# Choose the signs of vectors as to maximize modulus of their sum.

## Main Question or Discussion Point

Hi,

I have a fairly simple problem which but I'm not sure if it should rather be in a computer science forum for algorithms or something.

Given n vectors, how do you choose the sign of each vector as to maximize the modulus of the sum of the vectors?

Sure you could go through all 2^n combinations, but that's not necessarily the most efficient way (really, you only need to go through 2^(n-1) since the second half is just negative the first half, but still). I can't figure out what all the dependencies are.

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I'm assuming that by "sign of each vector" you mean if you should add or subtract that vector from the accumulated/summed vector, and that by modulus you mean the length.

My immediate thought was that you don't want to go "backwards". So if the inner product between the summed vector and the next vector is negative, subtract the vector, otherwise add it.

Of course, this might be just silly.