Please don't provide handwritten solution **Question:**What is the recurrence relation that describes the asymptotic complexity of binary search, as a function of n, the number of items in the input list?**Options:**1) \( T(n) = T(n/2) + \Theta(1) \)2) \( T(n) = T(n-1) + o(1) \)3) \( T(n) = 2 \cdot T(n/2) + \Theta(1) \) (Selected)4) \( T(n) = 2 \cdot T(n-1) + \Theta(1) \)

Answered: What is the recurrence relation that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Step 1: Concept

Binary search is a divide-and-conquer algorithm that repeatedly divides the array into two halves and compares the middle element with the target value. If the middle element is equal to the target value, then the search is successful and the algorithm returns the index of the middle element. If the middle element is greater than the target value, then the algorithm discards the right half of the array and continues the search on the left half. If the middle element is less than the target value, then the algorithm discards the left half of the array and continues the search on the right half.