*[codility]CartesianSequence

https://codility.com/programmers/challenges/upsilon2012

求笛卡尔树的高度，可以用单调栈来做。

维持一个单调递减的栈，每次进栈的时候记录下它之后有多少元素，就是以它为根的子树的高度。出栈的时候再更新一次供新进栈者使用。

int solution(vector<int> &A) {

    A.push_back(1000000001); // an element larger than any one in A

    int size = A.size();

    vector<int> elem_stack;

    vector<int> ht_stack;

    int tailHt = 0;

    for (int i = 0; i < size; i++) {

        bool done = false;

        while (not done) {

            if (elem_stack.size() == 0

                || elem_stack.back() > A[i]) {

                elem_stack.push_back(A[i]);

                ht_stack.push_back(tailHt);

                tailHt = 0;

                done = true;

            } else { // pop up

                elem_stack.pop_back();

                tailHt = max(ht_stack.back(), tailHt) + 1;

                ht_stack.pop_back();

            }

        }

    }

    return ht_stack.back();

}