Question

I am trying to figure out how to reckon the number of combinations returned by combn function after exclusion of some selected combinations. Let's say, we have a vector c("var1","var2","var3","var4","var5") and I want to get all combinations of the elements of this one except these that consits of c("var4","var5"). Here is the code:

vector <- c("var1","var2","var3","var4","var5")
exclude <- matrix(c("var4","var5"),1,2)

for(i in 1:length(vector)){
  comb <- combn(vector,i)
  for(j in 1:ncol(comb)){
    newcomb <- c(comb[,j])
    if (any(as.logical("FALSE"),apply(exclude, 1, function(x) all(x %in% newcomb)))) {next}
      else {print(newcomb)}}
}

The number of combinations returned from combn function without any reduction is 31. It is reckoned as:

f <- function(nvars){
  a <- NULL
  for (i in 1:nvars){
    a[i] <- choose(nvars,i)}
  return(sum(a))}
f(5)

Any suggestions how to get the number of reduced combinations (for 5 variables and exclusion of combinations that contain "var4" and "var5" at same time, it should be 23). Thanks!

Answer 1

这将计算任何输入vector和exclude的组合数（它基于问题中的循环）...

sum(sapply(seq_along(vector),                   #sum for all combination lengths...
    function(i) sum(apply(combn(vector, i), 2,  #...the sum for all combinations...
        function(y) !any(apply(exclude, 1,      #...the value for each row of exclude...
            function(x) all(x %in% y)))))))     #...whether combn doesn't contain exclude row

[1] 71 #for the example you give

Answer 2

We loop through the sequence of vector, get the combn by specifying the 'm' as the sequence value, then check whether all the 'exclude' elements are there %in% the combination elements, negate (!), unlist the list and get the sum of logical elements

sum(unlist(lapply(seq_along(vector), function(i) combn(vector, i,
         FUN = function(x) !all(c(exclude) %in% x)))))
#[1] 23

Answer 3

我追求的解决方案之一：

f <- function(x,y){
  a <- NULL
  for (i in 1:x){
    a[i] <- choose(x,i) - choose(x-y,i-y)}
  return(sum(a))}
f(5,2)

@Andrew Gustar - 感谢您的建议！

我仍然需要为矩阵找到更通用的解决方案，其中要排除的变量（其中一些是不同的，其中一些不是）：

vector <- c("var1","var2","var3","var4","var5","var6","var7","var8")
exclude <- matrix(c(c("var3","var2"),c("var4","var3"),c("var5","var7")),3,2)).

Number of combs returned by combn reduced by some combs in R

3 个答案: