I have the following data frame:
> test = data.frame(A = sample(1:5, 10, replace = T)) %>% arrange(A)
> test
   A
1  1
2  1
3  1
4  2
5  2
6  2
7  2
8  4
9  4
10 5
I now want every row to have an ID that is only incremented when the value of A changes. This is what I have tried:
> test = test %>% mutate(id = as.numeric(rownames(test))) %>% group_by(A) %>% mutate(id = min(id))
> test
       A    id
   (int) (dbl)
1      1     1
2      1     1
3      1     1
4      2     4
5      2     4
6      2     4
7      2     4
8      4     8
9      4     8
10     5    10
However, I would like to get the following:
       A    id
   (int) (dbl)
1      1     1
2      1     1
3      1     1
4      2     2
5      2     2
6      2     2
7      2     2
8      4     3
9      4     3
10     5     4
                library(dplyr)
test %>% mutate(id = dense_rank(A))
                        One compact option would be using data.table.  Convert the 'data.frame' to 'data.table' (setDT(test)), grouped by 'A', we assign (:=) .GRP as the new 'id' column.  The .GRP will be a sequence of values for each unique value in 'A'.
library(data.table)
setDT(test)[, id:=.GRP, A]
In case the value of 'A' changes like 3, 3, 4, 3 and we want 1, 1, 2, 3 forthe 'id'
setDT(test)[, id:= rleid(A)]
Or we convert 'A' to factor class and then coerce it back to numeric/integer 
library(dplyr)
test %>%
    mutate(id = as.integer(factor(A)))
Or we can match 'A' with the unique values in 'A'.
test %>%
     mutate(id = match(A, unique(A)))
Or from the dplyr version > 0.4.0, we can use group_indices (it is in the dupe link)
test %>%
      mutate(id=group_indices_(test, .dots= "A"))
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