Creating groups of equal sum in R - r

Question

I am trying to group a column of my data.frame/data.table into three groups, all with equal sums.
The data is first ordered from smallest to largest, such that group one would be made up of a large number of rows with small values, and group three would have a small number of rows with large values. This is accomplished in spirit with:
test <- data.frame(x = as.numeric(1:100000))
store <- 0
total <- sum(test$x)
for(i in 1:100000){
store <- store + test$x[i]
if(store < total/3){
test$y[i] <- 1
} else {
if(store < 2*total/3){
test$y[i] <- 2
} else {
test$y[i] <- 3
}
}
}
While successful, I feel like there must be a better way (and maybe a very obvious solution that I am missing).
I never like resorting to loops, especially with nested ifs, when a vectorized approach is available - with even 100,000+ records this code becomes quite slow
This method would become impossibly complex to code to a larger number of groups (not necessarily the looping, but the ifs)
Requires pre-ordering of the column. Might not be able to get around this one.
As a nuance (not that it makes a difference) but the data to be summed would not always (or ever) be consecutive integers.

Answer 1

Maybe with cumsum:
test$z <- cumsum(test$x) %/% (ceiling(sum(test$x) / 3)) + 1

Answer 2

This is more or less a bin-packing problem.
Use the binPack function from the BBmisc package:
library(BBmisc)
test$bins <- binPack(test$x, sum(test$x)/3+1)
The sums of the 3 bins are nearly identical:
tapply(test$x, test$bins, sum)
1 2 3
1666683334 1666683334 1666683332

Answer 3

I thought that the cumsum/modulo division approach was very elegant, but it does retrun a somewhat irregular allocation:
> tapply(test$x, test$z, sum)
1 2 3
1666636245 1666684180 1666729575
> sum(test)/3
[1] 1666683333
So I though I would first create a random permutation and offer something similar:
test$x <- sample(test$x)
test$z2 <- cumsum(test$x)[ findInterval(cumsum(test$x),
c(0, 1666683333*(1:2), sum(test$x)+1))]
> tapply(test$x, test$z2, sum)
91099 116379 129539
1666676164 1666686837 1666686999
This also achieves a more even distribution of counts:
> table(test$z2)
91099 116379 129539
33245 33235 33520
> table(test$z)
1 2 3
57734 23915 18351
I must admit to puzzlement regarding the naming of the entries in z2.

Answer 4

Or you can just cut on the cumsum
test$z <- cut(cumsum(test$x), breaks = 3, labels = 1:3)
or use ggplot2::cut_interval instead of cut:
test$z <- cut_interval(cumsum(test$x), n = 3, labels = 1:3)

Answer 5

You can use fold() from groupdata2 and get an almost equal number of elements per group:
# Create data frame
test <- data.frame(x = as.numeric(1:100000))
# Use fold() to create 3 numerically balanced groups
test <- groupdata2::fold(k = 3, num_col = "x")
# Watch first 10 rows
head(test, 10)
## # A tibble: 10 x 2
## # Groups: .folds [3]
## x .folds
## <dbl> <fct>
## 1 1 1
## 2 2 3
## 3 3 2
## 4 4 1
## 5 5 2
## 6 6 2
## 7 7 1
## 8 8 3
## 9 9 2
## 10 10 3
# Check the sum and number of elements per group
test %>%
dplyr::group_by(.folds) %>%
dplyr::summarize(sum_ = sum(x),
n_members = dplyr::n())
## # A tibble: 3 x 3
## .folds sum_ n_members
## <fct> <dbl> <int>
## 1 1 1666690952 33333
## 2 2 1666716667 33334
## 3 3 1666642381 33333