R - matching values in a dataframe column to another dataframes row names - r

Question

I think this is a fairly challenging data manipulation problem in R, and have struggled constructing a function that can achieve this. The context is organizing basketball players who play different positions into a lineup together, subject to what position each player plays. For some clarity, here is an example of the dataframe I am working with, in two different forms:
dput(my_df)
structure(list(Name = c("C.J. McCollum", "DeMar DeRozan", "Jimmy Butler",
"Jonas Valanciunas", "Kevin Durant", "Markieff Morris", "Pascal Siakam",
"Pau Gasol"), Pos1 = c("PG", "SG", "SG", "C", "SF", "SF", "PF",
"C"), Pos2 = c("SG", "", "SF", "", "PF", "PF", "", "")), .Names = c("Name",
"Pos1", "Pos2"), class = "data.frame", row.names = c(18L, 33L,
62L, 68L, 78L, 92L, 106L, 111L))
my_df
Name Pos1 Pos2
18 C.J. McCollum PG SG
33 DeMar DeRozan SG
62 Jimmy Butler SG SF
68 Jonas Valanciunas C
78 Kevin Durant SF PF
92 Markieff Morris SF PF
106 Pascal Siakam PF
111 Pau Gasol C
dput(my_df2)
structure(list(Name = c("C.J. McCollum", "DeMar DeRozan", "Jimmy Butler",
"Jonas Valanciunas", "Kevin Durant", "Markieff Morris", "Pascal Siakam",
"Pau Gasol"), Pos1 = c("PG", "SG", "SG", "C", "SF", "SF", "PF",
"C"), Pos2 = c("SG", "", "SF", "", "PF", "PF", "", ""), PG = c(1,
0, 0, 0, 0, 0, 0, 0), SG = c(1, 1, 1, 0, 0, 0, 0, 0), SF = c(0,
0, 1, 0, 1, 1, 0, 0), PF = c(0, 0, 0, 0, 1, 1, 1, 0), C = c(0,
0, 0, 1, 0, 0, 0, 1), BackupG = c(1, 1, 1, 0, 0, 0, 0, 0), BackupF = c(0,
0, 1, 0, 1, 1, 1, 0), Man8 = c(1, 1, 1, 1, 1, 1, 1, 1)), .Names = c("Name",
"Pos1", "Pos2", "PG", "SG", "SF", "PF", "C", "BackupG", "BackupF",
"Man8"), row.names = c(18L, 33L, 62L, 68L, 78L, 92L, 106L, 111L
), class = "data.frame")
my_df2
Name Pos1 Pos2 PG SG SF PF C BackupG BackupF Man8
18 C.J. McCollum PG SG 1 1 0 0 0 1 0 1
33 DeMar DeRozan SG 0 1 0 0 0 1 0 1
62 Jimmy Butler SG SF 0 1 1 0 0 1 1 1
68 Jonas Valanciunas C 0 0 0 0 1 0 0 1
78 Kevin Durant SF PF 0 0 1 1 0 0 1 1
92 Markieff Morris SF PF 0 0 1 1 0 0 1 1
106 Pascal Siakam PF 0 0 0 1 0 0 1 1
111 Pau Gasol C 0 0 0 0 1 0 0 1
In a basketball lineup, we want 1 player set for each of the 5 positions in basketball (PG, SG, PF, SF, C), we also want 1 backup guard (a PG or SG is a guard), 1 backup forward (a PF or FS is a forward), and an 8th player who can play any position. With this group of 8 players, we could construct the lineup in this way:
Name
PG C.J. McCollum
SG DeMar DeRozan
PF Kevin Durant
SF Markieff Morris
C Pau Gasol
Backup G Jimmy Butler
Backup F Pascal Siakam
8th Man Jonas Valanciunas
Ofcourse there is some flexibility with this (Kevin Durant and Markieff Morris could have been switched, in fact theres several players who could have switched spots in the 2nd dataframe). I would like to be able to organize my_df into this 2nd dataframes format in a fairly quick matter, something that takes the Pos1 and Pos2 columns from my_df, is able to check the rownames of the 2nd dataframe, and then fill in the player names.
There is a puzzle aspect to this however. Of note is that, not all players have a second position, but those players who do have a second position can be listed at either of the two positions. (for example, Jimmy Butler can be set as a SG, a SF, a Backup G, a backup F, or the 8th man, whereas Pau Gasol can only be set as a C, or as the 8th man). Additionally, while C.J. McCollum is listed as a PG and SG, he is the only player in my_df who is listed as a PG, and therefore must go in the PG row of the second dataframe.
Any thoughts are appreciated with this! I can provide more context if needed.
(edit: potentially editing my_df, adding Pos3, Pos4, Pos5 columns for whether a player can be a backup G, backup F, or 8th Man, may help as well, and is something I am currently working with).
Edit - see Simplify this grid such that each row and column has 1 value for a revised version of my question, which is a simpler problem to solve but will give me a solution to this question!

Answer 1

This approach is guaranteed to return a result if there is one, in fact it will return all viable combinations.
st<-as.matrix(my_df2[4:dim(my_df2)[2]]) # Make a numeric matrix
## allCombinationsAux may not be necessary if you are using a combinatorics library
allCombinationsAux<-function(z,nreg,x){
if(sum(nreg)>1){
innerLoop<-do.call(rbind,lapply(x[nreg&(z!=x)], test1,nreg&(z!=x),x))
ret<-cbind(z,innerLoop )
}
else{
ret<-x[nreg]
}
ret
}
## Find all the possible row combinations for the matrix
combs<-do.call(rbind,lapply(x,function(y) allCombinationsAux(y,y!=x,x)))
## Identify which combinations are valid
inds<-which(apply(combs,1,function(x) sum(diag(st[x,]))==8))
## Select valid matricies
validChoices<-lapply(inds,function(x) st[combs[x,],])
Make a matrix out of my_df2
Find all possible matrix substitutions
Iterate through all possible matrices testing if the diags are all 1
Select those matrices that are valid
To get the output to look like your example you can run
validChoices<-lapply(inds,function(x) {
matr<-st[combs[x,],]
retVal<-data.frame(Name=my_df2[combs[x,],"Name"])
rownames(retVal)<-colnames(matr)
retVal
})