# The Knapsack Problem

July 10, 2009
By

(This article was first published on CYBAEA Data and Analysis, and kindly contributed to R-bloggers)

David posts a question about how to solve this knapsack problem using the R statistical computing and analysis platform. My reply in the comments seems to have disappeared for a while so here is my proposed solution. See David’s blog for my earlier proposed solution with a very common error.

## http://blog.revolution-computing.com/2009/07/because-its-friday-the-knapsack-problem.html
appetizer.solution <- local (
function (target) {
app <- c(2.15, 2.75, 3.35, 3.55, 4.20, 5.80)
r <- 2L
repeat {
c <- gtools::combinations(length(app), r=r, v=app, repeats.allowed=TRUE)
s <- rowSums(c)
if ( all(s > target) ) {
print("No solution found")
break
}
x <- which( abs(s-target) < 1e-4 )
if ( length(x) > 0L ) {
cat("Solution found: ", c[x,], "\n")
break
}
r <- r + 1L
}
})

appetizer.solution(15.05)
# Solution found:  2.15 3.55 3.55 5.8

Brute force works, it just doesn’t scale well. (Note that 7×2.15 is another solution.)

# You may also like these posts:

1. We have a mild obsession with employee productivity and how that declines as companies get bigger. We have previously found that when you treble the number of workers, you halve their individual productivity which is mildly scary. We revisit the analysis …

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...