Where it started
A 360 × 400 cm studio with a two-seat sofa, a table, a desk and a shelf, together using just 22% of the floor. The big pieces were lined up along the top wall, which leaves the middle of the room looking wonderfully open.
The sofa and the table are 17 cm apart, and the whole top of the room is blocked off. The planner couldn't find a route in. To sit on the sofa you'd go around the front of it, and the moment a chair goes up to the table that way is shut too.
Step 1: draw the line you walk most
With the furniture cleared out, I drew one line first: door to sofa and door to desk, the two trips that happen most. Both end up near the top of the room, so a single straight line up the middle covers them.
Step 2: keep 30 cm clear on each side
A line isn't a path, so 30 cm either side of it, 60 cm in total, stays empty. In the end there was 75 cm to spare.
Step 3: living on the left, working on the right
Left of the path: the sofa tight in the corner, the table 55 cm below it. Right of the path: the desk in the corner and the shelf halfway down the wall.
Step 4: check it
75 cm between the end of the sofa and the desk, and the planner finds a route. The bottom half of the room is now completely free, which leaves room for a bed later.
One thing still nags. The table is 55 cm from the sofa, so a dining chair at that table will nearly touch the sofa. If you eat at home a lot, turning the table 90° is probably better. The desk chair backing onto the walkway might bother a roommate; living alone, it won't matter.