Project Euler Problem #11

Problem 11 on Project Euler involves calculating the maximum product of adjacent numbers in any direction in a 20×20 matrix.

The solution below takes advantage of the symmetry of calculations to cut down on unnecessary loop operations:

problem11 < - function() {
    numbers <- scan("problem11.dat")
        m <- matrix(as.numeric(numbers), 20, byrow=TRUE)
        maxprd <- 0
        N <- 20; n <- 4
        prd1 <- 0; prd2 <- 0; prd3 <- 0
        dims <- dim(m)
        a <- (n-1)
        x <- c(0:a)
        for (i in 1:(dims[1])) {
            for (j in 1:(dims[2])) {
                prd1 <- ifelse(j <= N-a, prod(m[i,j+x]), 0) # row prod
                    prd2 <- ifelse(i <= N-a, prod(m[i+x,j]), 0) # column prod
# lower right diagonal
                    prd3 <- ifelse(i <= N-a && j <= N-a, prod(diag(m[i:(i+a),j:(j+a)])),0)
# lower left diagonal
                    prd4 <- ifelse(i <= N-a && j > a, prod(diag(m[i:(i+a),j:(j-a)])), 0)
                    maxprd < - max(prd1,prd2,prd3,prd4,maxprd)
            }
        }
    maxprd
}