[bash] How to create nonexistent subdirectories recursively using Bash?

I am creating a quick backup script that will dump some databases into a nice/neat directory structure and I realized that I need to test to make sure that the directories exist before I create them. The code I have works, but it seems that there is a better way to do it. Any suggestions?

[ -d "$BACKUP_DIR" ] || mkdir "$BACKUP_DIR"
[ -d "$BACKUP_DIR/$client" ] || mkdir "$BACKUP_DIR/$client"
[ -d "$BACKUP_DIR/$client/$year" ] || mkdir "$BACKUP_DIR/$client/$year"
[ -d "$BACKUP_DIR/$client/$year/$month" ] || mkdir "$BACKUP_DIR/$client/$year/$month"
[ -d "$BACKUP_DIR/$client/$year/$month/$day" ] || mkdir "$BACKUP_DIR/$client/$year/$month/$day"

$ mkdir -p "$BACKUP_DIR/$client/$year/$month/$day"

mkdir -p newDir/subdir{1..8}
ls newDir/
subdir1 subdir2 subdir3 subdir4 subdir5 subdir6 subdir7 subdir8

While existing answers definitely solve the purpose, if your'e looking to replicate nested directory structure under two different subdirectories, then you can do this

mkdir -p {main,test}/{resources,scala/com/company}

It will create following directory structure under the directory from where it is invoked

+-- main
¦   +-- resources
¦   +-- scala
¦       +-- com
¦           +-- company
+-- test
    +-- resources
    +-- scala
        +-- com
            +-- company

The example was taken from this link for creating SBT directory structure