Same sum, different sets of integers

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Same sum, different sets of integers

Atte Tenkanen
Hi,

Do you have ideas, how to find all those different combinations of
integers (>0) that produce as a sum, a certain integer.

i.e.: if that sum is

3, the possibilities are c(1,1,1), c(1,2), c(2,1)
4, the possibilities are
c(1,1,1,1),c(1,1,2),c(1,2,1),c(2,1,1),c(2,2),c(1,3),c(3,1)

etc.

Best regards,

Atte Tenkanen

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Re: Same sum, different sets of integers

Jim Lemon-4
Hi Atte,
I'm not sure that this actually works, and it's very much a quick hack:

sums_x<-function(x,addends=1,depth=1) {
 if(depth==1) {
  addends<-rep(addends,x)
  addlist<-list(addends)
 } else {
  addlist<-list()
 }
 lenadd<-length(addends)
 while(lenadd > 2) {
  addends<-c(addends[depth]+1,addends[-c(depth,depth+1)])
  lenadd<-lenadd-1
  if(sum(addends) == x) addlist[[length(addlist)+1]]<-addends
  cat(depth,"-",addends,"\n")
  if(lenadd > 2 && depth+1 < lenadd)
   addlist<-c(addlist,(sums_x(x,addends=addends,depth=depth+1)))
 }
 return(addlist)
}

This doesn't return all the permutations of the addends, but it's all
the time I have to waste this morning.

Jim

On Thu, Apr 28, 2016 at 1:46 AM, Atte Tenkanen <[hidden email]> wrote:

> Hi,
>
> Do you have ideas, how to find all those different combinations of integers
> (>0) that produce as a sum, a certain integer.
>
> i.e.: if that sum is
>
> 3, the possibilities are c(1,1,1), c(1,2), c(2,1)
> 4, the possibilities are
> c(1,1,1,1),c(1,1,2),c(1,2,1),c(2,1,1),c(2,2),c(1,3),c(3,1)
>
> etc.
>
> Best regards,
>
> Atte Tenkanen
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
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and provide commented, minimal, self-contained, reproducible code.
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Re: Same sum, different sets of integers

jholtman
In reply to this post by Atte Tenkanen
This is not the most efficient, but gets the idea across.  This is the
largest sum I can compute on my laptop with 16GB of memory.  If I try to
set N to 9, I run out of memory due to the size of the expand.grid.

> N <- 8  # value to add up to
> # create expand.grid for all combinations and convert to matrix
> x <- as.matrix(expand.grid(rep(list(0:(N - 1)), N)))
>
> # generate rowSums and determine which rows add to N
> z <- rowSums(x)
>
> # now extract those rows, sort and convert to strings to remove dups
> add2N <- x[z == N, ]
> strings <- apply(
+             t(apply(add2N, 1, sort))  # sort
+             , 1
+             , toString
+             )
>
> # remove dups
> strings <- strings[!duplicated(strings)]
>
> # remove leading zeros
> strings <- gsub("0, ", "", strings)
>
> # print out
> cat(strings, sep = '\n')
1, 7
2, 6
3, 5
4, 4
1, 1, 6
1, 2, 5
1, 3, 4
2, 2, 4
2, 3, 3
1, 1, 1, 5
1, 1, 2, 4
1, 1, 3, 3
1, 2, 2, 3
2, 2, 2, 2
1, 1, 1, 1, 4
1, 1, 1, 2, 3
1, 1, 2, 2, 2
1, 1, 1, 1, 1, 3
1, 1, 1, 1, 2, 2
1, 1, 1, 1, 1, 1, 2
1, 1, 1, 1, 1, 1, 1, 1



Jim Holtman
Data Munger Guru

What is the problem that you are trying to solve?
Tell me what you want to do, not how you want to do it.

On Wed, Apr 27, 2016 at 11:46 AM, Atte Tenkanen <[hidden email]> wrote:

> Hi,
>
> Do you have ideas, how to find all those different combinations of
> integers (>0) that produce as a sum, a certain integer.
>
> i.e.: if that sum is
>
> 3, the possibilities are c(1,1,1), c(1,2), c(2,1)
> 4, the possibilities are
> c(1,1,1,1),c(1,1,2),c(1,2,1),c(2,1,1),c(2,2),c(1,3),c(3,1)
>
> etc.
>
> Best regards,
>
> Atte Tenkanen
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

        [[alternative HTML version deleted]]

______________________________________________
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https://stat.ethz.ch/mailman/listinfo/r-help
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Re: Same sum, different sets of integers

plangfelder
I came up with this, using recursion. Short and should work for n
greater than 9 :)

