Data Structures: 5-Chapter Comprehensive Practice & 75 Verified MCQs

Question 1

Which data structure operates on a Last-In, First-Out (LIFO) principle and is fundamentally used for function call runtime stacks?

Accepted Answer

B. Stack. A stack enforces a Last-In, First-Out (LIFO) discipline where the most recently inserted item is the first one retrieved. Compilers and OS kernels utilize the call stack to manage stack frames, local variables, and return addresses during nested function calls.

Question 2

What is the equivalent postfix notation (Reverse Polish Notation) for the infix expression: (A + B) * (C - D)?

Accepted Answer

A. A B + C D - *. In infix notation, parentheses dictate order. (A + B) converts to 'A B +', and (C - D) converts to 'C D -'. Multiplying the two sub-expressions places the operator at the end: 'A B + C D - *'.

Question 3

In a circular queue implemented using a fixed-size array of capacity N, what formula computes the next insertion index for the 'rear' pointer?

Accepted Answer

B. rear = (rear + 1) % N. The modulo arithmetic 'rear = (rear + 1) % N' ensures that once the rear pointer reaches the end of the array (index N - 1), incrementing it wraps around smoothly to index 0, enabling full reuse of deallocated space from earlier dequeues.

Question 4

What is the time complexity of detecting a cycle in a singly linked list using Floyd’s Cycle-Finding Algorithm (Tortoise and Hare)?

Accepted Answer

B. O(N) time and O(1) auxiliary space. Floyd's algorithm uses two pointers moving at different speeds: a slow pointer (1 node per step) and a fast pointer (2 nodes per step). If a loop exists, the relative distance between them decreases by 1 on every iteration, guaranteeing they meet in at most O(N) steps while requiring only O(1) extra memory pointers.

Question 5

Why does iterating through an array generally exhibit significantly faster wall-clock execution time than iterating through an identical length linked list on modern CPU hardware?

Accepted Answer

B. Contiguous array memory leverages CPU cache lines and spatial locality, whereas linked lists trigger frequent cache misses due to pointer chasing across scattered heap allocations.. CPUs fetch data from main memory into L1/L2/L3 caches in blocks called cache lines (typically 64 bytes). Because arrays are contiguous, fetching one element pre-loads adjacent elements. Linked lists allocate individual nodes dynamically on the heap, scattering memory across random addresses and causing costly CPU pipeline stalls on cache misses.

Question 6

What is the minimum number of queues required to implement a functional Last-In, First-Out (LIFO) Stack?

Accepted Answer

A. 1 (using recursion or rotation) or 2 standard FIFO queues. A stack can be implemented using two FIFO queues by either making push costly (enqueuing into an auxiliary queue, transferring all items from the primary queue, and swapping) or making pop costly. It can also be implemented using a single queue by rotating elements (dequeuing and re-enqueuing size - 1 times).

Question 7

In a doubly linked list, what operations are required to delete a given node 'curr' (assuming curr is neither head nor tail)?

Accepted Answer

A. curr.prev.next = curr.next; curr.next.prev = curr.prev; free(curr);. To bypass 'curr', the node before it ('curr.prev') must link its next pointer to the node after it ('curr.next'). Simultaneously, the node after it ('curr.next') must update its prev pointer back to 'curr.prev'. Finally, curr's allocated memory is safely released.

Question 8

What is the optimal worst-case time complexity of finding the 'Next Greater Element' for all elements in an array of size N using a Monotonic Stack?

Accepted Answer

C. O(N). A monotonic decreasing stack maintains elements in order. While iterating through the array, each element is pushed onto the stack exactly once, and popped at most once. Because the total number of push and pop operations across the entire algorithm is bounded by 2N, the amortized time complexity is strictly linear O(N).

Question 9

What is the primary operational advantage of a Double-Ended Queue (Deque) over a standard Queue?

Accepted Answer

A. Deques allow insertion and deletion at both the front and rear ends in O(1) time.. A deque (double-ended queue) supports four primary operations: push_front, pop_front, push_back, and pop_back—all operating in O(1) constant time. This flexibility enables algorithms like sliding window minimum/maximum.

Question 10

When evaluating the postfix expression '5 3 + 8 2 - *' using an operand stack, what is the final evaluated result?

