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In R, is there a way to get the time difference between two times in two different columns using lag, but ignoring all null values?

I have a dataframe that looks like this:

a<-data.frame(Time = c("Time1",
                   "Time2",
                   "Time3",
                   "Time4",
                   "Time5",
                   "Time6"),
          Start = c("2018-03-17 08:38:00",
                    NA,
                    NA,
                    NA,
                    NA,
                    NA),
          End = c(NA,
                  NA,
                  NA,
                  NA,
                  NA,
                  "2018-03-17 14:31:00"))

I am trying to add another column with the time difference between the "End" time and the "Start" time.

I've tried to use difftime(End, lag(Start), units = "mins"). But I can't seem to figure out how to ignore the null values to use the last non-null value in "Start".

This is how I expect the result to look:

b<-data.frame(Time = c("Time1",
                   "Time2",
                   "Time3",
                   "Time4",
                   "Time5",
                   "Time6"),
          Start = c("2018-03-17 08:38:00",
                    NA,
                    NA,
                    NA,
                    NA,
                    NA),
          End = c(NA,
                  NA,
                  NA,
                  NA,
                  NA,
                  "2018-03-17 14:31:00"),
          Time_Diff_min = c(rep(353, times = 6)))

Thank you!

Apply na.locf0 to both columns and subtract.

library(zoo)
transform(a, diff = as.numeric(difftime(na.locf0(as.POSIXct(End), fromLast = TRUE), 
                                        na.locf0(as.POSIXct(Start)),
                                        unit = "min")))

giving:

   Time               Start                 End diff
1 Time1 2018-03-17 08:38:00                <NA>  353
2 Time2                <NA>                <NA>  353
3 Time3                <NA>                <NA>  353
4 Time4                <NA>                <NA>  353
5 Time5                <NA>                <NA>  353
6 Time6                <NA> 2018-03-17 14:31:00  353

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