What's the most efficient way of generating all possible combinations of skyrim (PC Game) potions?

Question

So each ingredient has 4 effects http://www.uesp.net/wiki/Skyrim:Ingredients

If I combine two ingredients. The potions will have the bonus effects of where the two s

Answer 1

Sounds like a job for everybody's favorite programming language, R!

library(XML)
tables <- readHTMLTable('http://www.uesp.net/wiki/Skyrim:Ingredients', 
    stringsAsFactors=FALSE)
potions <- tables[[1]]
twoway <- data.frame(t(combn(potions$Name,2)))
threeway <- data.frame(t(combn(potions$Name,3)))

BAM!

> head(twoway)
               X1                  X2
1 Abecean Longfin          Bear Claws
2 Abecean Longfin                 Bee
3 Abecean Longfin        Beehive Husk
4 Abecean Longfin      Bleeding Crown
5 Abecean Longfin         Blisterwort
6 Abecean Longfin Blue Butterfly Wing
> head(threeway)
               X1         X2                  X3
1 Abecean Longfin Bear Claws                 Bee
2 Abecean Longfin Bear Claws        Beehive Husk
3 Abecean Longfin Bear Claws      Bleeding Crown
4 Abecean Longfin Bear Claws         Blisterwort
5 Abecean Longfin Bear Claws Blue Butterfly Wing
6 Abecean Longfin Bear Claws       Blue Dartwing

Use the write.csv command to save the tables as csv files.

/Edit: To explain what I'm doing: The XML package contains the readHTMLTable function, which pulls all the html tables from a website as data.frames and saves them as a list. The first table in this list is the one we want. The combn function finds all the 2-way, 3-way, and n way combinations of potion names, and returns the result as a matrix. I use the t function to transpose this matrix, so each combination is one row, and then convert it to a data frame. This easily extends to combinations of n ingredients.

/Edit 2: I wrote a function to save the n-way table to a user-specified csv file. I also re-worked it a bit, because transposing huge matricies is computationally expensive. This version should allow you to calculate the 4-way table, although it takes a long time and I don't know if it's relevant to the game.

nway <- function(n, filepath, data=potions) {
    nway <- combn(data$Name, n, simplify = FALSE)
    nway <- do.call(rbind,nway)
    write.csv(nway,filepath, row.names=FALSE)
}
nway(4,'~/Desktop/4way.csv')

/Edit 3: Here's some code to find the actual working potions. It's not very efficient and can probably be greatly improved:

#Given an ingredient, lookup effects
findEffects <- function(Name) { #Given a name, lookup effects
    potions[potions$Name==Name,3:6]
}

#2-way potions
intersectTwoEffects <- function(x) {
    Effects1 <- findEffects(x[1])
    Effects2 <- findEffects(x[2])
    Effects <- unlist(intersect(Effects1,Effects2))
    Effects <- c(x[1],x[2],Effects)
    length(Effects) <- 6
    names(Effects) <- NULL
    c(Effects,sum(is.na(Effects)))

}
twoway <- lapply(twoway,intersectTwoEffects)
twoway <- do.call(rbind,twoway)
twoway <- twoway[twoway[,7]<4,-7] #remove combos with no effect
write.csv(twoway,'~/Desktop/twoway.csv',row.names=FALSE)

#3-way potions
intersectThreeEffects <- function(x) {
    Effects1 <- findEffects(x[1])
    Effects2 <- findEffects(x[2])
    Effects3 <- findEffects(x[3])
    Effects <- c(intersect(Effects1,Effects2),intersect(Effects1,Effects3),intersect(Effects2,Effects3))
    Effects <- unlist(unique(Effects))
    Effects <- c(x[1],x[2],x[3],Effects)
    length(Effects) <- 8
    names(Effects) <- NULL
    c(Effects,sum(is.na(Effects)))

}
threeway <- lapply(threeway,intersectThreeEffects)
threeway <- do.call(rbind,threeway)
threeway <- threeway[threeway[,9]<5,-9] #remove combos with no effect
write.csv(threeway,'~/Desktop/threeway.csv',row.names=FALSE)