find len of LIS using patience sort like piles

len_lis.cpp

int lengthOfLIS(vector<int>& nums) {
  vector<int> piles;
  for(auto i: nums) {
    auto it = std::lower_bound(piles.begin(), piles.end(), i);
    if(it==piles.end()) piles.push_back(i);
    else *it = i;
  }
  return piles.size();
}