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{{Infobox Algorithm | |||
|image = | |||
|class=[[Sorting algorithm]] | |||
|data=[[Array data structure|Array]] | |||
|time=Unbounded<ref name="Fun07"/> | |||
|average-time={{math|''O''(n × n!)}}<ref name="Fun07"/> | |||
|best-time={{math|''Ω''(n)}}<ref name="Fun07"/> | |||
|space={{math|''O''(n)}} | |||
|optimal=No | |||
}} | |||
In [[computer science]], '''bogosort'''<ref name="Fun07"/><ref name="KSFS">{{citation | |||
| last1 = Kiselyov | first1 = Oleg | |||
| last2 = Shan | first2 = Chung-chieh | |||
| last3 = Friedman | first3 = Daniel P. | |||
| last4 = Sabry | first4 = Amr | |||
| contribution = Backtracking, interleaving, and terminating monad transformers: (functional pearl) | |||
| doi = 10.1145/1086365.1086390 | |||
| pages = 192–203 | |||
| series = SIGPLAN Notices | |||
| title = Proceedings of the Tenth ACM SIGPLAN International Conference on Functional Programming (ICFP '05) | |||
| url = http://www.dicta.org.uk/programming/LogicT.pdf | |||
| year = 2005}}</ref> (also '''stupid sort'''<ref>E. S. Raymond. "bogo-sort". ''The New Hacker’s Dictionary''. MIT Press, 1996.</ref> or '''slowsort'''<ref name="Naish86">{{citation | |||
| last = Naish | first = Lee | |||
| contribution = Negation and quantifiers in NU-Prolog | |||
| doi = 10.1007/3-540-16492-8_111 | |||
| pages = 624–634 | |||
| publisher = Springer-Verlag | |||
| series = Lecture Notes in Computer Science | |||
| title = Proceedings of the Third International Conference on Logic Programming | |||
| volume = 225 | |||
| year = 1986}}.</ref><ref name="Naish95">{{citation | |||
| last = Naish | first = Lee | |||
| date = June 1995 | |||
| location = Melbourne, Australia | |||
| publisher = Department of Computer Science, University of Melbourne | |||
| series = Tech. Report 95/16 | |||
| title = Pruning in logic programming | |||
| id = {{citeseerx|10.1.1.54.2347}} }}.</ref>) is a particularly ineffective [[sorting algorithm]] based on the [[Trial and error|generate and test]] paradigm. It is not useful for sorting, but may be used for educational purposes, to contrast it with other more realistic algorithms; it has also been used as an example in [[logic programming]].<ref name="KSFS"/><ref name="Naish86"/><ref name="Naish95"/> If bogosort were used to sort a [[deck of cards]], it would consist of checking if the deck were in order, and if it were not, throwing the deck into the air, picking the cards up at random, and repeating the process until the deck is sorted. Its name comes from the word ''bogus''.<ref>{{cite web|title=Bogosort|url=http://www.catb.org/jargon/html/B/bogo-sort.html|work=The Jargon File 4.4.8|accessdate=11 April 2013|year=2003}}</ref> | |||
==Description of the algorithm== | |||
The following is a description of the algorithm in [[pseudocode]]: | |||
'''while not''' isInOrder(deck): | |||
shuffle(deck) | |||
==Running time and termination== | |||
This [[sorting algorithm]] is probabilistic in nature. If all elements to be sorted are distinct, the expected number of comparisons in the average case is [[Asymptotic analysis|asymptotically equivalent to]] <math>(e-1) n!</math>, and the expected number of swaps in the average case equals <math>(n-1) n!</math>.<ref name="Fun07">{{citation | |||
| last1 = Gruber | first1 = H. | |||
| last2 = Holzer | first2 = M. | |||
| last3 = Ruepp | first3 = O. | |||
| contribution = Sorting the slow way: an analysis of perversely awful randomized sorting algorithms | |||
| doi = 10.1007/978-3-540-72914-3_17 | |||
| pages = 183–197 | |||
| publisher = Springer-Verlag | |||
| series = Lecture Notes in Computer Science | |||
| title = 4th International Conference on Fun with Algorithms, Castiglioncello, Italy, 2007 | |||
| url = http://www.hermann-gruber.com/data/fun07-final.pdf | |||
| volume = 4475}}.</ref> The expected number of swaps grows faster than the expected number of comparisons, because if the elements are not in order, this will usually be discovered after only a few comparisons no matter how many elements there are, but the work of shuffling the collection is proportional to its size. In the worst case, the number of comparisons and swaps are both unbounded, for the same reason that a tossed coin might turn up heads any number of times in a row. | |||
