Constant-time distinct-size counter ($D=|\{i:c_i>0\}|$)

Maintain a counter equal to the number of positive count-array entries. Increment it only when an addition changes zero to one; decrement it only when a removal changes one to zero. Other count changes leave the support unchanged. Initialization at zero and these cases prove the representation invariant by induction over completed operations, giving a constant-time distinct-size query.