PlacementPrepWhat is the time complexity of binary search on a sorted array of n elements?
Solution
Each step halves the search range.
Answer: (D) O(log n)
Technical · CSE / IT
Algorithms MCQs for placement tests
20 technical questions of moderate difficulty, as asked in campus placement and company tests. Each has a short explanation.
What is the worst-case time complexity of quicksort?
Solution
With poor pivots (for example, an already sorted array with the first element as pivot), quicksort takes O(n²).
Answer: (C) O(n²)
What is the time complexity of merge sort in all cases?
Solution
Merge sort always splits in half and merges in linear time.
Answer: (A) O(n log n)
Which sorting algorithm is stable and takes O(n log n) time in the worst case?
Solution
Merge sort is stable with guaranteed O(n log n); heap sort and quicksort are not stable.
Answer: (D) Merge sort
What is the best-case time complexity of bubble sort with an early-exit check?
Solution
On an already sorted array, one pass with no swaps ends the algorithm.
Answer: (C) O(n)
Which algorithm finds the shortest paths from one source in a graph with non-negative edge weights?
Solution
Dijkstra's algorithm computes single-source shortest paths when weights are non-negative.
Answer: (B) Dijkstra's algorithm
Which algorithm can handle negative edge weights when finding single-source shortest paths?
Solution
Bellman-Ford works with negative weights and can detect negative cycles.
Answer: (A) Bellman-Ford algorithm
Kruskal's and Prim's algorithms are used to find:
Solution
Both build a minimum spanning tree of a weighted graph.
Answer: (D) A minimum spanning tree
Which design technique solves problems by storing the results of overlapping subproblems?
Solution
Dynamic programming saves subproblem results to avoid recomputation.
Answer: (C) Dynamic programming
Merge sort is an example of which design technique?
Solution
It divides the array, sorts halves and combines them.
Answer: (D) Divide and conquer
What is the time complexity of the naive recursive Fibonacci function?
Solution
Each call makes two more calls, giving exponential growth.
Answer: (B) O(2n)
How many comparisons does linear search need in the worst case for n elements?
Solution
In the worst case, every element is checked.
Answer: (C) n
Topological sorting is possible only for:
Solution
A cycle makes a valid ordering impossible.
Answer: (A) Directed acyclic graphs
The 0/1 knapsack problem is typically solved optimally using:
Solution
The greedy approach works only for the fractional knapsack; 0/1 needs dynamic programming.
Answer: (B) Dynamic programming
What is the space complexity of merge sort on an array?
Solution
Merging needs an auxiliary array of size n.
Answer: (A) O(n)
Which of these grows the fastest as n increases?
Solution
Exponential growth eventually exceeds any polynomial.
Answer: (A) O(2n)
Using binary search on a sorted array of 1024 elements, what is the maximum number of comparisons needed?
Solution
⌊log₂ 1024⌋ + 1 = 10 + 1 = 11 comparisons in the worst case.
Answer: (B) 11
Which sorting algorithm repeatedly selects the smallest remaining element and places it next?
Solution
Selection sort selects the minimum of the unsorted part in each pass.
Answer: (B) Selection sort
Insertion sort performs best when the input is:
Solution
On nearly sorted data, few shifts are needed, giving close to O(n).
Answer: (A) Already nearly sorted
The N-Queens problem is commonly solved using:
Solution
Queens are placed one by one, and the algorithm backtracks when a placement fails.
Answer: (A) Backtracking
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