title: Worst case in Max-Heapify - How do you get 2n/3?
body: <p>In CLRS, third Edition, on page 155, it is given that in MAX-HEAPIFY,</p>
  
  <blockquote>
    <p>The children’s subtrees each have size at most <strong>2n/3</strong>—the worst case
    occurs when the bottom level of the tree is exactly half full.</p>
  </blockquote>
  
  <p>I understand why it is worst when the bottom level of the tree is exactly half full. And it is also answered in this question <a href="https://stackoverflow.com/questions/6859514/worst-case-in-max-heapify">worst case in MAX-HEAPIFY: &quot;the worst case occurs when the bottom level of the tree is exactly half full&quot;</a></p>
  
  <p>My question is how to get 2n/3? </p>
  
  <p>Why if the bottom level is half full, then the size of the child tree is up to 2n/3?</p>
  
  <p>How to calculate that?</p>
  
  <p>Thanks</p>