title: Factorial-time algorithms and P/NP
body: <p>It's quite easy to see that n! grows slower than almost anything to the N power (say, 100^N) and so, if a problems is considered NP complete and one happened upon a n! algorithm that approximates the solution, one would do the Snoopy dance.</p>
  
  <p>I have 2 questions about this situation:</p>
  
  <ol>
  <li>Would the n! algorithm be considered a solution in polynomial time? A factorial certainly doesn't appear to be a term raised to a power.</li>
  <li>If finding a n! solution means we have a decently fast algorithm and since n! grows faster than 2^N, then does this mean that some NP-complete problems do not need heuristic/approximation algorithms (except for obscure cases)?</li>
  </ol>
  
  <p>Of course, these two questions rely on the first paragraph being true; if I've erred, please let me know.</p>