Largest Subarray

/**
* Find the continuous sequence with the largest sum in a array.
*/

/*
The Algorithm:
- First cut off negative edges on the right and left hand side of 
  the array. The intuition is that starting or ending with an 
  negative number cannot do us any good in finding the max
  continous sum.
- Iterate from left to right. As we go along, we measure a cur_max
  which is a local maximum from a particular substring starting 
  from a positive integer. Once the sequence hits less than a cumulative
  sum that is less than zero, we know that it is equivalent to 
  starting from a negative number. Starting from any positive number is better.
  I.e. we cannot only benefit from positive numbers.
- As we go, we also maintain a final_max, that records the maximums as we
  go along in the array.

*/

template<typename iter>
int next_positive_i(iter begin, iter end, int start_i)
{
    int count = start_i;
    for (iter i = begin + start_i; i != end; i++) {
        if (*i > 0) return count;
        count++;
    }
}

int sum_max_subarray(const vector<int> &elements)
{
    // rid of first negatives
    int memory_positive = next_positive_i(elements.begin(), elements.end(), 0);
    int end_stop = elements.size()
        - next_positive_i(elements.rbegin(), elements.rend(), 0);

    int cur_max = 0;
    int final_max = 0;

    for (int i = memory_positive; i < end_stop; i++)
    {
        cur_max += elements[i];
        final_max = max(cur_max, final_max);
        if (cur_max < 0) {
            i = next_positive_i(elements.begin(), elements.end(), memory_positive + 1) - 1;
            memory_positive = i;
            cur_max = 0;
        }
    }

    return final_max;
}


int main()
{
    // return 6
    cout << sum_max_subarray(vector<int>() = { -2, 1, -3, 4, -1, 2, 1, -5, 4 }) << endl;

    // return 7
    cout << sum_max_subarray(vector<int>() = { -2, -3, 4, -1, -2, 1, 5, -3 }) << endl;
}