Matthew Gretton-Dann
3095d38b8a
As an optimisation we know that if a square with side length N fits in a certain position, then one of side length N - 1 does too. And conversely, if a square of side length N does not fit then one of side length N + 1 does not. So our implementation which asked if every square fitted in a certain position called Grid::fits() too many times, once for each side length. We replace this by a function Grid::largest_square which gives the appropriate side length to start with. Naïvely the optimisation here is that instead of checking whether N squares fit, and so having to do (N * (N + 1)) / 2 comparisons in fits per position, we instead do one scan in largest_square and do at most N comparisons. A performance improvement is also seen in real life.