holic - 1 year ago 67
R Question

# unique permutations of zero-one-vector in R

My problem is as follows:

Imagine we have a vector

`(1,1,1,...,0,0)`
of length
`n`
with
`k`
ones in the beginning. Think of this vector as of vector with realizations of some variables
`L1`
till
`Ln`
. What i need to calculate is

`sum over all unique permutations of (1,1,1,...,0,0) of Function(L1,...,Ln)`

I have searched for solutions of my problem and yes, there are some, which work as long as
`n`
isn't too big.

As long as
`n`
is under 30 my PC doesn't die and following idea works:

1) creating a data.frame of all unique permutations with a help of following code (found it here)

``````uniqueperm2 <- function(d) {
dat <- factor(d)
N <- length(dat)
n <- tabulate(dat)
ng <- length(n)
if(ng==1) return(d)
a <- N-c(0,cumsum(n))[-(ng+1)]
foo <- lapply(1:ng, function(i) matrix(combn(a[i],n[i]),nrow=n[i]))
out <- matrix(NA, nrow=N, ncol=prod(sapply(foo, ncol)))
xxx <- c(0,cumsum(sapply(foo, nrow)))
xxx <- cbind(xxx[-length(xxx)]+1, xxx[-1])
miss <- matrix(1:N,ncol=1)
for(i in seq_len(length(foo)-1)) {
l1 <- foo[[i]]
nn <- ncol(miss)
miss <- matrix(rep(miss, ncol(l1)), nrow=nrow(miss))
k <- (rep(0:(ncol(miss)-1), each=nrow(l1)))*nrow(miss) +
l1[,rep(1:ncol(l1), each=nn)]
out[xxx[i,1]:xxx[i,2],] <- matrix(miss[k], ncol=ncol(miss))
miss <- matrix(miss[-k], ncol=ncol(miss))
}
k <- length(foo)
out[xxx[k,1]:xxx[k,2],] <- miss
out <- out[rank(as.numeric(dat), ties="first"),]
foo <- cbind(as.vector(out), as.vector(col(out)))
out[foo] <- d
t(out)
}
``````

2) sum over components of this data.frame

`n`
is 100 and above. Good news for me are that i actually do not need whole data.frame in my RAM. An algorithm which would remember last permutation, use it to evaluate
`Funktion(L1,...,Ln)`
and compute next permutation and so on in a loop would be enough. Any help is appreciated.

EDIT
Hack-R asked for an example, here what i get

``````    > d <- c()
> d[1:25]=0
> d[25:50]=1
> d
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
> uniqueperm2(d)
Error: cannot allocate vector of size 905608.1 Gb
1: In vector("list", count) :
Reached total allocation of 8109Mb: see help(memory.size)
2: In vector("list", count) :
Reached total allocation of 8109Mb: see help(memory.size)
3: In vector("list", count) :
Reached total allocation of 8109Mb: see help(memory.size)
4: In vector("list", count) :
Reached total allocation of 8109Mb: see help(memory.size)
``````

Here's one way to walk the permutations. I still think there is a better way but haven't figured it out yet.

This function looks at an array of 1's an 0's and tries to move the right most 1 to the left if possible. (Basically thinking of the vector as a binary number and trying to find the next largest number with exactly `n` bits)

``````next_x <- function(x) {
i <- tail(which(diff(x)==1),1)
if (length(i)>0) {
x[c(i, i+1)]<-c(1,0)
x[(i+1):length(x)] <- sort(x[(i+1):length(x)])
} else {
stop("no more moves")
}
x
}
``````

You start out with `x` all to the right and you can iterate with

``````x <- c(0,0,0,0,1,1,1)
while(!all(x==c(1,1,1,0,0,0,0))) {
x <- next_x(x)
print(x)
}
``````
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