Programming and Data Structures · Recursion

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

GATE CSE 2014 Set 1 Q12 · NAT · 1 mark

Consider a rooted $n$ 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 $O(n^a \log^b n)$ . Then the value of $a + 10b$ is _________.

Numerical answer

Enter a value to check

Key concept

Recursion

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Recursion

GATE tests Recursion primarily through direct execution tracing of recursive C code snippets, stack-unwinding behavior (pre-order vs. post-order execution), and termination/infinite recursion analysis. Questions frequently incorporate static variables, pointer/reference aliasing, mutual recursion, and tree/array traversals to test whether candidates can systematically maintain call frames. In recent years, the focus has expanded from standard tracing to higher-order mathematical characterizations (e.g., finding the smallest input or maximum output value of composed recurrences).

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Programming and Data Structures · Recursion

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 1 Q12 · NAT · 1 mark

Consider a rooted $n$ 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 $O(n^a \log^b n)$ . Then the value of $a + 10b$ is _________.

Numerical answer

Enter a value to check

Key concept

Recursion

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Recursion

Full Recursion guide →

More on Recursion

All 19 questions on Recursion →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Consider a rooted $n$ 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 $O(n^a \log^b n)$ . Then the value of $a + 10b$ is _________.

Step-by-step verified solution

Check you can still solve Recursion under a clock

More from GATE CSE 2014 Set 1

More on Recursion

Consider a rooted $n$ 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 $O(n^a \log^b n)$ . Then the value of $a + 10b$ is _________.

Step-by-step verified solution

Check you can still solve Recursion under a clock

More from GATE CSE 2014 Set 1

More on Recursion

Consider a rooted nnn 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 O(nalog⁡bn)O(n^a \log^b n)O(nalogbn). Then the value of a+10ba + 10ba+10b is _________.

Step-by-step verified solution

Check you can still solve Recursion under a clock

More from GATE CSE 2014 Set 1

More on Recursion

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Consider a rooted nnn 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 O(nalog⁡bn)O(n^a \log^b n)O(nalogbn). Then the value of a+10ba + 10ba+10b is _________.

Step-by-step verified solution

Check you can still solve Recursion under a clock

More from GATE CSE 2014 Set 1

More on Recursion

Share this solution

Consider a rooted $n$ 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 $O(n^a \log^b n)$ . Then the value of $a + 10b$ is _________.

Consider a rooted $n$ 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 $O(n^a \log^b n)$ . Then the value of $a + 10b$ is _________.