Accepted Answer

A. 48. 1) Push 5, push 3. 2) Encounter '+': pop 3 and 5, compute 5 + 3 = 8, push 8. 3) Push 8, push 2. 4) Encounter '-': pop 2 and 8, compute 8 - 2 = 6, push 6. 5) Encounter '*': pop 6 and 8, compute 8 * 6 = 48. Final result = 48.

Question 11

In a singly linked list, which operation cannot be performed in O(1) time even if a pointer to the target node is provided?

Accepted Answer

A. Deleting the last node (tail) of the list. Even with a direct pointer to the tail node, updating the list requires setting the second-to-last node's next pointer to NULL. Because singly linked lists have only unidirectional links, finding the preceding node demands an O(N) traversal from head.

Question 12

What problem occurs when implementing a queue using a simple, non-circular array where 'front' and 'rear' continuously increment?

Accepted Answer

B. False overflow: the queue appears full because rear reaches the array end, even if front has advanced leaving empty slots at the beginning.. In a linear array queue, every dequeue increments 'front', and every enqueue increments 'rear'. Once 'rear == capacity - 1', no new items can be added despite unused memory at indices before 'front'. This is 'false overflow', solved completely by circular queues.

Question 13

How does reversing a singly linked list iteratively in O(N) time and O(1) space operate?

Accepted Answer

B. It maintains three pointers (prev, curr, next), redirecting curr.next to prev at each step.. The standard iterative reversal uses three pointers: 'prev' (initialized to NULL), 'curr' (initialized to head), and 'next'. In each iteration, 'next = curr.next' saves the remainder of the list, 'curr.next = prev' reverses the link, 'prev = curr' advances the previous pointer, and 'curr = next' advances to the next node.

Question 14

What data structure is ideally suited to check for balanced brackets and nested parentheses in compilers and syntax linters?

Accepted Answer

B. Stack. Because brackets must close in reverse order of opening (the innermost bracket closes first), a stack perfectly models nested parentheses: opening brackets ('(', '[', '{') are pushed onto the stack, and closing brackets pop the top element to verify matching bracket types.

Question 15

What is the auxiliary space complexity of recursively reversing a singly linked list of N nodes?

Accepted Answer

B. O(N) due to call stack frames. Although recursive reversal requires no explicit auxiliary collections, the runtime call stack allocates a stack frame for every recursive call until reaching the base case (the last node). For a list of N elements, N frames reside on the stack, consuming O(N) auxiliary space.

Question 16

In a singly linked list with head pointer only, what is the time complexity to insert a new node at the beginning vs at the end?

Accepted Answer

A. O(1) at beginning, O(N) at end. Inserting at head requires updating the new node's next pointer and head in O(1) time. Inserting at end without a tail pointer requires traversing all N nodes from head to reach the last node, taking O(N) time.

Question 17

What is the primary architectural feature of a Circular Singly Linked List?

Accepted Answer

B. The next pointer of the last node points back to the head node instead of holding NULL.. In a circular linked list, no node points to NULL; the final node links back to the head. This enables continuous cyclical round-robin scheduling algorithms.

Question 18

What is the memory overhead of a Doubly Linked List node compared to a Singly Linked List node on a 64-bit architecture?

Accepted Answer

B. 8 additional bytes per node for the backward (prev) pointer.. Each node in a doubly linked list stores an additional 'prev' pointer (8 bytes on 64-bit CPUs), allowing bidirectional traversal at the expense of increased memory footprint.

Question 19

How does Floyd's Cycle Detection algorithm identify the starting node of a cycle after detecting that a loop exists?

Accepted Answer

B. Reset one pointer to head and advance both pointers at 1 step per iteration; their meeting point is the exact cycle start.. Mathematically, the distance from head to cycle start equals the distance from the initial meeting point to cycle start along the perimeter. Moving one pointer to head and stepping both at speed 1 guarantees they meet at the cycle entry node.

Question 20

What is a 'Skip List' data structure?

Accepted Answer

B. A probabilistic hierarchy of linked lists layered with express lanes that achieves O(log N) search, insertion, and deletion.. Invented by William Pugh, Skip Lists layer linked lists with probabilistic promotion. Higher levels skip over multiple items, providing O(log N) expected search and update performance comparable to balanced trees, with simpler concurrent locking (used in Redis Sorted Sets).