Peter

sumsToN = function(n)
{
  if (n==1) return(1);
  out = lapply(1:(n-1), function(i) {
    s1 = sumsToN(n-i);
    lapply(s1, c, i)
  })
  c(n, unlist(out, recursive = FALSE));
}

> sumsToN(4)
[[1]]
[1] 4

[[2]]
[1] 3 1

[[3]]
[1] 2 1 1

[[4]]
[1] 1 1 1 1

[[5]]
[1] 1 2 1

[[6]]
[1] 2 2

[[7]]
[1] 1 1 2

[[8]]
[1] 1 3

> sumsToN(5)
[[1]]
[1] 5

[[2]]
[1] 4 1

[[3]]
[1] 3 1 1

[[4]]
[1] 2 1 1 1

[[5]]
[1] 1 1 1 1 1

[[6]]
[1] 1 2 1 1

[[7]]
[1] 2 2 1

[[8]]
[1] 1 1 2 1

[[9]]
[1] 1 3 1

[[10]]
[1] 3 2

[[11]]
[1] 2 1 2

[[12]]
[1] 1 1 1 2

[[13]]
[1] 1 2 2

[[14]]
[1] 2 3

[[15]]
[1] 1 1 3

[[16]]
[1] 1 4


On Wed, Apr 27, 2016 at 6:10 PM, jim holtman <[hidden email]> wrote:

> This is not the most efficient, but gets the idea across.  This is the
> largest sum I can compute on my laptop with 16GB of memory.  If I try to
> set N to 9, I run out of memory due to the size of the expand.grid.
>
>> N <- 8  # value to add up to
>> # create expand.grid for all combinations and convert to matrix
>> x <- as.matrix(expand.grid(rep(list(0:(N - 1)), N)))
>>
>> # generate rowSums and determine which rows add to N
>> z <- rowSums(x)
>>
>> # now extract those rows, sort and convert to strings to remove dups
>> add2N <- x[z == N, ]
>> strings <- apply(
> +             t(apply(add2N, 1, sort))  # sort
> +             , 1
> +             , toString
> +             )
>>
>> # remove dups
>> strings <- strings[!duplicated(strings)]
>>
>> # remove leading zeros
>> strings <- gsub("0, ", "", strings)
>>
>> # print out
>> cat(strings, sep = '\n')
> 1, 7
> 2, 6
> 3, 5
> 4, 4
> 1, 1, 6
> 1, 2, 5
> 1, 3, 4
> 2, 2, 4
> 2, 3, 3
> 1, 1, 1, 5
> 1, 1, 2, 4
> 1, 1, 3, 3
> 1, 2, 2, 3
> 2, 2, 2, 2
> 1, 1, 1, 1, 4
> 1, 1, 1, 2, 3
> 1, 1, 2, 2, 2
> 1, 1, 1, 1, 1, 3
> 1, 1, 1, 1, 2, 2
> 1, 1, 1, 1, 1, 1, 2
> 1, 1, 1, 1, 1, 1, 1, 1
>
>
>
> Jim Holtman
> Data Munger Guru
>
> What is the problem that you are trying to solve?
> Tell me what you want to do, not how you want to do it.
>
> On Wed, Apr 27, 2016 at 11:46 AM, Atte Tenkanen <[hidden email]> wrote:
>
>> Hi,
>>
>> Do you have ideas, how to find all those different combinations of
>> integers (>0) that produce as a sum, a certain integer.
>>
>> i.e.: if that sum is
>>
>> 3, the possibilities are c(1,1,1), c(1,2), c(2,1)
>> 4, the possibilities are
>> c(1,1,1,1),c(1,1,2),c(1,2,1),c(2,1,1),c(2,2),c(1,3),c(3,1)
>>
>> etc.
>>
>> Best regards,
>>
>> Atte Tenkanen
>>
>> ______________________________________________
>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Same sum, different sets of integers

Atte Tenkanen
Thanks for the suggestions, all of you!
I first began to think about using somehow permutations of the
gtools-package. I will continue utilizing Peter's solution.

My purpose is to divide basic musical rhythm units (whole note, half
note, quarter note etc durations) to meaningful entities in algorithmic
composition. I use R for that. Usually, there are - in the composition
algorithm - random number generators, which "composes" different
versions of music. Those RNG's (sample in R) can be - for their part -
conducted by using different constraints and probabilities. Here I draw
rhythms.

For example, if my quarter note (1/4) is 1024 ticks in MIDI format, I
may like to split it into quintuples, ie. five units, using ties
differently:

1024*c(1/5, 4/5), 1024*c(2/5, 3/5),... This way I can produce and output
rich and still usable rhythms to music notation software, keep the
rhythmic entities playable and readable over barlines.

