Note that you don't need to store the entire P matrix. You really just need the last column. Don
On Jan 7, 10:29 am, Don <dondod...@gmail.com> wrote: > 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 --