hash tables where is the ith probe in the sequencei home is the home positionwhich is the index to which the key was originally mapped by the hash function the modulus operator is used to wrap back around to the front of the array after reaching the end the use of the linear probe resulted in six collisions in our hash table of size ( = ( = ( = ( = ( = ( = ( = ( = = = = = = = when the keys are inserted in the order we can improve the linear probe by skipping over multiple elements instead of probing the immediate successor of each element this can be done by changing the step size in the probe equation to some fixed constant cslot (home cm suppose we use linear probe with to build the hash table using the same set of keys this results in only two collisions as compared to six when (the resulting hash table is illustrated in figure ) ( = ( = ( = ( = ( = ( = ( = ( = = = figure the hash table using linear probe with any value can be used for the constant factorbut to ensure the probe sequence includes all table entriesthe constant factor and the table size must be relatively prime with hash table of size the linear probe with constant factor will visit every element for exampleif the key hashes to position the table entries will be visited in the following order if we use value of the probe sequence will be