[OJFord]

There's some complexity arising from zones, and travelcards being based on zonal travel. So it's more complex than just capping it, or comparing it to the price of a travelcard, because you have to consider different combinations of travelcard (period and zone) and which journeys to ignore, leaving at PAYG rate.

I don't know what alpha-beta pruning is, and I'm not necessarily asserting it's massively complex, and I don't know anything about/haven't worked in the area beyond as a user - just pointing out it's not as simple as it might at first seem.

[TylerE]

A-B pruning is a technique from chess engines.

Basically, you do a breadth-first full recursive solve, but bail out of any branch that is clearly worse than other candidates.