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 averagehalfway 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 average probe length unsuccessful successful figure load factor linear probe performance