You want to partition the array A into to subsets S1 and S2 such that
you minimize |Sum(S1)-Sum(S2)|.
The optimal sum for the subsets is S=SUM(A)/2
Use DP to build a matrix P:
P[i][j] = 1 if some subset of {A[0]..A[i]} has a sum of j, 0 otherwise
Now find a value of i such that P[n][i] = 1 which minimizes S-i.
The minimum sum is 2S-2i.
Don
On Jan 5, 12:58 pm, mukesh tiwari <mukeshtiwari.ii...@gmail.com>
wrote:
> Hello All!
> I have a given array of numbers and I have to change the sign of numbers to
> find out the minimum sum. The minimum sum will be 0 or greater than 0. Here
> is couple of test cases
> 1. [ 1 , 2 , 3 , 2 , 4 ]. Changing the sign [ -1 , -2 , -3 , 2 , 4 ] so
> minimum sum will be 0.
> 2. [ 3 , 5 , 7 , 11 , 13 ]. Changing the sign [ -3 , -5 , 7 , -11 , 13 ]
> so minimum sum is 1.
>
> So technically this problem boils down to divide the set into two subset
> and find out the minimum difference. I though of DP but the number of
> element in array could 10^5 so could some one please tell me how to solve
> this problem ? I didn't assume that number will be positive because it was
> not given in the problem.
>
> Regards
> Mukesh Tiwari
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