Take the first unique value form a function - r

Question

This is my function:
g <- function(x,y){
x <- (x-y):x
y <- 1:30 # ------> (y is always fixed 1:30)
z<- outer(x,y,fv) # ---->(fv is a previous function)
s <- colSums(z)
which(s==max(s),arr.ind=T)
}
It tells me the position of the max value in s. I basically have a problem in choosing y because given a small y, the max(s) appears more than once in s. For example:
#given x=53
> g(53,1)
[1] 13 16 20 22 25 26 27
> g(53,2)
[1] 20 25 26
> g(53,3)
[1] 20 25 26
> g(53,4)
[1] 20 25 26
> g(53,5)
[1] 20 25
> g(53,6)
[1] 25 -----> This is the only result i would like from my function (right y=6)
Another example:
# given x=71
> g(71,1)
[1] 7 9 14
> g(71,2)
[1] 7 14
> g(71,3)
[1] 14 -----> my desired result (right y=3)
Therefore, i would like a function resulting in the first unique solution given y as small as possible ( ex: g(53)=25 , g(71)=14, ...). Any help? Thanks
This is a simplify example. I hope to be more clear in questioning:
#The idea is the same:
n <- 1:9
e <- rep(nn,500)
p<- sample(e) # --->(Need to sample in order to have more max later (mixed matrix)
mat <- matrix(p,90)
g <- function(x,y){
x <- (x-y):x
k <- rowSums(mat[,x])
which(k==max(k), arr.ind=T)
}
#In my sample matrix :
k <- rowSums(mat[,44:45])
which(k==max(k), arr.ind=T)
[1] 44 71 90
#In fact
g(45,1)
[1] 44 71 90 # ---> more than one solution
g(45,2)
[1] 90 # ----> I would like to pick up this value wich is the first unique solution given x=45
Therefore, i would like a function resulting in the first unique solution for y as small as possible given x ( in this new ex: g(45)=90... ).

Answer 1

I got it. It is a bit long but i think right.
Taking into consideration the second simplify example:
g <- function(x,y){
x <- (x-y):x
k <- rowSums(mat[,x])
q <- which(k==max(k), arr.ind=T)
length(q)
}
gv <- Vectorize(g)
l <- function(x){
y<- 1:30 # <- (until 30 to be sure)
z<- outer(x,y,gv)
y <- which.min(z) # <- (min is surely length=1 and which.min takes the first)
x <- (x-y):x
k <- rowSums(mat[,x])
q <- which(k==max(k), arr.ind=T)
q
}
l(45)
[1] 90

Answer 2

It seems like you could just do this with a recursive function. Consider the following:
set.seed(42)
n = 1:9
e = rep(n, 500)
p = sample(e)
mat = matrix(p, 90)
g <- function(x, y=1) {
xv <- (x-y):x
k <- rowSums(mat[, xv])
i <- which(k == max(k), arr.ind=T)
n <- length(i)
if (n == 1) {
return(y) # want to know the min y that solves the problem, right?
} else {
y <- y + 1 # increase y by 1
g(x,y) # run our function again with a new value of y
}
}
You should now be able to run g(45) and get 1 as the result, since that is the value of y that solves the problem, and g(33) to get 2.