Yours,

Atte

28.4.2016, 5.00, Peter Langfelder kirjoitti:

> I came up with this, using recursion. Short and should work for n
> greater than 9 :)
>
> Peter
>
> sumsToN = function(n)
> {
>    if (n==1) return(1);
>    out = lapply(1:(n-1), function(i) {
>      s1 = sumsToN(n-i);
>      lapply(s1, c, i)
>    })
>    c(n, unlist(out, recursive = FALSE));
> }
>
>> sumsToN(4)
> [[1]]
> [1] 4
>
> [[2]]
> [1] 3 1
>
> [[3]]
> [1] 2 1 1
>
> [[4]]
> [1] 1 1 1 1
>
> [[5]]
> [1] 1 2 1
>
> [[6]]
> [1] 2 2
>
> [[7]]
> [1] 1 1 2
>
> [[8]]
> [1] 1 3
>
>> sumsToN(5)
> [[1]]
> [1] 5
>
> [[2]]
> [1] 4 1
>
> [[3]]
> [1] 3 1 1
>
> [[4]]
> [1] 2 1 1 1
>
> [[5]]
> [1] 1 1 1 1 1
>
> [[6]]
> [1] 1 2 1 1
>
> [[7]]
> [1] 2 2 1
>
> [[8]]
> [1] 1 1 2 1
>
> [[9]]
> [1] 1 3 1
>
> [[10]]
> [1] 3 2
>
> [[11]]
> [1] 2 1 2
>
> [[12]]
> [1] 1 1 1 2
>
> [[13]]
> [1] 1 2 2
>
> [[14]]
> [1] 2 3
>
> [[15]]
> [1] 1 1 3
>
> [[16]]
> [1] 1 4
>
>
> On Wed, Apr 27, 2016 at 6:10 PM, jim holtman <[hidden email]> wrote:
>> This is not the most efficient, but gets the idea across.  This is the
>> largest sum I can compute on my laptop with 16GB of memory.  If I try to
>> set N to 9, I run out of memory due to the size of the expand.grid.
>>
>>> N <- 8  # value to add up to
>>> # create expand.grid for all combinations and convert to matrix
>>> x <- as.matrix(expand.grid(rep(list(0:(N - 1)), N)))
>>>
>>> # generate rowSums and determine which rows add to N
>>> z <- rowSums(x)
>>>
>>> # now extract those rows, sort and convert to strings to remove dups
>>> add2N <- x[z == N, ]
>>> strings <- apply(
>> +             t(apply(add2N, 1, sort))  # sort
>> +             , 1
>> +             , toString
>> +             )
>>> # remove dups
>>> strings <- strings[!duplicated(strings)]
>>>
>>> # remove leading zeros
>>> strings <- gsub("0, ", "", strings)
>>>
>>> # print out
>>> cat(strings, sep = '\n')
>> 1, 7
>> 2, 6
>> 3, 5
>> 4, 4
>> 1, 1, 6
>> 1, 2, 5
>> 1, 3, 4
>> 2, 2, 4
>> 2, 3, 3
>> 1, 1, 1, 5
>> 1, 1, 2, 4
>> 1, 1, 3, 3
>> 1, 2, 2, 3
>> 2, 2, 2, 2
>> 1, 1, 1, 1, 4
>> 1, 1, 1, 2, 3
>> 1, 1, 2, 2, 2
>> 1, 1, 1, 1, 1, 3
>> 1, 1, 1, 1, 2, 2
>> 1, 1, 1, 1, 1, 1, 2
>> 1, 1, 1, 1, 1, 1, 1, 1
>>
>>
>>
>> Jim Holtman
>> Data Munger Guru
>>
>> What is the problem that you are trying to solve?
>> Tell me what you want to do, not how you want to do it.
>>
>> On Wed, Apr 27, 2016 at 11:46 AM, Atte Tenkanen <[hidden email]> wrote:
>>
>>> Hi,
>>>
>>> Do you have ideas, how to find all those different combinations of
>>> integers (>0) that produce as a sum, a certain integer.
>>>
>>> i.e.: if that sum is
>>>
>>> 3, the possibilities are c(1,1,1), c(1,2), c(2,1)
>>> 4, the possibilities are
>>> c(1,1,1,1),c(1,1,2),c(1,2,1),c(2,1,1),c(2,2),c(1,3),c(3,1)
>>>
>>> etc.
>>>
>>> Best regards,
>>>
>>> Atte Tenkanen
>>>
>>> ______________________________________________
>>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>          [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.