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'''Linear probing ''' is a scheme in [[computer programming]] for resolving [[hash collision]]s of values of [[hash function]]s by sequentially searching the [[hash table]] for a free location.<ref>{{cite book |last=Dale |first=Nell |title=C++ Plus Data Structures |year=2003 |publisher=Jones and Bartlett Computer Science |location=Sudbury, MA |isbn=0-7637-0481-4 }}</ref>  This is accomplished using two values - one as a starting value and one as an interval between successive values in [[modular arithmetic]]. The second value, which is the same for all keys and known as the ''stepsize'', is repeatedly added to the starting value until a free space is found, or the entire table is traversed.  (In order to traverse the entire table the stepsize should be [[relatively prime]] to the arraysize, which is why the array size is often chosen to be a prime number.)
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::newLocation = (startingValue + stepSize) % arraySize
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This algorithm, which is used in open-addressed [[hash table]]s, provides good memory caching (if stepsize is equal to one), through good locality of reference, but also results in clustering, an unfortunately high [[probability]] that where there has been one collision there will be more. The performance of linear probing is also more sensitive to input distribution when compared to [[double hashing]], where the stepsize is determined by another hash function applied to the value instead of a fixed stepsize as in linear probing.
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Given an ordinary hash function ''H(x)'', a linear probing function (''H(x, i)'') would be:
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::<math> H(x, i) = (H(x) + i) \pmod n.\, </math>
Here ''H(x)'' is the starting value, ''n'' the size of the hash table, and the ''stepsize'' is ''i'' in this case.


==Dictionary operation in constant time==
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Using linear probing, dictionary operation can be implemented in constant time. In other words, insert, remove and find operations can be implemented in O(1), as long as the [[load factor (computer science)|load factor]] of the hash table is a constant strictly less than one.<ref>{{citation|first=Donald|last=Knuth|authorlink=Donald Knuth|title=Notes on "Open" Addressing|year=1963|url=http://algo.inria.fr/AofA/Research/11-97.html}}</ref> This analysis makes the (unrealistic) assumption that the hash function is completely random, but can be extended also to [[K-independent hashing|5-independent hash functions]].<ref>{{citation
| last1 = Pagh | first1 = Anna
| last2 = Pagh | first2 = Rasmus
| last3 = Ružić | first3 = Milan
| doi = 10.1137/070702278
| issue = 3
| journal = SIAM Journal on Computing
| mr = 2538852
| pages = 1107–1120
| title = Linear probing with constant independence
| volume = 39
| year = 2009}}</ref> Weaker properties, such as [[universal hashing]], are not strong enough to ensure the constant-time operation of linear probing,<ref>{{citation
| last1 = Pătraşcu | first1 = Mihai | author1-link = Mihai Pătraşcu
| last2 = Thorup | first2 = Mikkel | author2-link = Mikkel Thorup
| contribution = On the k-independence required by linear probing and minwise independence
| doi = 10.1007/978-3-642-14165-2_60
| pages = 715–726
| publisher = Springer
| series = Lecture Notes in Computer Science
| title = Automata, Languages and Programming, 37th International Colloquium, ICALP 2010, Bordeaux, France, July 6-10, 2010, Proceedings, Part I
| url = http://people.csail.mit.edu/mip/papers/kwise-lb/kwise-lb.pdf
| volume = 6198
| year = 2010}}</ref> but one practical method of hash function generation, [[tabulation hashing]], again leads to a guaranteed constant expected time performance despite not being 5-independent.<ref>{{citation
| last1 = Pătraşcu | first1 = Mihai | author1-link = Mihai Pătraşcu
| last2 = Thorup | first2 = Mikkel | author2-link = Mikkel Thorup
| arxiv = 1011.5200
| contribution = The power of simple tabulation hashing
| doi = 10.1145/1993636.1993638
| pages = 1–10
| title = Proceedings of the 43rd annual ACM Symposium on Theory of Computing (STOC '11)
| year = 2011}}</ref>


==See also==
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* [[Quadratic probing]]
* [[Hash_table#Collision_resolution|Collision resolution]]


==References==
== UGG Cardy Snood ==
{{reflist}}


==External links==
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*[http://www.siam.org/meetings/alenex05/papers/13gheileman.pdf How Caching Affects Hashing] by Gregory L. Heileman and Wenbin Luo 2005.
*[http://opendatastructures.org/versions/edition-0.1e/ods-java/5_2_LinearHashTable_Linear_.html Open Data Structures - Section 5.2 - LinearHashTable: Linear Probing]


[[Category:Search algorithms]]
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[[Category:Hashing]]


{{datastructure-stub}}
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in this case, transform the thickness via the spices it has a structure is your decision, most cooking staff establish the company's sauces much in thickness; increase 1 or 2 teaspoons water to skinny the problem or simmer the type of gravy for a moment to lower and as a result thicken. whisk inside the frozen butter, while keeping the griddle and whisk taking until all the butter touches. (don't be it be seated possessing whisking maybe the butter does indeed price.) Season,UGG Acheter, in notice, all of the pepper, And just to make sure, a few more drops concerning vinegar,UGG Noir Pas Cher,

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