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Searching Algorithms

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210 total MCQsShowing 30 with explanations10 Easy10 Medium10 Hard
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About This Topic

A searching algorithm locates a target value, or confirms its absence, within a collection of data such as an array, list or tree. Linear search is the baseline, scanning each element for O(n) worst-case time on unsorted data. Binary search halves a sorted range each step for O(log n), and questions often probe its midpoint calculation and preconditions. Beyond these, expect jump search with an optimal block size of the square root of n, interpolation search, which averages O(log log n) on uniform data but degrades to O(n), exponential search for unbounded lists, Fibonacci search, and ternary search for finding the peak of a unimodal function.

Below are 30 practice questions from a pool of 210 Searching Algorithms MCQs, one of 12 topics in Data Structures & Algorithms. Each shows the correct answer with an explanation; when you are ready, take a timed quiz to test recall under exam conditions.

Practice Questions

Each question below shows the correct answer with a full explanation. Use these to build conceptual understanding before attempting a timed quiz.

Searching AlgorithmsEasy

Q1. What does binary search return if the element is not found?

  1. A.The middle index of the array
  2. B.The value zero always
  3. C.The last index of the array
  4. D.An indicator such as -1 for not found✓ Correct

Explanation

Binary search typically returns -1 or a similar sentinel value to indicate the element was not found.

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Searching AlgorithmsEasy

Q2. What is the time complexity of binary search?

  1. A.O(log n)✓ Correct
  2. B.O(n^2)
  3. C.O(n)
  4. D.O(1)

Explanation

Binary search divides the search space in half at each step, giving O(log n) time complexity.

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Searching AlgorithmsEasy

Q3. What is the best-case time complexity of linear search?

  1. A.O(1)✓ Correct
  2. B.O(n)
  3. C.O(log n)
  4. D.O(n^2)

Explanation

The best case for linear search is O(1), when the target element is at the first position.

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Searching AlgorithmsEasy

Q4. Which search algorithm does not require the data to be sorted?

  1. A.Interpolation search
  2. B.Linear search✓ Correct
  3. C.Fibonacci search
  4. D.Binary search

Explanation

Linear search works on both sorted and unsorted data since it checks each element sequentially.

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Searching AlgorithmsEasy

Q5. What is the time complexity of linear search in the worst case?

  1. A.O(n^2)
  2. B.O(log n)
  3. C.O(n)✓ Correct
  4. D.O(1)

Explanation

In the worst case, linear search must check every element, giving O(n) time complexity.

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Searching AlgorithmsEasy

Q6. How many comparisons does binary search make for an array of 1024 elements in the worst case?

  1. A.100
  2. B.10✓ Correct
  3. C.1024
  4. D.512

Explanation

Binary search makes at most log2(1024) + 1 = 11 comparisons, approximately 10 divisions of the search space.

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Searching AlgorithmsEasy

Q7. What is the prerequisite for binary search?

  1. A.The array must be sorted✓ Correct
  2. B.The array must be of fixed size
  3. C.The array must contain unique elements
  4. D.The array must be unsorted

Explanation

Binary search requires the array to be sorted in order to repeatedly divide the search space in half.

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Searching AlgorithmsEasy

Q8. What is linear search?

  1. A.Searching using a hash table for lookups
  2. B.Searching only in a sorted array format
  3. C.Searching each element sequentially from start✓ Correct
  4. D.Searching by dividing the array in half

Explanation

Linear search checks each element of the list sequentially until the target element is found or the list ends.

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Searching AlgorithmsEasy

Q9. In binary search, if the target is greater than the middle element, where do you search next?

  1. A.Start over again
  2. B.Middle element only
  3. C.Left half only
  4. D.Right half only✓ Correct

Explanation

If the target is greater than the middle element in a sorted array, it must be in the right half.

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Searching AlgorithmsMedium

Q10. What is the average time complexity of interpolation search on uniformly distributed data?

