R: change cell value by comparing to cell above

I have the following dataframe

ID year level
1  2000  NA
1  2001  3
1  2002  3
1  2003  2
1  2004  1
2  2000  1
2  2001  3
2  2002  3
2  2003  3
2  2004  3

I want to update each value in "level" column by ID based on the previous one if the previous one is smaller.

the dataframe should look like this

ID year level
1  2000  NA
1  2001  3
1  2002  3
1  2003  2
1  2004  1
2  2000  1
2  2001  1
2  2002  1
2  2003  1
2  2004  1

I tried using shift from data table but it only changes one cell.
I got this result

ID year level
1  2000  NA
1  2001  3
1  2002  3
1  2003  2
1  2004  1
2  2000  1
2  2001  1
2  2002  3
2  2003  3
2  2004  3

>Solution :

You can use

df$level <- Reduce(function(...) min(..., na.rm = T), df$level, accumulate = T)

to obtain your desired result:

ID  year level
  1 2000    NA
  1 2001     3
  1 2002     3
  1 2003     2
  1 2004     1
  2 2000     1
  2 2001     1
  2 2002     1
  2 2003     1
  2 2004     1