Harry Ron Hermione figure Helga Hufflepuffs cup horcrux through encounter Bellatrix Lestrange Hermione come know cup present Bellatrixs family vault Gringotts Wizarding Bank the Wizarding bank form tree total n vault vault type denote number 1 m a tree undirecte connect graph cyclesthe vault high security type k vault type k high securityThere x vault high security also vault high security adjacent vault guarantee high security type guarantee kHarry want consider possibility easily find good path reach Bellatrixs vault so tell give tree structure Gringotts number possible way give vault type condition hold