title: AVL specific case balancing
body: <p>I have been revisiting old basic algorithms for a class I an online course I am about to watch after christmass. It had been a generally light read, until I reached AVLs. Back when I was learning them, I do not remember having any problem, but after a little more than 10 years, I am no longer as good. While I solve most cases easily, I have stuck for more than 5 hrs on this example:</p>
  
  <pre><code>    51
     /  \
    19   55
   / \    \
  10  37   61
      / \  
     28 46
  </code></pre>
  
  <p>Inserting 40 into the tree, left child of 46, requires a Single Left Rotation to fix the balance...why? Isn't 40 inserted into the left side of the Right child of 19, who becomes unbalanced? Why is it not a double rotation? What do I fail to see?</p>