RobinvG RobinvG - 2 months ago 6
R Question

All possible ways to split n over k groups - R

I am stuck in a mathematical problem. I would like to make a function that outputs all the ways an integer "n" can be divide into "k" groups in such a way that in each group "k" is at least 1 (k >= 1).

The function could look something like:

n_ways <- function(n,k) {...}


I would like a dataFrame as an output. So for: n_ways(5,3)

A B C
1 3 1 1
2 1 3 1
3 1 1 3
4 2 2 1
5 2 1 2
6 1 2 2


The order in which the solutions are presented in the dataFrame is not important.

I looked for solutions like here and in other languages like here and here. Unfortunately I am not that good to make a function that suits my problem based on this, but hopefully you are.

Thanks a lot in advance!

Answer

You can use the partitions package:

library(partitions)
t(compositions(5,3,FALSE))
#[1,] 3 1 1
#[2,] 2 2 1
#[3,] 1 3 1
#[4,] 2 1 2
#[5,] 1 2 2
#[6,] 1 1 3

From the respective help file

Function compositions() returns all 2^(n-1) ways of partitioning an integer; thus 4+1+1 is distinct from 1+4+1 or 1+1+4.

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