you want to find the best way to route flow through multiple paths to maximize the total amount reaching the end. The key insight is the **max-flow min-cut theorem**: the maximum flow equals the minimum capacity you'd need to cut to completely disconnect the source from the destination. Algorithms like Ford-Fulkerson solve this by repeatedly finding paths with available capacity and pushing flow through them until no more improvement is possible.