Function assign_or_hall_capacitated 

pub fn assign_or_hall_capacitated(
    adj: &[Vec<usize>],
    capacities: &[usize],
) -> CapMatchOutcome

Decide whether every item can be assigned a slot when slot s holds at most capacities[s] items (a b-matching / resource-allocation feasibility — e.g. traffic movements sharing capacity-limited green windows). Reduces to plain matching by splitting each slot into that many interchangeable copies, then maps the result (and any Hall witness) back to original slots.