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| In [[computer science]], a '''jump search''' or '''block search''' refers to a [[search algorithm]] for [[list (computing)|ordered lists]]. It works by first checking all items ''L''<sub>''km''</sub>, where <math>k \in \mathbb{N}</math> and ''m'' is the block size, until an item is found that is larger than the [[search key]]. To find the exact position of the search key in the list a [[linear search]] is performed on the [[sublist]] ''L''<sub>[(''k''-1)''m'', ''km'']</sub>.
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| The optimal value of ''m'' is √''n'', where ''n'' is the length of the list ''L''. Because both steps of the [[algorithm]] look at, at most, √''n'' items the algorithm runs in O(√''n'') time. This is better than a [[linear search]], but worse than a [[binary search]]. The advantage over the latter is that a jump search only needs to jump backwards once, while a binary can jump backwards up to log ''n'' times. This can be important if a jumping backwards takes significantly more time than jumping forward.
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| The algorithm can be modified by performing multiple levels of jump search on the sublists, before finally performing the [[linear search]]. For an ''k''-level jump search the optimum block size ''m''<sub>''l''</sub> for the ''l''<sup>th</sup> level (counting from 1) is ''n''<sup>(k-l)/k</sup>. The modified algorithm will perform ''k'' backward jumps and runs in O(''kn''<sup>1/(''k''+1)</sup>) time.
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| ==Implementation==
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| '''Algorithm''' JumpSeach
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| Input: An ordered list ''L'', its length ''n'' and a search key ''s''.
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| Output: The position of ''s'' in ''L'', or '''nothing''' if ''s'' is not in ''L''.
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| ''a'' ← 0
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| ''b'' ← ⌊√''n''⌋
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|
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| '''while''' ''L''<sub>min(''b'',''n'')-1</sub> < ''s'' '''do'''
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| ''a'' ← ''b''
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| ''b'' ← ''b'' + ⌊√''n''⌋
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| '''if''' ''a'' ≥ ''n'' '''then'''
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| '''return''' '''nothing'''
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| '''while''' ''L''<sub>''a''</sub> < ''s'' '''do'''
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| ''a'' ← ''a'' + 1
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| '''if''' ''a'' = min(''b'',''n'')
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| '''return''' '''nothing'''
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| '''if''' ''L''<sub>''a''</sub> = ''s'' '''then'''
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| '''return''' ''a''
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| '''else'''
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| '''return''' '''nothing'''
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| ==See also==
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| * [[Jump list]]
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| * [[Interpolation search]]
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| * [[Linear search]] - runs in O(''n'') time, only looks forward
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| * [[Binary search]] - runs in O(log ''n'') time, looks both forward and backward
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| ==References== | |
| * {{DADS|jump search|jumpsearch}}
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| * [[Ben Shneiderman]], ''Jump Searching: A Fast Sequential Search Technique'', CACM, 21(10):831-834, October 1978.
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| [[Category:Search algorithms]]
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