Question

Given a rectangle with width and height, fill it with n squares (n is integer, also given), such that the squares cover as much of the rectangle’s area as possible.
The size of a single square should be returned.

Ideas?

Answer 1

Assuming that all the squares are aligned and they are the same size, you can find this by binary searching on the side length of the square:

import math

def best_square(w, h, n):
    hi, lo = float(max(w, h)), 0.0
    while abs(hi - lo) > 0.000001:
        mid = (lo+hi)/2.0
        midval = math.floor(w / mid) * math.floor(h / mid)
        if midval >= n:
            lo = mid
        elif midval < n: 
            hi = mid
    return min(w/math.floor(w/lo), h/math.floor(h/lo))