Preparing to build a career in Algorithms? This Algorithms MCQs collection is designed to help you test your knowledge of algorithm fundamentals, complexity analysis, arrays, searching, linked lists, stacks, queues, sorting, hashing, trees, heaps, recursion, greedy algorithms, dynamic programming, graphs, shortest paths, and advanced problem-solving techniques.
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1. What is an algorithm?
2. Which property means an algorithm must eventually stop?
3. What does time complexity describe?
4. What does space complexity measure?
5. What does Big-O notation usually describe?
6. Which notation commonly represents an asymptotic lower bound?
7. What does Theta (Θ) notation represent?
8. What is the time complexity of array access by index in a random-access array?
9. What is the usual complexity of scanning an unsorted array to find a value?
10. Why is asymptotic analysis useful?
11. Which structure provides contiguous indexed storage in a typical array implementation?
12. What is the worst-case complexity of linear search?
13. Binary search requires what condition in its standard form?
14. What is binary search complexity on a sorted array?
15. Which technique is commonly used to find a target pair in a sorted array?
16. What is a sliding window useful for?
17. Which algorithm finds maximum subarray sum in O(n)?
18. Which string algorithm uses an LPS/prefix table?
19. What is the key idea of Rabin-Karp?
20. What is the worst-case complexity of naive substring search for text n and pattern m?
21. What does a singly linked-list node typically contain?
22. What is head insertion complexity when the head pointer is known?
23. Why is random access inefficient in a linked list?
24. Which technique detects a linked-list cycle using O(1) extra space?
25. In Floyd’s cycle detection, how do the pointers move?
26. How can a singly linked list be reversed in O(n)?
27. Deleting a known node from a doubly linked list can take what time when its node pointer is available?
28. Which linked-list variant has links in both directions?
29. What is a circular linked list?
30. Which structure is often paired with a hash map for an LRU cache?
31. Which principle does a stack follow?
32. Which principle does a queue follow?
33. Which operation adds an item to a stack?
34. Which operation removes the next item from a queue?
35. Which structure implements function-call recursion?
36. What is a deque?
37. Which problem is commonly solved with a stack?
38. Which traversal commonly uses a queue?
39. What is the push/pop complexity on a stack with sufficient array capacity?
40. What is a monotonic stack commonly used for?
41. What is merge sort worst-case complexity?
42. What is quicksort average-case complexity?
43. What is quicksort worst-case complexity with poor pivots?
44. Which sort repeatedly selects the minimum remaining element?
45. What is insertion sort worst-case complexity?
46. Which simple sort performs well on nearly sorted data?
47. Which sort is generally stable in its standard merge-based implementation?
48. What is the key idea of counting sort?
49. When is radix sort especially useful?
50. Which sort has O(n log n) worst-case time and uses a heap?
51. What is average expected lookup time in a well-designed hash table?
52. What is a hash collision?
53. Which technique stores collisions in buckets?
54. What does open addressing do after a collision?
55. Which probing checks consecutive table positions?
56. What is hash-table load factor?
57. Why can resizing a hash table be expensive?
58. What should a good hash function provide?
59. What is worst-case lookup time with severe hash collisions?
60. Which structure is commonly used for a frequency counter?
61. What is the root of a tree?
62. What is a leaf node?
63. What is the maximum number of children of a binary-tree node?
64. What property defines a binary search tree?
65. Which BST traversal produces sorted keys?
66. What is average search complexity in a reasonably balanced BST?
67. What is worst-case search complexity in an unbalanced BST?
68. What is a tree rotation used for?
69. Which self-balancing BST guarantees O(log n) basic operations?
70. Which self-balancing tree uses node colors?
71. What is the defining property of a min-heap?
72. What is at the root of a max-heap?
73. What is binary-heap insertion complexity?
74. What is min-heap extract-min complexity?
75. What is min-heap minimum lookup without removal?
76. Which algorithm commonly uses a priority queue for closest vertices?
77. What is bottom-up heap construction complexity?
78. Which sort repeatedly extracts elements from a heap?
79. What is a priority queue?
