所有将k个组拆分为k个组的方法-R [英] All possible ways to split n over k groups - R

问题描述

我陷入了数学难题.我想制作一个函数，以所有方式将整数"n"划分为"k"个组，这样每个组中的"k"至少为1(k> = 1).

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).

该函数可能类似于:

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

我想要一个dataFrame作为输出.因此适用于: n_ways(5,3)

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

dataFrame中解决方案的显示顺序并不重要.

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

我正在寻找类似此处和

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.

非常感谢！

推荐答案

您可以使用partitions软件包:

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

从相应的帮助文件中

函数composition()返回所有2 ^(n-1)种对整数进行分区的方式；因此4 + 1 + 1不同于1 + 4 + 1或1 + 1 + 4.

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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