How to use bash string formatting to reverse date format?

I have a lot of files that are named as: MM-DD-YYYY.pdf. I want to rename them as YYYY-MM-DD.pdf I’m sure there is some bash magic to do this. What is it?

For files in the current directory:

for name in ./??-??-????.pdf; do
    if [[ "$name" =~ (.*)/([0-9]{2})-([0-9]{2})-([0-9]{4})\.pdf ]]; then
        echo mv "$name" "${BASH_REMATCH[1]}/${BASH_REMATCH[4]}-${BASH_REMATCH[3]}-${BASH_REMATCH[2]}.pdf"
    fi
done

Recursively, in or under the current directory:

find . -type f -name '??-??-????.pdf' -exec bash -c '
    for name do
        if [[ "$name" =~ (.*)/([0-9]{2})-([0-9]{2})-([0-9]{4})\.pdf ]]; then
            echo mv "$name" "${BASH_REMATCH[1]}/${BASH_REMATCH[4]}-${BASH_REMATCH[3]}-${BASH_REMATCH[2]}.pdf"
        fi
    done' bash {} +

Enabling the globstar shell option in bash lets us do the following (will also, like the above solution, handle all files in or below the current directory):

shopt -s globstar

for name in **/??-??-????.pdf; do
    if [[ "$name" =~ (.*)/([0-9]{2})-([0-9]{2})-([0-9]{4})\.pdf ]]; then
        echo mv "$name" "${BASH_REMATCH[1]}/${BASH_REMATCH[4]}-${BASH_REMATCH[3]}-${BASH_REMATCH[2]}.pdf"
    fi
done

All three of these solutions uses a regular expression to pick out the relevant parts of the filenames, and then rearranges these parts into the new name. The only difference between them is how the list of pathnames is generated.

The code prefixes mv with echo for safety. To actually rename files, remove the echo (but run at least once with echo to see that it does what you want).