found alternativelyif the hash table size is power of two and the probe function is (ki( )/ then every slot in the table will be visited by the probe function both pseudo-random probing and quadratic probing eliminate primary clusteringwhich is the problem of keys sharing substantial segments of probe sequence if two keys hash to the same home positionhoweverthen they will always follow the same probe sequence for every collision resolution method that we have seen so far the probe sequences generated by pseudo-random and quadratic probing (for exampleare entirely function of the home positionnot the original key value this is because function ignores its input parameter for these collision resolution methods if the hash function generates cluster at particular home positionthen the cluster remains under pseudo-random and quadratic probing this problem is called secondary clustering to avoid secondary clusteringwe need to have the probe sequence make use of the original key value in its decision-making process simple technique for doing this is to return to linear probing by constant step size for the probe functionbut to have that constant be determined by second hash functionh thusthe probe sequence would be of the form (kii (kthis method is called double hashing example assume hash table has size and that there are three keys and with ( ( ( ( ( and ( thenthe probe sequence for will be and so on the probe sequence for will be and so on the probe sequence for will be and so on thusnone of the keys share substantial portions of the same probe sequence of courseif fourth key has ( and ( then it will follow the same probe sequence as pseudorandom or quadratic probing can be combined with double hashing to solve this problem good implementation of double hashing should ensure that all of the probe sequence constants are relatively prime to the table size this can be achieved easily one way is to select to be prime numberand have return value in the range < ( < another way is to set for some value and have return an odd value between and figure shows an implementation of the dictionary adt by means of hash table the simplest hash function is usedwith collision resolution by linear probingas the basis for the structure of hash table implementation suggested