sec hashing number of records storedand refuse to insert into table that has only one free slot the discussion on bucket hashing presented simple method of collision resolution if the home position for the record is occupiedthen move down the bucket until free slot is found this is an example of technique for collision resolution known as linear probing the probe function for simple linear probing is (kii that isthe ith offset on the probe sequence is just imeaning that the ith step is simply to move down slots in the table once the bottom of the table is reachedthe probe sequence wraps around to the beginning of the table linear probing has the virtue that all slots in the table will be candidates for inserting new record before the probe sequence returns to the home position it is important to understand thatwhile linear probing is probably the first idea that comes to mind when considering collision resolution policiesit is not the only one possible probe function allows us many options for how to do collision resolution in factlinear probing is one of the worst collision resolution methods the main problem is illustrated by figure herewe see hash table of ten slots used to store four-digit numberswith hash function (kk mod in figure ( )five numbers have been placed in the tableleaving five slots remaining the ideal behavior for collision resolution mechanism is that each empty slot in the table will have equal probability of receiving the next record inserted (assuming that every slot in the table has equal probability of being hashed to initiallyin this examplethe hash function gives each slot (roughlyequal probability of being the home position for the next key howeverconsider what happens to the next record if its key has its home position at slot linear probing will send the record to slot the same will happen to records whose home position is at slot record with home position at slot will remain in slot thusthe probability is / that the next record inserted will end up in slot in similar mannerrecords hashing to slots or will end up in slot howeveronly records hashing to slot will be stored in slot yielding one chance in ten of this happening likewisethere is only one chance in ten that the next record will be stored in slot one chance in ten for slot and one chance in ten for slot thusthe resulting probabilities are not equal to make matters worseif the next record ends up in slot (which already has higher than normal chance of happening)then the following record will end up