, , figure number of probes plotted against load factor for linear probing (dashedand random strategy ( is successful searchu is unsuccessful searchand is insertionempty table after after after after after figure hash table with quadratic probingafter each insertion triedbut another collision occurs vacant cell is found at the next cell triedwhich is away is thus placed in cell the same thing happens for for linear probingit is bad idea to let the hash table get nearly fullbecause performance degrades for quadratic probingthe situation is even more drasticthere is no guarantee of finding an empty cell once the table gets more than half fullor even before the table gets half full if the table size is not prime this is because at most half of the table can be used as alternative locations to resolve collisions indeedwe prove now that if the table is half empty and the table size is primethen we are always guaranteed to be able to insert new element