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difftime in R dataframe based on subset

I've got this sample dataframe, that keeps track of the time when a lamp is switched on and off.

                  time lamp status
1  2015-01-01 12:18:17    2     ON
2  2015-01-01 13:07:29   28     ON
3  2015-01-01 13:11:50   28    OFF
4  2015-01-01 13:18:28    2    OFF
5  2015-01-01 14:07:29   28     ON
6  2015-01-01 14:11:35   28    OFF
7  2015-01-01 14:18:28    2     ON
5  2015-01-01 14:18:57    2    OFF

What I want to achieve is to add a fourth column, containing the duration of a period where a lamp has been switched on (in seconds).

The desired output:

                  time lamp status duration
1  2015-01-01 12:18:17    2     ON     3611
2  2015-01-01 13:07:29   28     ON      261
3  2015-01-01 13:11:50   28    OFF       NA  
4  2015-01-01 13:18:28    2    OFF       NA
5  2015-01-01 14:07:29   28     ON      246
6  2015-01-01 14:11:35   28    OFF       NA
7  2015-01-01 14:18:28    2     ON       29
5  2015-01-01 14:18:57    2    OFF       NA

I already succeeded in doing this with a custom function, involving while and for-loops. BUT... I'm a beginner in R, and I'm pretty sure this can be done more simple and elegant (using subsets, apply, and/or ....). I just can't figure out how?

Any ideas, of leads in the right direction?

This works for me:

library(dplyr)
df <- df %>% mutate(sec=as.numeric(time)) %>% group_by(lamp) %>% mutate(duration=c(diff(sec), NA)) %>% select(-sec)
df$duration[df$status=="OFF"] <- NA
#### 1 2015-01-01 12:18:17     2     ON     3611
#### 2 2015-01-01 13:07:29    28     ON      261
#### 3 2015-01-01 13:11:50    28    OFF       NA

Your data:

df=structure(list(time = structure(c(1420111097, 1420114049, 1420114310, 
1420114708, 1420117649, 1420117895, 1420118308, 1420118337), class = c("POSIXct", 
"POSIXt"), tzone = ""), lamp = c(2L, 28L, 28L, 2L, 28L, 28L, 
2L, 2L), status = structure(c(2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L), .Label = c("OFF", 
"ON"), class = "factor"), duration = c(2952, 261, NA, NA, 246, 
NA, 29, NA)), .Names = c("time", "lamp", "status", "duration"
), row.names = c(NA, -8L), class = "data.frame")

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