The best case occurs if the list as given is already sorted; in this case the expected number of comparisons is <math>n-1</math>, and no swaps at all are carried out.<ref name="Fun07"/> | |||
For any collection of fixed size, the expected running time of the algorithm is finite for much the same reason that the [[infinite monkey theorem]] holds: there is some probability of getting the right permutation, so given an unbounded number of tries it will [[almost surely]] eventually be chosen. | |||
==Related algorithms== | |||
;Gorosort: is a sorting algorithm introduced in the 2011 [[Google Code Jam]].<ref>[http://code.google.com/codejam/contest/dashboard?c=975485#s=p3 Google Code Jam 2011, Qualification Rounds, Problem D]</ref> As long as the list is not in order, a subset of all elements is randomly permuted. If this subset is optimally chosen each time this is performed, the [[expected value]] of the total number of times this operation needs to be done is equal to the number of misplaced elements. | |||
;Bogobogosort: is an algorithm that was designed not to succeed before the [[heat death of the universe]] on any sizable list. It works by implementing the bogosort on the first two elements in the list. If they are in order, then it bogosorts the first three elements, and so on, increasing by one until the entire list is sorted. Should the list not be in order at any point, the sort starts over with the first two elements. | |||
;Bozosort: is another sorting algorithm based on random numbers. If the list is not in order, it picks two items at random and swaps them, then checks to see if the list is sorted. The running time analysis of a bozosort is more difficult, but some estimates are found in H. Gruber's analysis of "perversely awful" randomized sorting algorithms.<ref name="Fun07"/> O(n!) is found to be the expected average case. | |||
<!--It also faces the same pseudo-random problems as bogosort—it may never terminate in a real-world implementation.--> | |||
;{{anchor|Quantum bogosort}}Quantum Bogosort: An [[in-joke]] among some computer scientists is that [[quantum computing]] could be used to effectively implement a bogosort with a time complexity of O(n).<ref>[http://www.mathnews.uwaterloo.ca/Issues/mn11103/QuantumBogoSort.php mathNEWS Issue 111.3: Friday, October 23, 2009 - Quantum Bogosort]</ref> It uses true quantum randomness to randomly permute the list. The list is then inspected, and if it is not in order, the universe is destroyed. By the [[many-worlds interpretation]] of quantum physics, the quantum randomization spawns <math>2^N</math> (where N is the number of random bits) universes and one of these will be such that this single shuffle had produced the list in sorted order. Quantum physics prohibits the useful implementation of such an algorithm, since (assuming the many worlds interpretation is correct) all but one of the spawned universes will have the algorithm fail. | |||
== See also == | |||
* [[Las Vegas algorithm]] | |||
* [[Stooge sort]] | |||
== References == | |||
<references/> | |||
==External links== | |||
{{wikibooks|Algorithm Implementation|Sorting/Bogosort|Bogosort}} | |||
* [[c2:BogoSort|BogoSort]] on [[WikiWikiWeb]] | |||
* [http://richardhartersworld.com/cri_d/cri/2001/badsort.html Inefficient sort algorithms] | |||
* [http://www.lysator.liu.se/~qha/bogosort/ Bogosort]: an implementation that runs on [[Unix-like]] systems, similar to the standard [[sort (Unix)|sort]] program. | |||
* [http://github.com/versesane/algorithms-and-data-structures-in-c/tree/master/bogosort.c Bogosort] and [http://libjmmcg.cvs.sourceforge.net/viewvc/libjmmcg/libjmmcg/core/bogo_sort.hpp jmmcg::bogosort]: Simple, yet perverse, C++ implementations of the bogosort algorithm. | |||
{{sorting}} | |||
{{Use dmy dates|date=June 2011}} | |||
[[Category:Sorting algorithms]] | |||
[[Category:Comparison sorts]] | |||
[[Category:Computer humor]] | |||
Revision as of 15:34, 18 January 2014
In computer science, bogosort[1][2] (also stupid sort[3] or slowsort[4][5]) is a particularly ineffective sorting algorithm based on the generate and test paradigm. It is not useful for sorting, but may be used for educational purposes, to contrast it with other more realistic algorithms; it has also been used as an example in logic programming.[2][4][5] If bogosort were used to sort a deck of cards, it would consist of checking if the deck were in order, and if it were not, throwing the deck into the air, picking the cards up at random, and repeating the process until the deck is sorted. Its name comes from the word bogus.[6]
