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# Maximum flow problem

Maximum flow problems involve finding a feasible flow through a flow network that maximizes the flow rate.

The order of the path from source to sink is not important.

After finding the max flow, draw the `residual graph`

and check if there is room for further improvement.

### Residual Network:

c(u, v) is

- c(u, v) - f(u, v): send the amount about empty room
- f(v, u): give back the amount I recieved
- Give back what you received and receive the available amount.