"Using this route, it's possible to finish the game in 14 hours (Day 1, 10 PM) or less.

Follow the arrows.

At the first lab, store the two cure plants and synthesize the tonic. Go outside grab the flowers for basic medicine and synthesize that quickly. Then follow the rest of the directions.

The Algae is located in two spots (that I know of) on the map. I stumbled across the second location completely by random accident. It's in the swamp at the top left of the map (yellow 'x' next to the blue circle). This location is far more convenient in the speed run.

I've uploaded screenshots (see my content) of the location to help you pinpoint the exact spot of the algae."