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copied!<p>Here's a function I've written in R, which currently finds its (unexported) home in the <a href="http://r-forge.r-project.org/projects/lspm" rel="nofollow">LSPM</a> package. You give it the total number of items <code>n</code>, the number of items to select <code>r</code>, and the index of the combination you want <code>i</code>; it returns the values in <code>1:n</code> corresponding to combination <code>i</code>.</p> <pre><code>".combinadic" <- function(n, r, i) { # http://msdn.microsoft.com/en-us/library/aa289166(VS.71).aspx # http://en.wikipedia.org/wiki/Combinadic if(i < 1 | i > choose(n,r)) stop("'i' must be 0 < i <= n!/(n-r)!") largestV <- function(n, r, i) { #v <- n-1 v <- n # Adjusted for one-based indexing #while(choose(v,r) > i) v <- v-1 while(choose(v,r) >= i) v <- v-1 # Adjusted for one-based indexing return(v) } res <- rep(NA,r) for(j in 1:r) { res[j] <- largestV(n,r,i) i <- i-choose(res[j],r) n <- res[j] r <- r-1 } res <- res + 1 return(res) } </code></pre> <p>It allows you to generate each combination based on the value of the lexicographic index:</p> <pre><code>> .combinadic(1344, 3, 1) [1] 3 2 1 > .combinadic(1344, 3, 2) [1] 4 2 1 > .combinadic(1344, 3, 403716544) [1] 1344 1343 1342 </code></pre> <p>So you just need to loop over 1:403716544 and append the results to a file. It may take awhile, but it's at least feasible (see Dirk's answer). You also may need to do it in several loops, since the vector <code>1:403716544</code> will not fit in memory on my machine.</p> <p>Or you could just port the R code to C/C++ and do the looping / writing there, since it would be <em>a lot</em> faster.</p>

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