R filling matrix element from edge

Question

I have a problem with making matrix

The problem has this condition: if I get size of matrix like n by m, i should return matrix that is filled with integer from 1 to n*m.

fill_matrix = function(n,m){
  #i want to fill but don't know how.......
  return(mat)
}
 > fill_matrix(5,5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    1   16   15   14   13
[2,]    2   17   24   23   12
[3,]    3   18   25   22   11
[4,]    4   19   20   21   10
[5,]    5    6    7    8    9

at first time, it seems possible by using direction_change_vector(ex, down : i+1, right:j+1....) or recursion, but i can't get exact result.

If somebody has good idea, plz let me know......

I'm, so frustrated with this problem.

Thank you.

Answer 1

I think the problem in your question is looking for a spiral matrix. It has various implementation ways. Here is one iteration-based approach to make such a spiral matrix as you requested

Code

# n and m deonte matrix row and column numbers, respectively
SpiralMatrix <- function(n, m) {
    mat <- matrix(NA, n, m)
    N <- m*n
    u <- l <- 1
    d <- n
    r <- m
    idx <- 1
    while (u <= d && l <= r) {
        # up to down
        for (i in u:d) {
            mat[i, l] <- idx
            if (idx == N) {
                return(mat)
            }
            idx <- idx + 1
        }
        l <- l + 1
        # left to right
        for (i in l:r) {
            mat[d, i] <- idx
            if (idx == N) {
                return(mat)
            }
            idx <- idx + 1
        }
        d <- d - 1
        # down to up
        for (i in d:u) {
            mat[i, r] <- idx
            if (idx == N) {
                return(mat)
            }
            idx <- idx + 1
        }
        r <- r - 1
        # right to left
        for (i in r:l) {
            mat[u, i] <- idx
            if (idx == N) {
                return(mat)
            }
            idx <- idx + 1
        }
        u <- u + 1
    }
}

Output Examples

> SpiralMatrix(3, 4)
     [,1] [,2] [,3] [,4]
[1,]    1   10    9    8
[2,]    2   11   12    7
[3,]    3    4    5    6

> SpiralMatrix(5, 3)
     [,1] [,2] [,3]
[1,]    1   12   11
[2,]    2   13   10
[3,]    3   14    9
[4,]    4   15    8
[5,]    5    6    7

> SpiralMatrix(4, 4)
     [,1] [,2] [,3] [,4]
[1,]    1   12   11   10
[2,]    2   13   16    9
[3,]    3   14   15    8
[4,]    4    5    6    7