title: Time complexity of Quick Sort when pivot (split list into 90%:10%) (always smallest element for even depth)
body: <p>What is the time complexity of quicksort in the following 2 cases:</p>
  
  <ol>
  <li>Pivot always split the list into 9:1 ratio</li>
  <li>Pivot is always the smallest element(worst case) for even depth and the middle element(best case) for odd depth.</li>
  </ol>
  
  <p>For 1, I guess we have the recurrence equation:</p>
  
  <pre><code>F(N) = F(N/10) + F(9N/10) + N
  </code></pre>
  
  <p>For 2,</p>
  
  <pre><code>F(N) = F(N-1) + N if even
  F(N) = 2*F(N/2) + N if odd
  </code></pre>
  
  <p>Am I correct with these equations and how do I solve both of these recurrence equations?</p>