CODEWITHSUNDEEP
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Evans Otieno
Evans Otieno

Reputation: 309

Combinations and Permutations in R

I have a very big data frame but for the sake of this question let's consider a subset of it which follows;

i j k l m n o p q
1 1 1 1 1 1 3 4 4
1 1 1 1 1 1 4 3 4
1 1 1 1 1 1 4 4 3
1 1 1 1 1 2 2 4 4
1 1 1 1 1 2 3 3 4
1 1 1 1 1 2 3 4 3

In the above data frame values that are in the rows can be arranged in a particular number of ways; for example, let's consider the first row which is (1,1,1,1 1,1,3,4,4). Any assistance leading in computing this number of ways in R will be highly appreciated.

Upvotes: 1

Views: 361

Answers (1)

josliber
josliber

Reputation: 44340

You can calculate the number of unique permutations of each row with:

apply(dat, 1, function(x) factorial(length(x)) / prod(factorial(table(x))))
# [1]  252  252  252  756 1512 1512

If all elements of a row of length n were unique there would be n! (n factorial) permutations. However, if there are k1, k2, ..., kj total copies of each of the j unique elements, then we can reverse the overcounting of duplicates by dividing by k1! * k2! * ... * kj!. There are more details about multinomial coefficients here.

If two rows have identical elements (possibly in a different ordering) then all their permutations will also be identical. We can take this into account by checking for duplicate ordered rows:

apply(dat, 1, function(x) factorial(length(x)) / prod(factorial(table(x)))) *
  !duplicated(t(apply(dat, 1, sort)))
# [1]  252    0    0  756 1512    0

Upvotes: 5

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