Find the augmenting path in the following graph

Which of the following paths is an augmenting path for the graph below?

The following graph shows a set of vertices and edges. Each edge shows two numbers: its current flow divided by its capacity.

Graph in the middle of a max flow algorithm Graph in the middle of a max flow algorithm

{source, A, B, D, sink} {source, C, B, D, sink} {source, A, B, sink} {source, A, B, C, D, sink}

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2 solutions

Aisthu Lucky
Mar 2, 2019

{source, a, b, c, d, sink} is one augmented path. If we pass a single car more, it will fill up most of the pipes.

There are others as a subset of this path, but from the answers given, it's the only correct one

Anu Sandhu
Jun 2, 2020

We use paths that have residual capacity left. Hence, {source, A, B, C, D, sink} is one of the augmenting path

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