chap searching example consider table of size with perm[ perm[ and perm[ assume that we have two keys and where ( and ( the probe sequence for is then then then the probe sequence for is then then then thuswhile will probe to ' home position as its second choicethe two keysprobe sequences diverge immediately thereafter another probe function that eliminates primary clustering is called quadratic probing here the probe function is some quadratic function (kic for some choice of constants and the simplest variation is (kii ( and then the ith value in the probe sequence would be ( (ki mod under quadratic probingtwo keys with different home positions will have diverging probe sequences example given hash table of size assume for keys and that ( and ( the probe sequence for is then then then the probe sequence for is then then then thuswhile will probe to ' home position as its second choicethe two keysprobe sequences diverge immediately thereafter unfortunatelyquadratic probing has the disadvantage that typically not all hash table slots will be on the probe sequence using (kii gives particularly inconsistent results for many hash table sizesthis probe function will cycle through relatively small number of slots if all slots on that cycle happen to be fullthen the record cannot be inserted at allfor exampleif our hash table has three slotsthen records that hash to slot can probe only to slots and (that isthe probe sequence will never visit slot in the tablethusif slots and are fullthen the record cannot be inserted even though the table is not fulla more realistic example is table with slots the probe sequence starting from any given slot will only visit other slots in the table if all of these slots should happen to be fulleven if other slots in the table are emptythen the record cannot be inserted because the probe sequence will continually hit only those same slots fortunatelyit is possible to get good results from quadratic probing at low cost the right combination of probe function and table size will visit many slots in the table in particularif the hash table size is prime number and the probe function is (kii then at least half the slots in the table will be visited thusif the table is less than half fullwe can be certain that free slot will be