# what is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?

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## GATE | GATE CS 2021 | Set 2 | Question 18

Last Updated : 23 May, 2021

What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?

**(A)**Θ(√n)

**(B)**Θ(log2(n))

**(C)**Θ(n2)

**(D)**Θ(n)

**Answer:**

**(B)**

**Explanation:**Arithmetic operations performed by binary search on sorted data items means computation of mid element required arithmetic operation. So it will be computed log(n) time and Hence option (C) will be correct.

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## Algorithms: GATE CSE 2021 Set 2

What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size ... $\Theta(n^2)$ $\Theta(n)$

## GATE CSE 2021 Set 2 | Question: 8

asked in Algorithms Feb 18, 2021

recategorized Apr 11, 2021 by Lakshman Patel RJIT

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## [Solved] What is the worst

The correct answer is option 3: Key Points Binary search has the Worst-case and avg case time complexity O(log2n) and best case O(1) in an array. So, i

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## What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?

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θ(n) θ(√n) θ(log2(n)) θ(n2)

## Answer (Detailed Solution Below)

Option 3 : θ(log2(n))

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## Detailed Solution

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The correct answer is** option 3:**

**Key Points**

Binary search has the Worst-case and avg case time complexity O(log2n) and best case O(1) in an array. So, it is can also be written as θ(log2n)

and θ (1).

No of arithmetic operations will be θ (logn) in the worst case as every comparison needs 2 operations + and / by 2.

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