gen-briefly-explain-maximum-flow-and-one-common-misconception-ab-8a92

Briefly explain maximum flow and one common misconception about it.

# Maximum Flow **Maximum flow** is a graph algorithm problem where you find the greatest amount of "flow" that can be sent from a source node to a sink node through a network of edges with limited capacities. Think of it like water flowing through pipes: each pipe (edge) has a maximum capacity, and you want to push as much water as possible from the source to the sink without exceeding any pipe's limit. ## Common Misconception **"Maximum flow just means finding the path with the largest capacity."** This is wrong! Maximum flow typically uses *multiple paths simultaneously*. The solution often involves sending flow along several different routes from source to sink, even if individual paths have small capacities. The key insight is that the sum of flows across all paths (that don't violate capacity constraints) can be much larger than any single path could carry. For example, ten paths each carrying 5 units gives you a total flow of 50 — much better than finding one "fat" path carrying 20 units.