80. Which structure is useful for maintaining the top k largest stream values?
81. What must recursion have to avoid infinite recursion?
82. What is divide and conquer?
83. Which sorting algorithm is classic divide and conquer?
84. Binary search is an example of which strategy?
85. Which recurrence models merge sort?
86. What is tail recursion?
87. Why can deep recursion be problematic?
88. What is memoization?
89. Which problem is commonly solved with backtracking?
90. What happens after a backtracking choice fails?
91. What is the main idea of a greedy algorithm?
92. Which problem is optimally solved by earliest finishing times?
93. Which algorithm builds an MST by selecting cheapest safe edges without cycles?
94. Which algorithm grows an MST from a starting vertex?
95. Which structure helps Kruskal detect whether an edge joins components?
96. Which shortest-path algorithm is greedy for nonnegative edge weights?
97. Why can greedy fail on optimization problems?
98. Which knapsack problem is not generally solved optimally by basic value/weight greedy selection?
99. Which knapsack variant is solved optimally by value/weight greedy selection?
100. What does an exchange argument often prove?
101. Which pair often indicates a DP problem?
102. What is memoization?
103. What is tabulation?
104. Which is a classic DP problem?
105. What does Fibonacci DP avoid?
106. What is 0/1 knapsack DP complexity for n items and capacity W?
107. Which problem asks for the minimum coins needed for a target amount?
108. What is DP state compression?
109. Which sequence problem commonly uses a 2D DP table?
110. What is optimal substructure?
111. Which representation is efficient for sparse graphs?
112. What is adjacency-matrix space complexity for V vertices?
113. Which traversal explores level by level?
114. Which traversal naturally uses a stack or recursion?
115. What is BFS complexity with an adjacency list?
116. What is a directed graph?
117. What is a weighted graph?
118. What is a connected component?
119. Topological ordering is defined for what kind of graph?
120. Which algorithm removes zero-indegree vertices for topological sorting?
121. Which algorithm handles negative edge weights without reachable negative cycles?
122. Which algorithm computes all-pairs shortest paths using DP?
123. What is Floyd-Warshall complexity?
124. What is a negative cycle?
125. Why can standard Dijkstra fail with negative edges?
126. What does an MST provide?
127. How many edges does a spanning tree of V vertices contain?
128. How does an MST differ from a shortest-path tree?
129. Which algorithm is often attractive for edge-heavy graphs using sorted edges?
130. Which algorithm is commonly implemented with a min-priority queue for nonnegative weights?
131. What is the result of x XOR x for any integer x?
132. Which bitwise operation can test whether a bit is set using a mask?
133. What does shifting a nonnegative integer left by one bit generally do?
134. Which algorithm computes the greatest common divisor efficiently using repeated remainders?
135. What is the usual time complexity of the Euclidean GCD algorithm?
136. Which algorithm finds primes up to n efficiently using repeated marking of multiples?
137. What is the time complexity of the Sieve of Eratosthenes in its standard form?
138. Which technique computes a^b efficiently using repeated squaring?
139. What is the main advantage of exponentiation by squaring?
140. Which algorithmic technique is useful for checking whether an integer is a power of two using bits?
141. A service must process a huge stream and keep only the 100 highest scores. What is a practical approach?
142. A graph has millions of edges and must find connected components repeatedly. Which structure is useful for incremental unions?
143. A search feature needs autocomplete by prefix. Which structure is a natural fit?
144. A scheduler repeatedly needs the job with the earliest deadline. Which structure is suitable?
145. A dataset is nearly sorted and must be sorted with simple in-place logic. Which algorithm can be effective?
146. A graph has unweighted edges and needs the shortest number of edges from a source. Which algorithm is appropriate?
147. A graph has nonnegative weighted edges and needs shortest paths from one source. Which algorithm is a common choice?
148. A graph may contain negative edges and must detect a reachable negative cycle. Which algorithm is appropriate?
149. A problem has overlapping subproblems and optimal substructure. Which technique should be evaluated?
150. A database-like workload needs frequent exact key lookup and updates. Which structure is commonly suitable?
