AlgoScope

Ford-Fulkerson

AlgorithmadvancedNetwork Flow

Any augmenting path will do; push its bottleneck, and undoing flow along a backward residual edge is allowed.

Decision · step 2 of 7Maximum Flow: Ford-Fulkerson with a cancelled edge
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DFS finds an augmenting path 0 > 1 > 2 > 3, residual capacities 1, 1, 1. The bottleneck is 1.

Open in the player →or start at step 2

What you will see

A path lights up, its bottleneck is found, flow labels increase and residual edges appear.

How maximum flow works →

Cost

BestO(E)
AverageO(E * max flow)
WorstO(E * max flow)
SpaceO(V + E)

May not terminate with irrational capacities.

How you work with it here

play it through, step one change at a time, scrub to any step, run it on your own input.

Screen readers: Edges announce capacity, flow and residual; each step announces the augmenting path and bottleneck.

Reduced motion: Flow labels update with a crossfade; the augmenting path is emphasized statically.

Leads to

Topics that need this one first.

Taught by the same lesson

Maximum Flow covers these too, in the same run.