minimum subset sum difference

// S1 -s2 min means s1+s2 = total sum ..
// we need to find min (S - 2*s1)  .. so we itrate till s/2. and find the minimum diff of s and 2*s1

int solve(vector<int> value){
    int  n = value.size();
    int sum=0;
    for(int a=0;a<n;a++)sum+=value[a];

    vector<vector<bool>> dp (n+1 ,vector<bool>(sum+1,false));
    // a represents the ath element .. b represents the knapsack present

    for(int a=0;a<=n;a++)dp[a][0] = true;// sum 0 is possible even if do not select anything

    for(int a=1;a<=n;a++){
        for(int b=1;b<=sum;b++){
            if(value[a-1]<=b){
            dp[a][b] = dp[a-1][b-value[a-1]] || dp[a-1][b]; //either i choose the ath element or not
            }else{
            dp[a][b] = dp[a-1][b]; // cant choose the ath element becuase its weight is more
            }
        }
    }
    int mn = INT_MAX;
    for(int a=0;a<=sum/2;a++){
        if(dp[n][a] == true){
        //means sum a exists
            mn = min(mn , sum - 2*a);
        }
    }
    return mn;
}