https://drive.google.com/open?id=0B-2O13fpsnI4aWNBZzlxYUtOa1E

The fastest way to go from Flitwick (2nd floor) until DAtDA (3rd floor):

• Don't try to go by Library, you'll lose 2sec, but just use the stairs below (From near Flitwick after you've finished the minigame until you enter the DatDA classroom it will take you 26.6sec by Library and 24sec by stairs)

The fastest way to go from DAtDA classroom (3rd floor) until Room before Cursed Troll's Fight (5th floor in front of the Stairs, the Muggles Studies Class):

• When you leave the DAtDA classroom until the Room where's the TV for the Troll fight -> take the 2nd floor Hallway and the 5th floor Hallway (refer to the doc) and walk above the statue and left to reach the Room we're talking about. It takes 19.8sec~
• The others path took 23.5sec (when you take stairs) and 20.5sec by 2nd floor Hallway, 4th floor Hallway and to use the final stairs to reach the 5th floor (in front of the room).

The fastest way to go from the Muggles Studies Class (5th floor) until the DAtDA classroom (3rd floor):

• 2nd floor Hallway (Statue) and you use the stairs and walk until you enter in the classroom.

The fastest way to go from the DAtDA classroom (3rd floor) until the History of Magic Class (4th floor):

• 2nd floor Hallway and 4th floor Hallway and you walk until you enter in the classroom.