nowconsider the case where the table size is and the constant factor is the probe sequence will only include the even numbered entries and will repeat the same sequence without possibly finding the key or an available entry to store new key quadratic probing the linear probe with constant factor larger than spreads the keys out from the initial hash positionbut it can still result in clustering the clusters simply move equal distance from the initial hash positions better approach for reducing primary clustering is with the use of quadratic probing which is specified by the equationslot (home quadratic probing eliminates primary clustering by increasing the distance between each probe in the sequence when used to build the hash table using the sample set of keyswe get seven collisions (the resulting hash table is illustrated in figure ) ( = ( = ( = ( = ( = ( = ( = ( = = = = = = = = while the number of collisions has increasedthe primary clustering has been reduced in practicequadratic probing typically reduces the number of collisions but introduces the problem of secondary clustering secondary clustering occurs when two keys map to the same table entry and have the same probe sequence for exampleif we were to add key to our tableit would hash to slot and follow the same probe sequence as key finallythere is no guarantee the quadratic probe will visit every entry in the table but if the table size is prime numberat least half of the entries will be visited figure the hash table using quadratic probe double hashing the quadratic probe distributes the keys by increasing steps in the probe sequence but the same sequence is followed by multiple keys that map to the same table