[Verse 1]
Graph connections weave like spider silk
Each edge carries weight, each node holds milk
Source pumps data, sink collects the stream
Between them paths create a flowing dream
Residual capacity shows what remains
After current flows through digital veins
Augmenting paths reveal the secret route
To maximize the algorithmic fruit
[Chorus]
Ford and Fulkerson found the way
Saturate until no path can stay
Residual graph reveals the truth
Maximum flow through network proof
Cut the minimum, seal the deal
Bottlenecks show what flows are real
Ford and Fulkerson found the way
Maximum flow saves the day
[Verse 2]
Breadth-first search scouts the terrain
Depth-first works but might cause strain
Forward edges push the current high
Backward edges let the flow reverse and fly
Each iteration builds upon the last
Augmenting paths accumulate fast
When no more paths can carry weight
The algorithm seals your flow's fate
[Chorus]
Ford and Fulkerson found the way
Saturate until no path can stay
Residual graph reveals the truth
Maximum flow through network proof
Cut the minimum, seal the deal
Bottlenecks show what flows are real
Ford and Fulkerson found the way
Maximum flow saves the day
[Bridge]
Minimum cut equals maximum flow
Duality theorem helps us know
Partition vertices with precision
Source and sink in different division
Saturated edges form the barrier
Nothing more can be a carrier
[Verse 3]
Time complexity depends on approach
Edmonds-Karp refines the coach
Polynomial bounds keep runtime tight
While basic version might take flight
Applications span from pipes to matching
Network optimization keeps dispatching
Bipartite graphs and transport schemes
Ford-Fulkerson powers up your dreams
[Chorus]
Ford and Fulkerson found the way
Saturate until no path can stay
Residual graph reveals the truth
Maximum flow through network proof
Cut the minimum, seal the deal
Bottlenecks show what flows are real
Ford and Fulkerson found the way
Maximum flow saves the day
[Outro]
When networks need their limits tested
Ford-Fulkerson leaves you well-rested
Maximum flow achieved at last
Algorithm mastery unsurpassed