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Very good. Pre-memoization you are exponential. With memoization your memory usage scales like O(n**3), and your performance is O(n**4). If you passed the array by reference, and added 2 indices, you would drop a factor of n off of both.

By contrast the efficient algorithm is sub-exponential pre-memoization, and is sub-quadratic after.

Which shows that good algorithms are a big win, but being straightforward, and then applying well-known speedups to that, can still result in a usable algorithm.


In reply to Re: Re: Puzzle: need a more general algorithm by Anonymous Monk
in thread Puzzle: need a more general algorithm by Ovid

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