Search in Rotated Sorted Array in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a rotated sorted array?

A rotated sorted array is an array that was originally sorted in ascending order but then rotated (shifted) at some pivot point. For example, [4,5,6,7,0,1,2] is a rotated version of [0,1,2,4,5,6,7].

beginner

Why can't we use simple binary search directly on a rotated sorted array?

Because the array is not fully sorted in ascending order due to rotation, simple binary search may fail. The array has two sorted parts separated by the pivot, so we need to identify which part to search in.

intermediate

In the rotated sorted array search algorithm, how do we decide which half to search next?

We check if the left half is sorted by comparing the start and middle elements. If sorted, we check if the target lies within this half. If yes, search left half; else, search right half. If left half is not sorted, the right half must be sorted, so we do the same check there.

beginner

What is the time complexity of searching in a rotated sorted array using the modified binary search?

The time complexity is O(log n) because each step halves the search space, similar to normal binary search.

beginner

Show the base case condition when the target is found in the rotated sorted array search.

If the middle element equals the target, return the middle index immediately. This stops the search.

What does a rotated sorted array look like?

A [1,3,2,4,5,7,6]

B [1,2,3,4,5,6,7]

C [4,5,6,7,0,1,2]

D [7,6,5,4,3,2,1]

Option C is a sorted array rotated at a pivot. Others are fully sorted or unsorted.

Which method is best to search in a rotated sorted array?

A Simple binary search

B Modified binary search

C Linear search

D Bubble sort

Modified binary search handles the rotation by checking sorted halves.

If the left half of the array is sorted, and the target is within that range, where do we search next?

A Left half

B Both halves

C Right half

D None

We search the left half because the target lies there.

What is the worst-case time complexity of searching in a rotated sorted array using modified binary search?

A O(log n)

B O(n)

C O(n log n)

D O(1)

The search halves the array each time, so O(log n).

What should you check first in each step of the modified binary search?

A If target is at end

B If array is sorted

C If target is at start

D If middle element equals target

Always check if middle element is the target before other checks.

Explain how to search for a target in a rotated sorted array using binary search.

Think about how rotation splits the array into two sorted parts.

Describe why a simple binary search fails on a rotated sorted array and how the modified approach fixes it.

Focus on the effect of rotation on array order.