thuswhen probing to add new key or in searching for an existing keywe know the search must continue past the slot since the target may be stored beyond this point figure illustrates the correct way to delete key from the hash table the delta symbol is used to indicate deleted entry figure the correct way to delete key from the hash table clustering as more keys are added to the hash tablemore collisions are likely to occur since each collision requires linear probe to find the next available slotthe keys begin to form clusters as the clusters grow largerso too does the probability that the next key added to the table will result in collision if our table were emptythe probability of key being added to any of the empty slots is out of since it is equally likely the key can hash to any of the slots now consider the hash table in figure what is the probability the next key will occupy the empty slot at position if the next key hashes to this positionit can be stored directly into the slot without the need to probe this also results in probability of out of but the probability the next key will occupy slot is out of if the next key hashes to any of the slots between and it will be stored in slot due to the linear probe required to find the first position beyond the cluster of keys thusthe key is five times more likely to occupy slot than slot this type of clustering is known as primary clustering since it occurs near the original hash position as the clusters grow largerso too does the length of the search needed to find the next available slot we can reduce the amount of primary clustering by changing the technique used in the probing in this sectionwe examine several different probing techniques that can be employed to reduce primary clustering modified linear probe when probing to find the next available slota loop is used to iterate through the table entries the order in which the entries are visited form probe sequence the linear probe searches for the next available slot by stepping through the hash table entries in sequential order the next array slot in the probe sequence can be represented as an equationslot (home im