sec hashing sequence that cycles through only the even slots likewisethe probe sequence for key whose home position is in an odd slot will cycle through the odd slots thusthis combination of table size and linear probing constant effectively divides the records into two sets stored in two disjoint sections of the hash table so long as both sections of the table contain the same number of recordsthis is not really important howeverjust from chance it is likely that one section will become fuller than the otherleading to more collisions and poorer performance for those records the other section would have fewer recordsand thus better performance but the overall system performance will be degradedas the additional cost to the side that is more full outweighs the improved performance of the less-full side constant must be relatively prime to to generate linear probing sequence that visits all slots in the table (that isc and must share no factorsfor hash table of size if is any one of or then the probe sequence will visit all slots for any key when any value for between and generates probe sequence that visits all slots for every key consider the situation where and we wish to insert record with key such that ( the probe sequence for is and so on if another key has home position at slot then its probe sequence will be and so on the probe sequences of and are linked together in manner that contributes to clustering in other wordslinear probing with value of does not solve the problem of primary clustering we would like to find probe function that does not link keys together in this way we would prefer that the probe sequence for after the first step on the sequence should not be identical to the probe sequence of insteadtheir probe sequences should diverge the ideal probe function would select the next position on the probe sequence at random from among the unvisited slotsthat isthe probe sequence should be random permutation of the hash table positions unfortunatelywe cannot actually select the next position in the probe sequence at randombecause then we would not be able to duplicate this same probe sequence when searching for the key howeverwe can do something similar called pseudo-random probing in pseudo-random probingthe ith slot in the probe sequence is ( (kri mod where ri is the ith value in random permutation of the numbers from to all insertion and search operations must use the same random permutation the probe function would be (kiperm[ ]where perm is an array of length containing random permutation of the values from to