Just to supplement purnawirman's algorithm explanation. http://algorithmsandme.in/2014/02/stacks-stock-span-problem/ This page gives an excellent illustration of the "stock span problem". This problem is similar to the stock span problem, but more complicated. The following is my C++ code, which passed all the test cases. Just for reference.

struct Node 
{
    int plantID; // we label plants from 0 to N - 1
    int daysToDie; // the days a plant needs to die, -1 means it will not die
};

int main()
{
    std::vector<int> pesticides;
    int N;
    std::cin >> N;
    for (int i = 0; i < N; i++)
    {
        int pesiticide;
        std::cin >> pesiticide;
        pesticides.push_back(pesiticide);
    }

    std::stack<Node> s;
    s.push({ 0, -1 });
    int maxDaysToDie = -1; // the max days needed to die among all the plants
    for (int i = 1; i < N; i++)
    {
        // we only care about the plants whose pesticide is smaller (potential killer)
        int daysToDie = 1;
        while (!s.empty())
        {
            if (pesticides[s.top().plantID] >= pesticides[i])
            {
                // need to wait the front plants to die, like "1 5 4", 4 will die only after 5 died
                daysToDie = std::max(daysToDie, s.top().daysToDie + 1);
                s.pop();
            }
            else // find the killer
            {
                break;
            }
        }
        if (s.empty()) // this means no preceding plants have less pesticide than ith plant
        {
            daysToDie = -1;
        }
        maxDaysToDie = std::max(maxDaysToDie, daysToDie);
        s.push({ i, daysToDie });
    }

    std::cout << (maxDaysToDie < 0 ? 0 : maxDaysToDie) << std::endl;
    return 0;

}