Test if a directory is writable by a given UID?

Here’s a long, roundabout way of checking.

USER=johndoe
DIR=/path/to/somewhere

# Use -L to get information about the target of a symlink,
# not the link itself, as pointed out in the comments
INFO=( $(stat -L -c "%a %G %U" "$DIR") )
PERM=${INFO[0]}
GROUP=${INFO[1]}
OWNER=${INFO[2]}

ACCESS=no
if (( ($PERM & 0002) != 0 )); then
    # Everyone has write access
    ACCESS=yes
elif (( ($PERM & 0020) != 0 )); then
    # Some group has write access.
    # Is user in that group?
    gs=( $(groups $USER) )
    for g in "${gs[@]}"; do
        if [[ $GROUP == $g ]]; then
            ACCESS=yes
            break
        fi
    done
elif (( ($PERM & 0200) != 0 )); then
    # The owner has write access.
    # Does the user own the file?
    [[ $USER == $OWNER ]] && ACCESS=yes
fi