  1. A.O(log n)
  2. B.O(1)
  3. C.O(n)
  4. D.O(log log n)✓ Correct

Explanation

For uniformly distributed sorted data, interpolation search achieves O(log log n) average time complexity.

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Searching AlgorithmsMedium

Q11. What is the optimal block size for jump search on an array of n elements?

  1. A.log n
  2. B.√n✓ Correct
  3. C.n
  4. D.n/2

Explanation

The optimal block size for jump search is √n, which minimizes the total number of comparisons to O(√n).

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Searching AlgorithmsMedium

Q12. What is jump search?

  1. A.A search that uses recursion to jump elements
  2. B.A search that jumps by blocks then does linear scan✓ Correct
  3. C.A search that jumps to random positions in array
  4. D.A search that skips every other element each pass

Explanation

Jump search divides a sorted array into blocks of size √n, jumps ahead block by block, then does a linear search within the identified block.

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Searching AlgorithmsEasy

Q13. What is the space complexity of iterative binary search?

  1. A.O(log n)
  2. B.O(n)
  3. C.O(n^2)
  4. D.O(1)✓ Correct

Explanation

Iterative binary search uses a constant amount of extra space (a few variables), giving O(1) space complexity.

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Searching AlgorithmsMedium

Q14. What is exponential search?

  1. A.A search with exponential time complexity overall
  2. B.A search designed for exponentially growing datasets
  3. C.A search that doubles the index then uses binary search✓ Correct
  4. D.A search that uses exponential mathematical functions

Explanation

Exponential search finds the range where the element may exist by doubling the index (1, 2, 4, 8, ...), then performs binary search within that range.

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Searching AlgorithmsMedium

Q15. What is interpolation search?

  1. A.A recursive linear search with memoization cache
  2. B.A search that always checks the middle element
  3. C.A search that uses a hash table for fast lookups
  4. D.A search that estimates position based on value distribution✓ Correct

Explanation

Interpolation search estimates the position of the target using the formula based on the distribution of values, working best on uniformly distributed sorted data.

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Searching AlgorithmsMedium

Q16. What is ternary search?

  1. A.A three-pass sequential linear search method
  2. B.A search specifically for the third element only
  3. C.A search dividing array into three parts each step✓ Correct
  4. D.A search that checks three elements at a time

Explanation

Ternary search divides the sorted array into three parts using two mid-points and eliminates one-third of the array at each step.

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Searching AlgorithmsMedium

Q17. What is the space complexity of recursive binary search?

  1. A.O(n)
  2. B.O(n^2)
  3. C.O(log n)✓ Correct
  4. D.O(1)

Explanation

Recursive binary search uses O(log n) space due to the recursion stack, as it makes at most log n recursive calls.

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Searching AlgorithmsMedium

Q18. Why is binary search preferred over ternary search in practice?

  1. A.Binary search uses less memory per recursive call
  2. B.Binary search is always faster in every case
  3. C.Ternary search does not work on sorted arrays at all
  4. D.Ternary search makes more comparisons per step overall✓ Correct

Explanation

Ternary search makes 2 comparisons per step vs 1 for binary search. Though it has fewer levels (log3 n vs log2 n), the total comparisons are higher.

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Searching AlgorithmsMedium

Q19. What is the time complexity of exponential search?

  1. A.O(n)
  2. B.O(√n)
  3. C.O(n log n)
  4. D.O(log n)✓ Correct

Explanation

Exponential search runs in O(log n) time: O(log i) to find the range and O(log i) for binary search within it, where i is the index of the target.

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Searching AlgorithmsMedium

Q20. In which scenario is linear search more efficient than binary search?

  1. A.When the array has millions of elements
  2. B.Linear search is never more efficient
  3. C.Large sorted arrays with many elements
  4. D.When the array is unsorted and small✓ Correct

Explanation

For small or unsorted arrays, linear search can be more efficient since binary search requires sorting first and has overhead from index calculations.

