Two subsets with minimum difference [closed] - c++

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Consider an array arr.
s1 and s2 are any two sub sets of our original array arr. We should partition our original array such that these two sub sets have the minimum difference, i.e., min(sum(s1) - sum(s2)) where sum(s1) >= sum(s2).
I'm supposed to print these two sub sets, i.e., s1 and s2, as my output.
You can store these sub sets in a vector.
For example if arr[] = [0,1,5,6], then the minimal difference is 0 and my two sub sets are s1[] = [0,1,5] and s2[] = [6].
Another example could be arr[] = [16,14,13,13,12,10,9,3], and the two sub sets would be s1[]=[16,13,13,3] and s2[] = [14,12,10,9] with a minimum difference of 0 again.
I can't seem to figure out how to get to these two sub sets.
Much appreciated!
Note: I know how to obtain the minimum difference from the two sub sets using DP but I am unable to proceed further. It's getting the two sub sets (with the minimal difference) that I'm unable to do.
Just an algorithm with a nudge along the right direction would do.
#include<iostream>
#include<vector>
using namespace std;
int min_subset_sum_diff(int a[], int n,int sum) {
vector<vector<bool>> go(n + 1, vector<bool>(sum + 1, false));
for (int i = 0; i < n + 1; ++i) {
go[i][0] = true;
}
for (int i = 1; i <= n; ++i) {
for (int j = 1; j <= sum; ++j) {
if (a[i - 1] <= j) {
go[i][j] = go[i - 1][j - a[i - 1]] || go[i - 1][j];
}
else {
go[i][j] = go[i - 1][j];
}
}
}
for (int j = (sum / 2); j >= 0; --j) {
if (go[n][j]) { // only need the last row as I need all the elements, which is n
return sum - 2 * j;
}
}
return INT_MAX;
}
int main() {
int a[] = { 3,100,4,4 };
int n = sizeof(a) / sizeof(a[0]);
int sum = 0;
for (auto i : a) {
sum += i;
}
cout << min_subset_sum_diff(a, n,sum);
}
s1 = sum(first_subset)
s2= sum(second_subset)
Assuming s2>=s1,
s1 + s2 = sum_arr
s2 = sum_arr - s1 //using this in the next equation
s2-s1 = difference
(sum_arr - s1) - s1 = difference
sum_arr - 2*s1 = difference
This is my underlying logic.
sum(s1) and sum(s2) lie between 0..sum_arr
Since I assume s1 < s2, s1 can have values only between 0..(sum_arr/2)
And my aim is to minimum value of sum_arr - 2*s1, this will be true for the largest s1 that is true

Answer 1

Make parallel table of int T[][] with the same dimensions as go[][]
When you make a decision here
if (a[i - 1] <= j)
put in T[i][j] some kind of information pointing onto true precursor coordinates for go[i][j]
After filling the tables you search for the best true entry in go[n] row of boolean table. When it is found, get value from the same cell of T table and follow to precursor, then to precursor of prcursor and so on ("unwind" subset information)