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Talk:Combinations with repetitions: Difference between revisions
Talk:Combinations with repetitions (view source)
Revision as of 20:11, 19 November 2010
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--[[User:Paddy3118|Paddy3118]] 02:37, 19 November 2010 (UTC)
:Maybe keep the name as [http://googlefight.com/index.php?lang=en_GB&word1=%22combinations+with+replacement%22&word2=%22combinations+with+repetition%22 googlefight] prefers it 465 to 91. --[[User:Paddy3118|Paddy3118]] 02:45, 19 November 2010 (UTC)
:I think we have two separate tasks here. We have the original task (where individual items could be repeated with counts independent of other items) and the new task (where the repetition count on all items is assumed to be at least as large as the number of elements in the desired results). --[[User:Rdm|Rdm]] 15:58, 19 November 2010 (UTC)
:: And yet I get the n=10, k=3 result of 220 which is mentioned in the Wikipedia article?
:: Looking again at the [http://rosettacode.org/mw/index.php?title=Combinations_with_repetitions&oldid=95620 previous description] of:
:::Write a program which generates the all [[wp:Combination|k-combination with repetitions]] of '''n''' different objects. (Practically numerals!)
:::An example about the task:
:::You have a hat, and you have '''n''' balls with numbers (1...n). Put the balls into the hat, and cover it. Take '''k'''-times one ball from the hat, but you must put back always immediately the ball after registration of the number into the hat. How many different combination can we have? (Of course the following two combination are not different: [1, 2, 2] and [2, 1, 2]).
::And comparing it to the new doughnut flavoured task of:
::::Q: How many ways can a person choose two doughnuts from a store selling three types of doughnut: iced, jam, and plain?
::::A: 6: iced and iced; iced and jam; iced and plain; jam and jam; jam and plain; plain and plain.
::I think the task descriptions are equivalent but the old J solution confuses me as it shows fixed repetitions of items, where I read the WP article and the description given as needing only the n types of allowable items - any kind of repetition (or omission), is allowed just so long as only k are chosen at once. Yep, it doesn't help that the wp article is hard to read :-)
:: --[[User:Paddy3118|Paddy3118]] 17:00, 19 November 2010 (UTC)
::: If you go back and look at the original entry, you will see that the original java code worked the same way as the old J example. But that code was deleted for copyright reasons and when it was deleted, the associated examples were also deleted, which makes talking about that issue a bit confusing. But, anyways, we have two tasks here: one based on a common interpretation of the wording of the original task description and another based on the original examples. Without those examples, the original task description does not distinguish between these two cases. --[[User:Rdm|Rdm]] 19:15, 19 November 2010 (UTC)
::::Hi Rdm. I went to the original blog with the Java code, and I think that it is probably a case of a loosely used term: "Combinations with repetitions" that is not what is mentioned in the wp article. Wolfram mathworld calls what is mentioned in the wp article [http://mathworld.wolfram.com/Multichoose.html multichoose], but it is not what the Java does - as you have been saying. If someone can come up with some good references for what the Java code is doing then I'd be grateful, Ta. --[[User:Paddy3118|Paddy3118]] 20:11, 19 November 2010 (UTC)
:: [https://docs.google.com/viewer?url=http://www.nitte.ac.in/userfiles/file/Combinations%2520with%2520Repetitions.pdf&embedded=true&chrome=true Another link] that might be a better explanation? --[[User:Paddy3118|Paddy3118]] 17:07, 19 November 2010 (UTC)
::: The WP article references [https://compprog.wordpress.com/2007/10/17/generating-combinations-1/ this], which seems fairly readable. --[[User:Short Circuit|Michael Mol]] 17:12, 19 November 2010 (UTC)
::::Hi Michael. Unfortunately that article seems to be about plain old combinations. No help with repetitions. --[[User:Paddy3118|Paddy3118]] 17:32, 19 November 2010 (UTC)
::::: Hm. Looking at it, it reminded me of nCr from a business stats class I paid too little attention to, too long ago. Googling for that turns up [[wp:Binomial Coefficient]]. There's a short debate on their relationship in [[wp:Talk:Combination#REDIRECT_to_Binomial_coefficient]], but there's a rather pointed note to [[wp:Multiset#Polynomial_notation]] to demonstrate their relationship. Of course, if I haven't been any help in shedding light on this, then I've probably completely enveloped it in a dense fog... --[[User:Short Circuit|Michael Mol]] 17:43, 19 November 2010 (UTC)
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