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Searching AlgorithmsHard

Q21. What is the worst-case time complexity of interpolation search?

  1. A.O(n)✓ Correct
  2. B.O(log n)
  3. C.O(log log n)
  4. D.O(√n)

Explanation

In the worst case (e.g., exponentially distributed data), interpolation search degrades to O(n).

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Searching AlgorithmsHard

Q22. What is the time complexity of the Quickselect algorithm in the average case?

  1. A.O(n log n)
  2. B.O(n^2)
  3. C.O(log n)
  4. D.O(n)✓ Correct

Explanation

Quickselect, based on the partition step of QuickSort, finds the k-th element in O(n) average time by only recursing on one side.

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Searching AlgorithmsHard

Q23. How does binary search handle finding the first occurrence of a duplicate element in a sorted array?

  1. A.Standard binary search always finds the first occurrence automatically
  2. B.Binary search cannot handle duplicate elements in sorted arrays
  3. C.By using linear search after binary search locates any occurrence
  4. D.By modifying binary search to continue searching left after finding it✓ Correct

Explanation

To find the first occurrence, modify binary search so that when the target is found, continue searching in the left half to check for earlier occurrences.

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Searching AlgorithmsHard

Q24. How can you search in a sorted and rotated array?

  1. A.Interpolation search handles rotation natively
  2. B.Only linear search works for this case
  3. C.Modified binary search identifies the sorted half✓ Correct
  4. D.Ternary search is the only viable approach

Explanation

A modified binary search can determine which half of the array is sorted and decide which half to search in, achieving O(log n) time.

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Searching AlgorithmsHard

Q25. What is the time complexity of searching in a balanced binary search tree?

  1. A.O(n log n)
  2. B.O(n)
  3. C.O(log n)✓ Correct
  4. D.O(1)

Explanation

A balanced BST has height O(log n), so searching follows a path from root to leaf in O(log n) time.

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Searching AlgorithmsHard

Q26. What is two-pointer technique in searching?

  1. A.Using two separate arrays for searching data
  2. B.Searching for two distinct elements at once
  3. C.Binary search implemented with two mid points
  4. D.Using two pointers from different positions to converge✓ Correct

Explanation

The two-pointer technique uses two pointers (often from opposite ends) that move toward each other based on conditions, commonly used for pair-sum problems in sorted arrays.

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Searching AlgorithmsHard

Q27. What is the time complexity of searching in a skip list?

  1. A.O(log n) expected✓ Correct
  2. B.O(1) constant
  3. C.O(n) linear
  4. D.O(n log n) total

Explanation

A skip list provides O(log n) expected search time by maintaining multiple levels of linked lists with probabilistic balancing.

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Searching AlgorithmsHard

Q28. What is the time complexity of finding the median of two sorted arrays of sizes m and n?

  1. A.O((m + n) log(m + n))
  2. B.O(m × n)
  3. C.O(m + n)
  4. D.O(log(min(m, n)))✓ Correct

Explanation

Using binary search on the smaller array, the median of two sorted arrays can be found in O(log(min(m, n))) time.

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Searching AlgorithmsHard

Q29. What is Fibonacci search?

  1. A.A search on Fibonacci heap data structures
  2. B.A recursive search with Fibonacci-like recurrence
  3. C.Searching for Fibonacci numbers in an array
  4. D.A search using Fibonacci numbers to divide array✓ Correct

Explanation

Fibonacci search uses Fibonacci numbers to divide the sorted array into sections of unequal sizes, avoiding division operations unlike binary search.

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Searching AlgorithmsHard

Q30. What is the order-statistic problem?

  1. A.Counting elements in a range
  2. B.Finding the median of sorted data
  3. C.Finding the k-th smallest element✓ Correct
  4. D.Sorting all elements into order

Explanation

The order-statistic problem involves finding the k-th smallest (or largest) element in an unsorted collection.

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