*[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();
}