Question 21

What is the time complexity to merge two sorted singly linked lists containing M and N elements respectively into a single sorted list?

Accepted Answer

B. O(M + N). Merging requires comparing the current heads of both lists and advancing the smaller element's pointer. Every element is examined once, yielding O(M + N) linear time with O(1) auxiliary pointer space.

Question 22

What is the advantage of using a Sentinel (Dummy) Head Node in linked list implementations?

Accepted Answer

B. Eliminates special-case edge handling for operations at the head of the list (e.g. inserting or deleting the first node).. A dummy head node ensures that every real data node has a preceding node, eliminating conditional checks like 'if (head == NULL)' or 'if (curr == head)'.

Question 23

How can you find the middle element of a singly linked list in a single pass without computing total length first?

Accepted Answer

B. Use two pointers (slow and fast); advance fast by 2 nodes and slow by 1 node; when fast reaches the end, slow is at the middle.. Because the fast pointer moves at twice the speed of the slow pointer, when the fast pointer reaches the end (NULL or last node), the slow pointer has traversed exactly half the distance, landing on the middle element in O(N) time and O(1) space.

Question 24

What happens if you attempt to traverse a circular linked list using standard 'while (ptr != NULL)' loop condition?

Accepted Answer

B. Infinite loop because the tail node points to head and never evaluates to NULL.. Because a circular linked list has no NULL terminator, 'ptr != NULL' is always true, trapping execution in an infinite traversal loop.

Question 25

In an unrolled linked list, what does each node store?

Accepted Answer

B. An array of multiple elements (e.g. 16 or 32 items) and a next pointer, combining cache locality of arrays with flexible allocation of linked lists.. Unrolled linked lists store a small array of elements in each node. This dramatically improves CPU cache performance by keeping data contiguous while preserving O(1) node insertion/deletion.

Question 26

What is the time complexity of deleting a node at index K from a singly linked list of size N?

Accepted Answer

B. O(K) to traverse to the K-th node. Finding the (K-1)th node requires traversing K steps from head, which takes O(K) time. Once reached, updating the link takes O(1) time.

Question 27

What is an XOR Linked List?

Accepted Answer

B. A memory-efficient doubly linked list where each node stores the bitwise XOR of the previous and next node memory addresses in a single pointer field.. In an XOR linked list, 'node->npx = prev ^ next'. When traversing forward, 'next = prev ^ node->npx'; traversing backward, 'prev = next ^ node->npx'. This halves pointer memory consumption.

Question 28

How do you detect if two singly linked lists intersect and merge into a common tail?

Accepted Answer

B. Traverse both lists to their tails; if the tail node pointers are identical, they intersect; calculate length difference to find intersection node.. If two lists intersect, they share the identical tail node pointer. By computing lengths L1 and L2 and advancing the longer list by |L1 - L2| steps, advancing both pointers simultaneously will meet at the exact intersection node.

Question 29

What is the space complexity of reversing a linked list of size N using an iterative approach?

Accepted Answer

B. O(1). Iterative reversal uses three pointer variables (prev, curr, next) to reverse links in-place, requiring strictly O(1) auxiliary space.

Question 30

Can binary search be implemented efficiently on a standard singly linked list?

Accepted Answer

B. No, because linked lists do not support O(1) random access; finding the midpoint takes O(N) time, making the overall search O(N).. Binary search relies on O(1) random indexing to jump to midpoints. In a linked list, locating the middle node requires linear traversal, making binary search O(N), offering no asymptotic improvement over linear search.

Question 31

What is the maximum number of nodes in a binary tree of depth (height) H (where a tree with 1 node has H = 1)?

Accepted Answer

B. 2^H - 1. Level 1 has 2^0 = 1 node; level 2 has 2^1 = 2 nodes; level H has 2^(H-1) nodes. Summing the geometric series 1 + 2 + 4 + ... + 2^(H-1) yields (2^H - 1) nodes.

Question 32

Which binary tree traversal algorithm visits nodes in strictly ascending sorted order when applied to a Binary Search Tree (BST)?

Accepted Answer

B. In-order Traversal (Left, Root, Right). In a BST, all keys in the left subtree are smaller than the root, and all keys in the right subtree are greater. In-order traversal visits Left -> Root -> Right, which naturally outputs keys in ascending sorted order.

