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I have four (partially overlapping) groups of eight unique applicants that have applied for 20%, 30%, 40%, and 50% of the work I have to assign:
g20 <- c("a","b","c","d","e","f")
g30 <- c("a","b","c","d","e","f","g","h")
g40 <- c("c","d","e","f","g","h")
g50 <- c("e","f","g","h")
Because I can only award the work in these four increments and I have to choose no fewer than two people and no more than four, I have six scenarios for awarding 100% of the work:
For each scenario, I need to find all the possible combinations (without replacement) for awarding the work to the applicants in the corresponding groups.
I can easily enough accomplish this for the first scenario using t(combn(g50,2)) but I am unsure how to handle the other scenarios where I have to pull combinations from different vectors AND ensure an applicant is only selected only once in any given combination. The output needs to be the actual combinations, not just the number of combinations.
Using R, how do I do get these combinations pulling from four different groups and (using scenario 5 as an example) ensure that "cdef", "cedf", "cfed", "cfde" etc. are all treated as the same result?
Is this possible?
711
asked May 30 '26 12:05
Also creating all possible combinations like Jon Spring's solution but using data.table package and removing dupe applicant.
If your real-life dimensions are per OP, you can consider expanding to all possible combinations and remove rows where an applicant is duplicated:
library(data.table)
g20 <- c("a","b","c","d","e","f")
g30 <- c("a","b","c","d","e","f","g","h")
g40 <- c("c","d","e","f","g","h")
g50 <- c("e","f","g","h")
scen <- paste0("g", c(30, 30, 20, 20))
allcombi <- do.call(CJ, mget(scen))
setnames(allcombi, paste0("V", 1L:length(allcombi)))
#remove rows with applicants that are repeated in different columns
nodupe <- allcombi[
allcombi[, .I[anyDuplicated(unlist(.SD)) == 0L],
by=1:allcombi[,.N]]$V1]
#sort within columns with the same percentage of work
for(cols in split(names(nodupe), scen))
nodupe[, (cols) := sort(.SD), by=seq_len(nodupe[,.N]), .SDcols=cols]
#remove identical combinations
ans <- unique(nodupe)
setnames(ans, scen)[]
output:
g30 g30 g20 g20
1: a b c d
2: a b c e
3: a b c f
4: a b d e
5: a b d f
---
221: g h c e
222: g h c f
223: g h d e
224: g h d f
225: g h e f
Code & results from running for all 6 scenarios:
scenarios <- list(c(50,50),
c(50,30,20),
c(40,40,20),
c(40,30,30),
c(40,20,20,20),
c(30,30,20,20))
lapply(scenarios,
function(scen) {
scen <- paste0("g", scen)
allcombi <- do.call(CJ, mget(scen, envir=.GlobalEnv))
setnames(allcombi, paste0("V", 1L:length(allcombi)))
nodupe <- allcombi[
allcombi[, .I[anyDuplicated(unlist(.SD)) == 0L],
by=1:allcombi[,.N]]$V1]
for(cols in split(names(nodupe), scen))
nodupe[, (cols) := sort(.SD), by=seq_len(nodupe[,.N]), .SDcols=cols]
ans <- unique(nodupe)
setnames(ans, scen)[]
})
output:
[[1]]
g50 g50
1: e f
2: e g
3: e h
4: f g
5: f h
6: g h
[[2]]
g50 g30 g20
1: e a b
2: e a c
3: e a d
4: e a f
5: e b a
---
128: h g b
129: h g c
130: h g d
131: h g e
132: h g f
[[3]]
g40 g40 g20
1: c d a
2: c d b
3: c d e
4: c d f
5: c e a
6: c e b
7: c e d
8: c e f
9: c f a
10: c f b
11: c f d
12: c f e
13: c g a
14: c g b
15: c g d
16: c g e
17: c g f
18: c h a
19: c h b
20: c h d
21: c h e
22: c h f
23: d e a
24: d e b
25: d e c
26: d e f
27: d f a
28: d f b
29: d f c
30: d f e
31: d g a
32: d g b
33: d g c
34: d g e
35: d g f
36: d h a
37: d h b
38: d h c
39: d h e
40: d h f
41: e f a
42: e f b
43: e f c
44: e f d
45: e g a
46: e g b
47: e g c
48: e g d
49: e g f
50: e h a
51: e h b
52: e h c
53: e h d
54: e h f
55: f g a
56: f g b
57: f g c
58: f g d
59: f g e
60: f h a
61: f h b
62: f h c
63: f h d
64: f h e
65: g h a
66: g h b
67: g h c
68: g h d
69: g h e
70: g h f
g40 g40 g20
[[4]]
g40 g30 g30
1: c a b
2: c a d
3: c a e
4: c a f
5: c a g
---
122: h d f
123: h d g
124: h e f
125: h e g
126: h f g
[[5]]
g40 g20 g20 g20
1: c a b d
2: c a b e
3: c a b f
4: c a d e
5: c a d f
6: c a e f
7: c b d e
8: c b d f
9: c b e f
10: c d e f
11: d a b c
12: d a b e
13: d a b f
14: d a c e
15: d a c f
16: d a e f
17: d b c e
18: d b c f
19: d b e f
20: d c e f
21: e a b c
22: e a b d
23: e a b f
24: e a c d
25: e a c f
26: e a d f
27: e b c d
28: e b c f
29: e b d f
30: e c d f
31: f a b c
32: f a b d
33: f a b e
34: f a c d
35: f a c e
36: f a d e
37: f b c d
38: f b c e
39: f b d e
40: f c d e
41: g a b c
42: g a b d
43: g a b e
44: g a b f
45: g a c d
46: g a c e
47: g a c f
48: g a d e
49: g a d f
50: g a e f
51: g b c d
52: g b c e
53: g b c f
54: g b d e
55: g b d f
56: g b e f
57: g c d e
58: g c d f
59: g c e f
60: g d e f
61: h a b c
62: h a b d
63: h a b e
64: h a b f
65: h a c d
66: h a c e
67: h a c f
68: h a d e
69: h a d f
70: h a e f
71: h b c d
72: h b c e
73: h b c f
74: h b d e
75: h b d f
76: h b e f
77: h c d e
78: h c d f
79: h c e f
80: h d e f
g40 g20 g20 g20
[[6]]
g30 g30 g20 g20
1: a b c d
2: a b c e
3: a b c f
4: a b d e
5: a b d f
---
221: g h c e
222: g h c f
223: g h d e
224: g h d f
225: g h e f
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