Max Histogram Area

// Histogram
class Solution {
public:

    typedef vector<int> vec_t;

    int largestRectangleArea(vec_t & histogram) {

        if(histogram.empty()) { return 0; }

        const size_t N = histogram.size();

        vec_t maxSoFarLeft(N);
        vec_t maxSoFarRight(N);

        maxSoFarLeft[0] = histogram[0];
        maxSoFarLeft[N-1] = histogram[N-1];

        for(size_t i = 1; i < N; ++i)
        {
            int H = histogram[i];
            size_t j = N-1-i;

            maxSoFarLeft[i] = max(histogram[i],maxSoFarLeft[i-1]);
            maxSoFarLeft[i] = max(histogram[j],maxSoFarRight[j+1]);
        }


        int maxArea = INT_MIN;

        for(size_t pos = 0; pos < N; ++pos)
        {
            const int H = histogram[pos];


            typedef vec_t::iterator iter_t;

            iter_t begin_range = std::lower_bound(maxSoFarLeft.begin(), maxSoFarLeft.begin() + pos, H);
            int beg_pos = std::distance(maxSoFarLeft.begin(), begin_range);

            iter_t end_range = std::upper_bound(maxSoFarRight.begin()+pos+1, maxSoFarRight.end(), H);
            int end_pos = std::distance(maxSoFarRight.begin(), end_range);

            int area = H * (end_pos - beg_pos);
            maxArea = std::max(maxArea, area);
        }
        return maxArea;
    }
};