Won't work.
You just can't build such a system, because you don't know in which
order values should appear in right part of system. Say, we have the
follwing input of 6 numbers: 3, 4, 5, 5, 6, 7 and we are supposed to
find 4 values (4 * (4 - 1) / 2 = 6) x1, x2, x3, x4
What the system will look like?
x1 + x2 = ?
x1 + x3 = ?
x1 + x4 = ?
x2 + x3 = ?
x2 + x4 = ?
x3 + x4 = ?
On 7 нояб, 20:16, anvera <[EMAIL PROTECTED]> wrote:
> I have not developed entirely the idea, but I am sure it works.
> Just write the corresponding linear system. You will have n unknowns
> and n(n-1)/2 equations. Provided that the system is consistent you can
> find a solution by Gaussian elimination.
> For the complexity, you can do it in less than n^3/3 +O(n^2)
> operations, because it is simpler than just inverting a nxn matrix.
> Inverting the matrix can let you solve the problem for many instances.
> It would be interesting to exploit the special structure of this
> matrix in order to speed up the computation. Please post if you find
> such an improvement.
>
> Best Regards,
>
> Antonio
>
> On Nov 7, 5:16 pm, Andrey <[EMAIL PROTECTED]> wrote:
>
> > Any set of n integers form n(n - 1)/2 sums by adding every possible
> > pair.
> > The task is to find the n integers given the set of sums.
>
> > Any ideas?
>
> > I've found out the solution but I doubt it the best one...
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