title: Induced height imbalance in AVL tree
body: <p>If a node is inserted in an AVL tree, it might happen that one of the nodes in the path to the new_node would lose height balance. But my question is if that node is fixed, can other nodes above it (the ancestors till the root) would still retain height imbalance (in case they lost the balance earlier).</p>
  
  <p>I have done some paper work and could observe that such a scenario is not possible. Once height imbalance is fixed at a node, all its ancestors should be fixed automatically (if they were affected).</p>