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Given a binary tree, find if it is height balanced or not.
A tree is height balanced if difference between heights of left
and right subtrees is not more than one for all nodes of tree.
A height balanced tree
1
I
10 39
.
5
An unbalanced tree
1
I
10
I
5
Example 1:
Input:
1
2
1
Output: 0

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Problem 3 Recall from lecture that a binary tree T is either: 1. null (the empty tree); or 2. a root noder with two subtrees T₁ and TR, both of which are binary trees. Consider the following algorithm numLeaves (T) that takes as input a binary tree T and returns the number of leaves in the tree. numLeaves (T): 1: if T == null then return 0 2: 3: else 4: 5: 6: 7: 8: TL, TR the left and right subtrees of T, respectively if T₁ == null and TR == null then return 1 else return numLeaves (TL) + numLeaves (TR) Prove by structural induction that for every binary tree T, numLeaves (T) returns the number of leaves of T.