Question 33

What is the balance factor of a node in an AVL Tree, and what are its permitted values?

Accepted Answer

B. Height(Left Subtree) - Height(Right Subtree); permitted values: -1, 0, +1. An AVL tree is a strictly self-balancing BST where the balance factor of every node is defined as Height(Left) - Height(Right). If balance factor deviates from {-1, 0, +1}, tree rotations (LL, RR, LR, RL) restore balance.

Question 34

What is the worst-case time complexity of searching for an element in an unbalanced (degenerate) Binary Search Tree?

Accepted Answer

B. O(N) when the tree degenerates into a linear linked list. If elements are inserted in already sorted order (e.g. 1, 2, 3, 4, 5), an unbalancing BST degenerates into a skewed line of right nodes, making search degrade to linear O(N) scanning.

Question 35

What tree rotation is performed when an AVL tree becomes unbalanced due to an insertion into the right subtree of the left child (LR Case)?

Accepted Answer

B. Left-Right Double Rotation (Left rotation on left child, then Right rotation on root). The LR imbalance is resolved with a double rotation: first a Left rotation on the left child node converts the shape to LL, followed by a Right rotation on the parent node.

Question 36

What is a 'Full Binary Tree'?

Accepted Answer

A. A tree where every node has either 0 or exactly 2 children.. A full (or strictly) binary tree is a tree in which every node has either zero or two children. No node has exactly one child.

Question 37

In a Red-Black Tree, what is the maximum possible height of a tree with N internal nodes?

Accepted Answer

B. 2 * log2(N + 1). Red-Black properties mandate that no red node can have a red child and every path from root to leaf has the same black-height. This ensures the longest path is at most twice the shortest path: Height <= 2 * log2(N + 1).

Question 38

How can you reconstruct a unique binary tree given its traversal sequences?

Accepted Answer

B. In-order traversal paired with either Pre-order or Post-order traversal is required.. In-order traversal is mandatory because it separates the left subtree from the right subtree. Pre-order (or Post-order) identifies the root node. Together, In-order and Pre-order uniquely reconstruct any binary tree.

Question 39

What is the Lowest Common Ancestor (LCA) of two nodes u and v in a Binary Search Tree?

Accepted Answer

B. The first node encountered during top-down traversal whose key value lies between u and v (min(u,v) <= key <= max(u,v)).. In a BST, starting from root: if both u and v are smaller than curr, LCA is in left subtree; if both are greater, LCA is in right subtree. The first node where the paths diverge (one on left, one on right, or curr equals u or v) is the LCA in O(H) time.

Question 40

What is a 'Trie' (Prefix Tree) primarily optimized for?

Accepted Answer

B. Fast retrieval and prefix-matching of strings with O(L) search time where L is string length, independent of the number of keys stored.. A Trie stores strings character by character along edges. Looking up a string of length L takes O(L) time regardless of whether the Trie holds 100 or 10,000,000 words, making it ideal for autocomplete and spell checkers.

Question 41

What is the diameter of a binary tree?

Accepted Answer

B. The length of the longest path between any two nodes in the tree (which may or may not pass through the root).. The diameter (width) of a tree is the maximum number of edges (or nodes) on the longest path between any two leaf nodes in the tree. It is computed in O(N) using post-order depth calculations.

Question 42

What is a B-Tree, and why is it preferred over BSTs for database storage engines on disk?

Accepted Answer

B. B-Trees are self-balancing multi-way search trees with high branching factor (fan-out), minimizing slow disk I/O seeks by fitting thousands of keys into single disk blocks.. Disk seeks take milliseconds, while CPU cycles take nanoseconds. B-Trees have broad fan-out (e.g. 512–1024 children per node), keeping tree height very low (3–4 levels for billions of rows) so each search needs only 3–4 disk block reads.

Question 43

What is the in-order successor of a node in a Binary Search Tree?

Accepted Answer

B. The node with the smallest key strictly greater than the given node (the leftmost child in its right subtree).. If the node has a right subtree, the in-order successor is the minimum node in that right subtree (walk right, then walk left as far as possible). If no right subtree exists, it is the lowest ancestor whose left child is also an ancestor of the node.

Question 44

What is a Segment Tree used for in algorithmic programming?

