tiling algorithm for maximum size of equal-sized tiles

Question

I'm trying to fit an arbitrary number of HD videos on screen so that they all have equal size, maximizing the size of the videos, with no scrollbars appearing.

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Given N number of tiles of equal aspect ratio (16:9), displayed in a viewport of arbitrary height and width, how can I resize the tiles so that:

a) all tiles are the same size
b) all tiles maintain their aspect ratio
c) all tiles fit within the viewport (i.e., no scrolling)
d) the tiles are as large as possible, while maintaining c)

Answer 1

The purpose of this answer is to illustrate how one would approach a similar problem, regardless of language, and also to illustrate in a way that can be used for many different problems as well.

Unknown

• Scale factor s
• Number of tiles horizontally nh
• Number of tiles vertically nv

Known

• Viewport vw, vh
• Original (full-size) video size w, h
• Total number of videos n

Constraints

• Constraint 1: nh * w * s <= vw
• Constraint 2: nv * h * s <= vh
• Constraint 3: nh * nv >= n

Optimization goal

• Maximize s

Remarks

• All values are strictly positive (none of them can be zero or negative.)

Suggestions

If you do not have a constraint solver, you can first enumerate the list of candidates of the pair (nh, nv), and then solve s for each candidate, and finally choose the one that maximizes s.