GATE CS 2014 Set 1 — Question 22
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Question
Consider a rooted node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly 4 nodes is . Then the value of is ________.
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Solution
To determine the number of subtrees with exactly 4 nodes, we can perform a post-order traversal (bottom-up approach). For each node, we calculate the size of the subtree rooted at that node as:If , we increment a counter. This process visits each node exactly once and performs constant work at each node. Thus, the time complexity is .Comparing with , we get:
The value of .
The value of .
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