of instead of so that multiplication can be effected using the shift (>>operatorwhich is faster than the modulo (%operator you can use an approach similar to this to convert any kind of string to number suitable for hashing the strings can be wordsnamesor any other concatenation of characters hashing efficiency we've noted that insertion and searching in hash tables can approach ( time if no collision occursonly call to the hash function and single array reference are necessary to insert new item or find an existing item this is the minimum access time if collisions occuraccess times become dependent on the resulting probe lengths each cell accessed during probe adds another time increment to the search for vacant cell (for insertionor for an existing cell during an accessa cell must be checked to see if it' emptyand--in the case of searching or deletion--if it contains the desired item thus an individual search or insertion time is proportional to the length of the probe this is in addition to constant time for the hash function the average probe length (and therefore the average access timeis dependent on the load factor (the ratio of items in the table to the size of the tableas the load factor increasesprobe lengths grow longer we'll look at the relationship between probe lengths and load factors for the various kinds of hash tables we've studied open addressing the loss of efficiency with high load factors is more serious for the various open addressing schemes than for separate chaining in open addressingunsuccessful searches generally take longer than successful searches during probe sequencethe algorithm can stop as soon as it finds the desired itemwhich ison the average halfway through the probe sequence on the other handit must go all the way to the end of the sequence before it' sure it can' find an item linear probing the following equations show the relationship between probe length (pand load factor (lfor linear probing for successful search it' ( - and for an unsuccessful search it' ( - these formulas are from knuth (see appendix "further reading")and their derivation is quite complicated figure shows the result of graphing these equations