###
Rewritten

I have a `data.table`

with different groups and objects within each group, where each row is an object. Each object has a `start`

and an `end`

value. I want to do the following:

- Create a new column containing all the numbers between the
`start`

and `end`

values.
- Group the
`data.table`

by group and get the unique numbers.
- Count the unique numbers for each group, accounting for overlapping numbers.

For example, for group `a`

the result should be:

```
group | (old cols) | numbers | unique_number_per_group | count_unique_numbers
"a" | ... | 3 4 5 6 7 8 9 | 3 4 5 6 7 8 9 10 11 15 16 17 18 19 20 | 15
```

To achieve the desired result, you can use the following code:

```
library(data.table)
# Create a sample data.table
dt <- data.table(
group = c("a", "a", "b", "b"),
start = c(3, 10, 5, 15),
end = c(9, 20, 8, 20)
)
# Step 1: Create a new column containing all the numbers between start and end values
dt[, numbers := list(seq(start, end)), by = group]
# Step 2: Group the data.table by group and get the unique numbers
dt[, unique_numbers := unique(unlist(numbers)), by = group]
# Step 3: Count the unique numbers for each group, accounting for overlapping numbers
dt[, count_unique_numbers := length(unique_numbers), by = group]
# Print the final result
dt
```

This code will generate the desired output, where the `numbers`

column contains all the numbers between the `start`

and `end`

values, the `unique_numbers`

column contains the unique numbers for each group, and the `count_unique_numbers`

column contains the count of unique numbers for each group.

Note: Make sure you have the `data.table`

package installed. If not, you can install it using `install.packages("data.table")`

.