combine rows in data frame containing NA to make complete row

We can use fill to fill all the missing values. And then filter just one row for each group.

library(dplyr)
library(tidyr)

df2 <- df %>%
  group_by(A) %>%
  fill(everything(), .direction = "down") %>%
  fill(everything(), .direction = "up") %>%
  slice(1)

And thanks to @Roger-123, the above code can be further simplified as follows.

df2 <- df %>%
  group_by(A) %>%
  fill(everything(), .direction = "downup") %>%
  slice(1)

I haven't figured out how to put the coalesce_by_column function inside the dplyr pipeline, but this works:

coalesce_by_column <- function(df) {
  return(coalesce(df[1], df[2]))
}

df %>%
  group_by(A) %>%
  summarise_all(coalesce_by_column)

##       A     B     C     D     E
##   <dbl> <dbl> <dbl> <dbl> <dbl>
## 1     1     2     3     2     5
## 2     2     4     5     3     4

---

Edit: include @Jon Harmon's solution for more than 2 members of a group

# Supply lists by splicing them into dots:
coalesce_by_column <- function(df) {
  return(dplyr::coalesce(!!! as.list(df)))
}

df %>%
  group_by(A) %>%
  summarise_all(coalesce_by_column)

#> # A tibble: 2 x 5
#>       A     B     C     D     E
#>   <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1     1     2     3     2     5
#> 2     2     4     5     3     4