Numbering rows within groups in a data frame

Use ave, ddply, dplyr or data.table:

df$num <- ave(df$val, df$cat, FUN = seq_along)

or:

library(plyr)
ddply(df, .(cat), mutate, id = seq_along(val))

or:

library(dplyr)
df %>% group_by(cat) %>% mutate(id = row_number())

or (the most memory efficient, as it assigns by reference within DT):

library(data.table)
DT <- data.table(df)

DT[, id := seq_len(.N), by = cat]
DT[, id := rowid(cat)]