Accepted Answer

B. Answering range queries (e.g. range sum, range minimum) and performing point updates in O(log N) time.. A Segment Tree stores precomputed intervals in a binary tree hierarchy, allowing arbitrary range queries (sum, min, max, gcd) and updates in O(log N) time on arrays of size N.

Question 45

What is a Fenwick Tree (Binary Indexed Tree)?

Accepted Answer

B. An array-backed structure that computes prefix sums and updates elements in O(log N) time using bitwise operations (i &#038; (-i)).. A Fenwick tree stores cumulative frequencies in an array where index isolation using the lowest set bit '(i &#038; -i)' enables prefix sum queries and point updates in O(log N) time with minimal O(N) space and low constant factors.

Question 46

In a zero-indexed array representation of a binary heap, what are the index formulas for the left child, right child, and parent of element at index i?

Accepted Answer

A. Left: 2*i + 1, Right: 2*i + 2, Parent: (i - 1) // 2. Zero-indexed binary heap array layout: parent of i is at (i - 1) // 2; left child is at (2 * i + 1); right child is at (2 * i + 2). This allows complete binary trees to be stored in contiguous arrays without pointer overhead.

Question 47

What is the time complexity to build a binary heap from an arbitrary unsorted array of N elements using the bottom-up heapify algorithm?

Accepted Answer

B. O(N) linear time. Bottom-up heap construction runs heapify starting from the lowest internal nodes up to the root. Summing the work across all levels: N/4*(1) + N/8*(2) + N/16*(3) ... converges mathematically to O(N) linear time, unlike inserting N elements one-by-one which takes O(N log N).

Question 48

What is the time complexity of extracting the minimum element (extract_min) from a Min-Heap of size N?

Accepted Answer

B. O(log N). Reading the min element takes O(1) time at root (index 0). But replacing the root with the last leaf and running sift-down (heapify) to restore heap order takes O(log N) time proportional to tree height.

Question 49

What collision resolution technique in hash tables chains colliding elements into a linked list or tree attached to each bucket?

Accepted Answer

B. Separate Chaining. Separate Chaining maintains an independent linked list (or balanced tree, as in Java 8 HashMap) at each bucket index. Colliding keys are simply appended to the list at that bucket.

Question 50

What is 'Primary Clustering' in open-addressing hash tables, and which probing technique is most vulnerable to it?

Accepted Answer

B. The tendency for occupied hash slots to form long contiguous blocks, increasing average probe sequence lengths; caused by Linear Probing.. Linear probing checks slots sequentially: (h(k) + i) % m. As occupied slots cluster together, any key hashing into the cluster extends it further, dramatically degrading lookup time to O(N).

Question 51

What is the 'Load Factor' (α) of a hash table, and what typical threshold triggers dynamic resizing?

Accepted Answer

B. α = Number of stored keys (n) / Number of allocated buckets (m); threshold typically 0.70 to 0.75. Load Factor α = n / m measures how full the table is. When α exceeds 0.75 in open addressing or separate chaining, the table allocates a doubled capacity array and rehashes all elements to maintain O(1) average lookup speed.

Question 52

What is a 'Bloom Filter' data structure?

Accepted Answer

B. A space-efficient probabilistic data structure that tests set membership: it can return false positives, but NEVER returns false negatives.. A Bloom filter uses a bit array and k independent hash functions. If any hashed bit is 0, the item is definitely NOT in the set (no false negatives). If all bits are 1, the item is PROBABLY in the set (possible false positive due to hash overlaps).

Question 53

What is 'Consistent Hashing', and where is it fundamentally utilized?

Accepted Answer

B. A hashing technique where keys and nodes are mapped to a circular ring, minimizing key remapping to K/N items when servers are added or removed in distributed caches.. In standard modulo hashing 'hash(k) % N', adding a server invalidates nearly all cached keys. Consistent Hashing maps both keys and servers to a 360-degree ring (0 to 2^32-1), so adding or removing a node reallocates only keys belonging to adjacent partitions.

Question 54

What is a 'Fibonacci Heap' and what is its theoretical asymptotic advantage over a Binary Heap?

Accepted Answer

B. It supports decrease-key and insert operations in O(1) amortized constant time (compared to O(log N) in binary heaps), speeding up Dijkstra's shortest path algorithm to O(E + V log V).. Fibonacci heaps delay tree consolidation until extract_min is called. This lazy structure allows insert, union, and decrease-key to execute in O(1) amortized time, improving Dijkstra's algorithm to O(E + V log V).

