Describe an efficient algorithm for computing the height of a given AVL tree. Yo

Question

Describe an efficient algorithm for computing the height of a given AVL tree. Your algorithm should run in time O(log n) on an AVL tree of size n. In the pseudocode, use the following terminology: T left, T.right, and T.parent indicate the left child, right child, and parent of a node T and T.balance indicates its balance factor (-1,0, or 1). For example if T is the root we have T.parent=nil and if T is a leaf we have T.left and T.right equal to nil. The input is the root of the AVL tree. Justify correctness of the algorithm and provide a brief justification of the runtime

Explanation / Answer

First we define the balance factor using the following function.

balance_factor(T)= Height(T.left)-Height(T.right)
Now using the following recursive procedures, we can compute the height of an AVL tree in O(log n).

Height(T):
step1: If T is a leaf node, return 0.
step2: If balance_factor(T)=+1, return Height(T.left).
step3: If balance_factor(T)=1, return Height(T.right).
step4: If balance_factor(T)=0, return Height(T.left).

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.