[C#,Math] Anyone think they can do this better?

Knight Sir Rick

knight sir Rick said: [Goto]

Not enough math in this "math" thread. Anyway, I found you a closed-form function for your problem:

$\reverse <br /> \mathbf{f}(n) = \sum_{p=0}^7 $ \sum_{k=\frac{2^p + H[p-1] +1}{2}}^{2^p} \(2^{(8-p) H[n-k]} + H[n-2k] + H[n-2k+1] -1$ \)<br />$

where $\reverse H[t]$ is the discrete Heaviside step function defined as

$\reverse H[t]=\begin{cases} 0, & t < 0, \\ 1, & t \ge 0. \end{cases}$

While I understand what you wrote. Converting it to code it seems like it would take longer to compute than WW's answer. Considering for each sigma, there's a for loop that must be run. As well as calls to the function H.

For a completely math based, non-linear, answer though, very impressive. You compressed it into two functions worth. Still much better than my original way of doing it.

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Also, what I meant by the "[Math...]" and "...mathematically..." was just because it isn't just some regular programming stuff. It requires a bit of math knowledge to try and make something that works.

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