bool is_subset(vi &v, int sum, int n) {
    // initialisation of dp matrix by false
    for(int i = 0; i <= sum; i++) dp[i] = false;
    dp[0] = true;

    // choice diagram code iterative version
    for(int i = 0; i < n; i++) {
        // the element to be included in the sum cannot be greater than the sum
        for(int j = sum; j >= v[i]; j--) {
            // check if sum - v[i] could be formed from a subset using elements before index i
            if(dp[j - v[i]]) dp[j] = 1;
        }
    }

    return dp[sum];
}