How to determine the height of a recursion tree from a recurrence relation?

Question

How does one go about determining the height of a recursion tree, built when dealing with recurrence run-times? How does it differ from determining the height of a regular tree

Answer 1

The height of the recursion tree depends on the recursive algorithm in question. Not all divide and conquer algorithms have uniformed height trees, just as not all tree structures have uniform heights. If you cannot determine the maximum possible height of the algorithm, or if you need to calculate the actual height of the tree at run time, you can use a variable global to the recursive function, increment it upon the entry to the function, and decrement it upon the function exit. This variable will indicate the current level of the recursive procedure. If necessary, you can maintain the maximum value of this variable in a second variable.