longest increasing subsequence(O(nlogn))

Question

LIS:wikipedia

There is one thing that I can\'t understand:

why is X[M[i]] a non-decreasing sequence?

Answer 1

i came up with this

set my_set;
set::iterator it;
vector  out;
out.clear();
my_set.clear();
for(int i = 1; i <= n; i++) {
    my_set.insert(a[i]);
    it = my_set.find(a[i]);
    it++;
    if(it != my_set.end()) 
        st.erase(it);
    else
        out.push_back(*it);
}
cout<< out.size();