Data recovery after interrupted partitioning
You will need to create an installable USB drive which you can boot from, follow these steps carefully to achieve that: 


Download the Mac OS (Yosemite) from the App Store
Format a USB in Disk Utility and name it Untitled (very Important) You should format your USB to Mac OS X Extended (Journaled) 
Launch Terminal and execute this command:

sudo /Applications/Install\ OS\ X\ Yosemite.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled --applicationpath /Applications/Install\ OS\ X\ Yosemite.app —nointeraction