nested loops and debugging

Question

Objective: Elaborate a function, that returns an array of dimension 4x4. An example of the possible outcome of the function is:

All I have done:

matriz<-function(M){

M<-matrix(ncol=4,nrow=4);

M[1,]<-sample(LETTERS[1:4]);

M[2,]<-sample(LETTERS[1:4]);

for(i in 2:4){
    for(j in 1:4){
    j<-j

        if(j<=4)
        if(M[i,j]!= M[i-1,j]){
            j<-j+1
            }
        else{
            M[i,]<-sample(LETTERS[1:4])
            }

    }
    i<-i+1
    if(i<=4){
        M[i,]<-sample(LETTERS[1:4])
        j=1
        }
    else{print(M)}
 }
}

debug(matriz); matriz(M)

Answer 1

This seems to work. It generates a list of all possible combinations, then deletes any that match previously selected rows, leaving just one at the end.

matriz <- function(n){
  combs <- as.matrix(expand.grid(rep(list(LETTERS[1:n]),n)))
  combs <- combs[apply(combs,1,function(r) all(LETTERS[1:n] %in% r)),]
  mat <- matrix(NA,nrow=n,ncol=n)
  for(i in 1:(n-1)){
    mat[i,] <- combs[sample(1:nrow(combs),1),]
    combs <- combs[!apply(combs,1,function(r) any(r == mat[i,])),]
  }
  mat[n,] <- combs
  return(mat)
  }

> matriz(5)
     [,1] [,2] [,3] [,4] [,5]
[1,] "B"  "D"  "A"  "E"  "C" 
[2,] "E"  "C"  "D"  "B"  "A" 
[3,] "D"  "A"  "B"  "C"  "E" 
[4,] "A"  "E"  "C"  "D"  "B" 
[5,] "C"  "B"  "E"  "A"  "D" 

> matriz(5)
     [,1] [,2] [,3] [,4] [,5]
[1,] "D"  "C"  "E"  "B"  "A" 
[2,] "E"  "A"  "C"  "D"  "B" 
[3,] "A"  "D"  "B"  "C"  "E" 
[4,] "B"  "E"  "D"  "A"  "C" 
[5,] "C"  "B"  "A"  "E"  "D" 

A slightly faster version using the combinat package would be

library(combinat)
matriz <- function(n){
  combs <- do.call(rbind,permn(LETTERS[1:n]))
  mat <- matrix(NA,nrow=n,ncol=n)
  #rest of function as above...

Both of these can be quite slow for n>10 or so. However, if you have generated one valid square m, then all others will be permutations m[sample(nrow(m)),sample(ncol(m))] so this might be a faster approach if you are doing lots of them.