data structures using hence the name double hashing in double hashingwe use two hash functions rather than single function the hash function in the case of double hashing can be given ash(ki[ (kih ( )mod where is the size of the hash tableh (kand (kare two hash functions given as (kk mod mh (kk mod ' is the probe number that varies from to - and mis chosen to be less than we can choose mm- or - when we have to insert key in the hash tablewe first probe the location given by applying [ (kmod mbecause during the first probei if the location is vacantthe key is inserted into itelse subsequent probes generate locations that are at an offset of [ (kmod mfrom the previous location since the offset may vary with every probe depending on the value generated by the second hash functionthe performance of double hashing is very close to the performance of the ideal scheme of uniform hashing pros and cons double hashing minimizes repeated collisions and the effects of clustering that isdouble hashing is free from problems associated with primary clustering as well as secondary clustering example consider hash table of size using double hashinginsert the keys and into the table take ( mod and ( mod solution let initiallythe hash table can be given as - - - - - - - - - - we haveh(ki[ (kih ( )mod step key ( [ mod ( mod )mod [ ( )mod mod = since [ is vacantinsert the key in [ the hash table now becomes - - - - - - - - - step key ( [ mod ( mod )mod [ ( )mod mod = since [ is vacantinsert the key in [ the hash table now becomes - - - - - - - -