How to create a random matching between the rows of two data.tables (or data.frames)

Question

For this example, I'll use the data.table package.

Suppose you have a table of coaches

coaches <- data.table(CoachID=c(1,2,3), CoachName=c("Bob","Sue","John"), NumPlayers=c(2,3,0))
coaches
   CoachID CoachName NumPlayers
1:       1       Bob          2
2:       2       Sue          3
3:       3      John          0

and a table of players

players <- data.table(PlayerID=c(1,2,3,4,5,6), PlayerName=c("Abe","Bart","Chad","Dalton","Egor","Frank"))
players
   PlayerID PlayerName
1:        1        Abe
2:        2       Bart
3:        3       Chad
4:        4     Dalton
5:        5       Egor
6:        6      Frank

You want to match each coach with a set of players such that

• The number of players tied to each coach is defined by the NumPlayers field
• No two coaches are tied to the same player
• Players and coaches are matched randomly

How do you this?

exampleResult <- data.table(CoachID=c(1,1,2,2,2,3), PlayerID=c(3,1,2,5,6,NA))
exampleResult

   CoachID PlayerID
1:       1        3
2:       1        1
3:       2        2
4:       2        5
5:       2        6
6:       3       NA

Answer 1

You could sample without replacement from the player IDs, grabbing the total number of players you need:

set.seed(144)
(selections <- sample(players$PlayerID, sum(coaches$NumPlayers)))
# [1] 1 4 3 2 6

Each player will have equal probability of being included in selections, and the ordering of that vector is random. Therefore you can just assign these players to each coaching slot:

data.frame(CoachID=rep(coaches$CoachID, coaches$NumPlayers),
           PlayerID=selections)
#   CoachID PlayerID
# 1       1        1
# 2       1        4
# 3       2        3
# 4       2        2
# 5       2        6

If you wanted to have an NA value for any coaches with no player selections, you could do something like:

rbind(data.frame(CoachID=rep(coaches$CoachID, coaches$NumPlayers),
                 PlayerID=selections),
      data.frame(CoachID=coaches$CoachID[coaches$NumPlayers==0],
                 PlayerID=rep(NA, sum(coaches$NumPlayers==0))))
#   CoachID PlayerID
# 1       1        1
# 2       1        4
# 3       2        3
# 4       2        2
# 5       2        6
# 6       3       NA

Answer 2

Get demand and supply on each side, so to speak:

demand <- with(coaches,rep(CoachID,NumPlayers))
supply <- players$PlayerID

Then I'd do...

randmatch <- function(demand,supply){
  n_demand  <- length(demand)
  n_supply  <- length(supply)
  n_matches <- min(n_demand,n_supply)

  if (n_demand >= n_supply) 
    data.frame(d=sample(demand,n_matches),s=supply)
  else 
    data.frame(d=demand,s=sample(supply,n_matches))
}

Examples:

set.seed(1)
randmatch(demand,supply)    # some players unmatched, OP's example
randmatch(rep(1:3,1:3),1:4) # some coaches unmatched 

I'm not sure if this is a case the OP wanted to cover, though.

---

For the OP's desired output...

m <- randmatch(demand,supply)
merge(m,coaches,by.x="d",by.y="CoachID",all=TRUE)
#   d  s CoachName NumPlayers
# 1 1  2       Bob          2
# 2 1  6       Bob          2
# 3 2  3       Sue          3
# 4 2  4       Sue          3
# 5 2  1       Sue          3
# 6 3 NA      John          0

Similarly...

merge(m,players,by.x="s",by.y="PlayerID",all=TRUE)
#   s  d PlayerName
# 1 1  2        Abe
# 2 2  1       Bart
# 3 3  2       Chad
# 4 4  2     Dalton
# 5 5 NA       Egor
# 6 6  1      Frank