UGC NET CSE | December 2025 | Part 2 | Question: 41

Question

Which of the following is correct order of increasing time complexity of algorithms

1. Tower of Hanoi with $n$ disk.
2. Binary search given $n$ sorted numbers.
3. Heap sort given $n$ numbers at the worst case.
4. Addition of two $n \times n$ matrices.

Choose the correct answer from the options given below:

• A. $\text{II, III, IV, I}$
• B. $\text{I, II, III, IV}$
• C. $\text{IV, III, II, I}$
• D. $\text{III, I, IV, II}$

Answer 1

As we know that the complexities are -->

Algorithm	Complexity
I. Tower of Hanoi (n disks)	O(2ⁿ) — exponential
II. Binary Search (n sorted numbers)	O(log n) — logarithmic
III. Heap Sort worst case	O(n log n) — linearithmic
IV. Addition of two n×n matrices	O(n²) — quadratic

Now, we know that-->> Logarithmic < Linearithmic < Quadratic < Exponential 
So,
O(logn)<O(nlogn)<O(n2)<O(2n).
Correct Order: II, III, IV, I
Option A.

 

Answer 2

option C is correct.

tower of hanoi = O(2^n )

binary serach = O(logn)

Heap sort = O(nlogn)

Addition of two matrix = O(n*n)

so option c is correct