title: Longest increasing subsequence
body: <p>Given an input sequence, what is the best way to find the longest (not necessarily continuous) increasing subsequence</p>
  <pre><code>[0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]  # input
  
  [1, 9, 13, 15]  # an example of an increasing subsequence (not the longest)
  
  [0, 2, 6, 9, 13, 15]  # longest increasing subsequence (not a unique answer)
  [0, 2, 6, 9, 11, 15]  # another possible solution
  </code></pre>
  <p>I'm looking for the best algorithm. If there is code, Python would be nice, but anything is alright.</p>