How to most efficiently increase values at a specified range in a large array and then find the largest value

Question

So I just had a programming test for an interview and I consider myself a decent programmer, however I was unable to meet time constraints on the online test (and there was

Answer 1

Detect local maximums while running through the instructions. The answer will be the maximum of local maximums. Please, note that the vector p must be sorted by start.

struct Instruction
{
    size_t start, stop;
    value_t value;

    bool operator > (const Instruction& b) const
    {
        return stop > b.stop;
    }
};

template
value_t do_work(const Ti&& b, const Ti&& e)
{
    value_t result = 0;
    value_t local = 0;

    auto q = priority_queue, 
                 greater>();

    for (auto i=b; i!=e; ++i)
    {
        q.push(*i);
        if (q.top().stop < i->start)
        {
            if (local > result)result = local;
            do
            {
                local -= q.top().value;
                q.pop();
            } while (q.top().stop < i->start);
        }

        local += i->value;
    }

    return max(local, result);
}

int main()
{
    vector p = { 
        {0,3,143}, {2,4,100}, {2,2,100}, 
        {3,5,1000}, {4,4,500} 
    };

    cout << do_work(begin(p),end(p)) << endl;

    return 0;
}