Description of the algorithm
The following is a description of the algorithm in pseudocode:
while not isInOrder(deck):
shuffle(deck)
Running time and termination
This sorting algorithm is probabilistic in nature. If all elements to be sorted are distinct, the expected number of comparisons in the average case is asymptotically equivalent to , and the expected number of swaps in the average case equals .[1] The expected number of swaps grows faster than the expected number of comparisons, because if the elements are not in order, this will usually be discovered after only a few comparisons no matter how many elements there are, but the work of shuffling the collection is proportional to its size. In the worst case, the number of comparisons and swaps are both unbounded, for the same reason that a tossed coin might turn up heads any number of times in a row.
The best case occurs if the list as given is already sorted; in this case the expected number of comparisons is , and no swaps at all are carried out.[1]
For any collection of fixed size, the expected running time of the algorithm is finite for much the same reason that the infinite monkey theorem holds: there is some probability of getting the right permutation, so given an unbounded number of tries it will almost surely eventually be chosen.
Related algorithms
- Gorosort
- is a sorting algorithm introduced in the 2011 Google Code Jam.[7] As long as the list is not in order, a subset of all elements is randomly permuted. If this subset is optimally chosen each time this is performed, the expected value of the total number of times this operation needs to be done is equal to the number of misplaced elements.
- Bogobogosort
- is an algorithm that was designed not to succeed before the heat death of the universe on any sizable list. It works by implementing the bogosort on the first two elements in the list. If they are in order, then it bogosorts the first three elements, and so on, increasing by one until the entire list is sorted. Should the list not be in order at any point, the sort starts over with the first two elements.
- Bozosort
- is another sorting algorithm based on random numbers. If the list is not in order, it picks two items at random and swaps them, then checks to see if the list is sorted. The running time analysis of a bozosort is more difficult, but some estimates are found in H. Gruber's analysis of "perversely awful" randomized sorting algorithms.[1] O(n!) is found to be the expected average case.
<Quantum bogosort>...</Quantum bogosort>Quantum Bogosort- An in-joke among some computer scientists is that quantum computing could be used to effectively implement a bogosort with a time complexity of O(n).[8] It uses true quantum randomness to randomly permute the list. The list is then inspected, and if it is not in order, the universe is destroyed. By the many-worlds interpretation of quantum physics, the quantum randomization spawns (where N is the number of random bits) universes and one of these will be such that this single shuffle had produced the list in sorted order. Quantum physics prohibits the useful implementation of such an algorithm, since (assuming the many worlds interpretation is correct) all but one of the spawned universes will have the algorithm fail.
See also
References
- ↑ 1.0 1.1 1.2 1.3 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ 2.0 2.1 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 - ↑ E. S. Raymond. "bogo-sort". The New Hacker’s Dictionary. MIT Press, 1996.
- ↑ 4.0 4.1 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ 5.0 5.1 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Template:Cite web
- ↑ Google Code Jam 2011, Qualification Rounds, Problem D
- ↑ mathNEWS Issue 111.3: Friday, October 23, 2009 - Quantum Bogosort
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- BogoSort on WikiWikiWeb
- Inefficient sort algorithms
- Bogosort: an implementation that runs on Unix-like systems, similar to the standard sort program.
- Bogosort and jmmcg::bogosort: Simple, yet perverse, C++ implementations of the bogosort algorithm.
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