Disjoint-set representative ($\mathrm{find}(x)$)

A disjoint-set representative is a chosen member of a block of a set partition. It may be any member; it need not be the minimum, the first inserted member or a permanent identifier. A merge may change the disjoint-set representative of an existing member. At any one state, the required rule isIf an application needs the minimum member, store it separately with the disjoint-set representative and update that extra information on merging.