push() expected running time

• How far to move up?
  • Half of the nodes are leaves, so half of the inserts will only move up one level
  • A quarter of the nodes are one level above the leaves, so one quarter of the inserts will move up two levels
  • One eighth will require moving up 3 levels
  • One sixteenth will require moving up 4 levels
  • Expected running time:
     
  1/2 * 1 + 1/4 * 2 + 1/8 * 3 + ... = Sum((1/(2^i))*i = 2