How to determine the longest increasing subsequence using dynamic programming?

Question

I have a set of integers. I want to find the longest increasing subsequence of that set using dynamic programming.

Answer 1

The O(NLog(N)) Approach To Find Longest Increasing Sub sequence
Let us maintain an array where the ith element is the smallest possible number with which a i sized sub sequence can end.

On purpose I am avoiding further details as the top voted answer already explains it, but this technique eventually leads to a neat implementation using the set data structure (at least in c++).

Here is the implementation in c++ (assuming strictly increasing longest sub sequence size is required)

#include  // gcc supported header to include (almost) everything
using namespace std;
typedef long long ll;

int main()
{
  ll n;
  cin >> n;
  ll arr[n];
  set S;

  for(ll i=0; i> arr[i];
    auto it = S.lower_bound(arr[i]);
    if(it != S.end())
      S.erase(it);
    S.insert(arr[i]);
  }

  cout << S.size() << endl; // Size of the set is the required answer

  return 0;
}