Question 55

How does Double Hashing compute the probe sequence for collision resolution?

Accepted Answer

B. (hash1(k) + i * hash2(k)) % TableSize (for i = 0, 1, 2...). Double hashing uses two independent hash functions: hash1 computes the initial index, and hash2 computes the step size. Because the step size depends on the key value, it avoids both primary and secondary clustering.

Question 56

What is the worst-case time complexity of Heapsort on an array of N elements?

Accepted Answer

B. O(N log N). Building the heap takes O(N) time. Then N extract_max operations are performed, each taking O(log N) time to sift down. Total time is strictly O(N log N) in all cases (best, average, worst) with O(1) in-place auxiliary space.

Question 57

What data structure does an LRU (Least Recently Used) Cache combine to achieve O(1) get() and O(1) put() operations?

Accepted Answer

B. Hash Map and Doubly Linked List. The Hash Map maps keys to nodes in O(1) time. The Doubly Linked List maintains usage order: accessing or adding an item moves its node to the head in O(1) time; evicting the least recently used item removes the tail node in O(1) time.

Question 58

What is a 'Cuckoo Hash Table'?

Accepted Answer

B. An open-addressing structure with 2 hash functions that achieves guaranteed O(1) worst-case lookup time by displacing existing keys to alternate locations.. Cuckoo hashing uses two hash functions h1 and h2. A key is stored in either h1(k) or h2(k). If both slots are occupied, the newly inserted key evicts the existing occupant to its alternate slot (like a cuckoo bird pushing eggs). Lookups check at most 2 locations, guaranteeing O(1) worst-case search.

Question 59

In a Max-Heap, where is the minimum element located?

Accepted Answer

B. In one of the leaf nodes (indices ⌊N/2⌋ to N - 1).. In a Max-Heap, every parent is greater than or equal to its children. Therefore, the minimum element cannot have children and must reside in one of the leaf nodes, which occupy indices from ⌊N/2⌋ to N - 1.

Question 60

What property must a cryptographic hash function satisfy to prevent pre-image attacks?

Accepted Answer

B. Given a hash value h, it must be computationally infeasible to find any message m such that hash(m) = h (One-way property).. Pre-image resistance (one-wayness) ensures that given an output hash, reversing it to discover the original input is computationally impossible.

Question 61

What is the time complexity of Breadth-First Search (BFS) and Depth-First Search (DFS) on a graph with V vertices and E edges represented using an Adjacency List?

Accepted Answer

B. O(V + E). In an adjacency list representation, BFS and DFS visit every vertex once (O(V)) and inspect each directed edge once (or undirected edge twice) (O(E)). Total time complexity is strictly linear: O(V + E).

Question 62

Which data structure is fundamentally used to implement Breadth-First Search (BFS) vs Depth-First Search (DFS)?

Accepted Answer

A. BFS uses a Queue (FIFO); DFS uses a Stack (LIFO) or system call stack recursion.. BFS explores neighbors level-by-level using a FIFO Queue. DFS explores deep along a single branch using a LIFO Stack (or recursive function calls).

Question 63

Why does Dijkstra's Single-Source Shortest Path algorithm fail or produce incorrect results on graphs with negative edge weights?

Accepted Answer

B. Dijkstra uses a greedy approach assuming that once a vertex distance is finalized, no shorter path can be found; negative edges violate this monotonic property.. Dijkstra marks a node's distance as finalized as soon as it is extracted from the min-priority queue, assuming edge additions only increase distance. A negative edge can retroactively provide a cheaper path to an already finalized node.

Question 64

What is the time complexity of Dijkstra’s Algorithm implemented with a Min-Heap (Binary Heap) on a graph with V vertices and E edges?

Accepted Answer

B. O((V + E) log V). Each vertex is extracted from the heap once (V * log V). In the worst case, each edge update (relaxation) triggers a decrease-key/insertion into the heap (E * log V). Total time is O((V + E) log V).

Data Structures: 5-Chapter Comprehensive Practice & 75 Verified MCQs

Data Structures: 5-Chapter Comprehensive Practice & 75 Verified MCQs

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