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Consider the problem of searching an element x in an array 'arr[]' of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k <= n 3) Array is sorted and rotated by k. k is NOT given to you and k <= n 4) Array is not sorted
- a)1 Only
- b)1 & 2 only
- c)1, 2 and 3 only
- d)1, 2, 3 and 4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the problem of searching an element x in an array arr[] of si...
Understanding the Problem
The problem focuses on how efficiently we can search for an element x in an array arr[] of size n. The time complexity for searching can vary based on the properties of the array.
Scenarios Explained
- 1) Array is sorted:
A sorted array allows us to use binary search, which operates in O(Log n) time. This is the most efficient way to find an element in a sorted dataset.
- 2) Array is sorted and rotated by k (k is given):
When an array is rotated, it is still possible to apply a modified binary search. Knowing the rotation count (k), we can efficiently find the pivot point and then perform binary search in the appropriate subarray, maintaining O(Log n) time complexity.
- 3) Array is sorted and rotated by k (k is NOT given):
Even without knowing k, we can still find the pivot (the point of rotation) using a modified binary search. After identifying the pivot, we can conduct a binary search on the relevant half of the array, achieving O(Log n) time complexity.
- 4) Array is not sorted:
In this scenario, the search complexity cannot be reduced to O(Log n). A linear search would be required, resulting in O(n) time complexity.
Conclusion
Thus, the correct answer is option 'C' because scenarios 1, 2, and 3 all allow for O(Log n) time complexity due to the properties of sorted arrays. However, scenario 4 does not meet this requirement.
The problem focuses on how efficiently we can search for an element x in an array arr[] of size n. The time complexity for searching can vary based on the properties of the array.
Scenarios Explained
- 1) Array is sorted:
A sorted array allows us to use binary search, which operates in O(Log n) time. This is the most efficient way to find an element in a sorted dataset.
- 2) Array is sorted and rotated by k (k is given):
When an array is rotated, it is still possible to apply a modified binary search. Knowing the rotation count (k), we can efficiently find the pivot point and then perform binary search in the appropriate subarray, maintaining O(Log n) time complexity.
- 3) Array is sorted and rotated by k (k is NOT given):
Even without knowing k, we can still find the pivot (the point of rotation) using a modified binary search. After identifying the pivot, we can conduct a binary search on the relevant half of the array, achieving O(Log n) time complexity.
- 4) Array is not sorted:
In this scenario, the search complexity cannot be reduced to O(Log n). A linear search would be required, resulting in O(n) time complexity.
Conclusion
Thus, the correct answer is option 'C' because scenarios 1, 2, and 3 all allow for O(Log n) time complexity due to the properties of sorted arrays. However, scenario 4 does not meet this requirement.
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Consider the problem of searching an element x in an array arr[] of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k = n 3) Array is sorted and rotated by k. k is NOT given to you and k = n 4) Array is not sorteda)1 Onlyb)1 2 onlyc)1, 2 and 3 onlyd)1, 2, 3 and 4Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the problem of searching an element x in an array arr[] of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k = n 3) Array is sorted and rotated by k. k is NOT given to you and k = n 4) Array is not sorteda)1 Onlyb)1 2 onlyc)1, 2 and 3 onlyd)1, 2, 3 and 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the problem of searching an element x in an array arr[] of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k = n 3) Array is sorted and rotated by k. k is NOT given to you and k = n 4) Array is not sorteda)1 Onlyb)1 2 onlyc)1, 2 and 3 onlyd)1, 2, 3 and 4Correct answer is option 'C'. Can you explain this answer?.
Consider the problem of searching an element x in an array arr[] of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k = n 3) Array is sorted and rotated by k. k is NOT given to you and k = n 4) Array is not sorteda)1 Onlyb)1 2 onlyc)1, 2 and 3 onlyd)1, 2, 3 and 4Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the problem of searching an element x in an array arr[] of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k = n 3) Array is sorted and rotated by k. k is NOT given to you and k = n 4) Array is not sorteda)1 Onlyb)1 2 onlyc)1, 2 and 3 onlyd)1, 2, 3 and 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the problem of searching an element x in an array arr[] of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k = n 3) Array is sorted and rotated by k. k is NOT given to you and k = n 4) Array is not sorteda)1 Onlyb)1 2 onlyc)1, 2 and 3 onlyd)1, 2, 3 and 4Correct answer is option 'C'. Can you explain this answer?.
Solutions for Consider the problem of searching an element x in an array arr[] of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k = n 3) Array is sorted and rotated by k. k is NOT given to you and k = n 4) Array is not sorteda)1 Onlyb)1 2 onlyc)1, 2 and 3 onlyd)1, 2, 3 and 4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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