DSA FAQ 150
150 frequently-asked data structures, algorithms, and CS-fundamentals interview questions with concise answers, grouped by topic: complexity, arrays and strings, linked lists, stacks and queues, trees, graphs, dynamic programming, object-oriented programming, operating systems, databases, and networking. Free to read, no signup required.
What does Big-O notation describe?
Big-O describes how an algorithm's running time or memory use grows as the input size grows, focusing on the worst case and dropping constants and lower-order terms.
What is the difference between O(n) and O(log n)?
O(n) time grows in direct proportion to input size, while O(log n) time grows much more slowly because the algorithm shrinks the problem at each step, like binary search halving the range.
What is the time complexity of accessing an array element by index?
O(1). Arrays store elements in contiguous memory, so the address of any index is computed directly.
What is the time complexity of searching an unsorted array?
O(n) in the worst case, since every element may need to be checked.
What is amortized time complexity?
The average time per operation over a sequence of operations, even if a single operation is occasionally expensive, as with dynamic array resizing during append.
What is the difference between time complexity and space complexity?
Time complexity measures how runtime scales with input size; space complexity measures how memory use scales with input size, including any extra structures the algorithm allocates.
Why do we usually care about worst-case complexity rather than best-case?
Worst-case complexity gives a reliable upper bound on how an algorithm will behave, which matters more for planning and guarantees than a best case that might rarely occur.
What is the time complexity of a nested loop over the same array?
O(n squared) in general, since the inner loop runs n times for each of the n iterations of the outer loop.
What is the time complexity of inserting an element at the beginning of an array?
O(n), because every existing element has to shift over by one position.
How do you reverse a string in place?
Use two pointers starting at each end, swapping characters and moving inward until they meet.
What is a sliding window and when is it useful?
A technique that maintains a moving subrange of a sequence and expands or shrinks it as it scans, useful for problems about contiguous subarrays or substrings such as longest substring without repeats.
How do you detect if two strings are anagrams?
Sort both strings and compare, or count character frequencies with a hash map and check they match, in O(n log n) or O(n) respectively.
What is the two-pointer technique?
Using two indices that move through a sequence, often from opposite ends or at different speeds, to avoid nested loops in problems like pair-sum or palindrome checks.
How is a dynamic array (like a Python list or Java ArrayList) different from a fixed-size array?
A dynamic array resizes itself by allocating a larger underlying array and copying elements over once it runs out of capacity, giving amortized O(1) append instead of a fixed size.
What is the difference between a shallow copy and a deep copy of an array?
A shallow copy duplicates the array structure but keeps references to the same nested objects, while a deep copy recursively duplicates the nested objects too.
How do you find the maximum subarray sum?
Kadane's algorithm scans once, keeping a running sum that resets to zero whenever it goes negative, and tracks the best sum seen, all in O(n).
What is string immutability and why does it matter?
In languages like Java and Python, strings cannot be modified after creation. Every "modification" creates a new string, which affects performance in loops that build strings repeatedly.
How do you check if a string is a palindrome efficiently?
Compare characters from both ends moving inward with two pointers, stopping early on a mismatch, in O(n) time and O(1) extra space.
What is the difference between a substring and a subsequence?
A substring is a contiguous block of characters, while a subsequence keeps relative order but does not need to be contiguous.
How would you find all pairs in an array that sum to a target value?
Use a hash set to track seen values while scanning once, checking for each element whether target minus that element has already been seen, giving O(n) time.
What causes an off-by-one error in array indexing?
Miscounting the loop boundary, commonly using <= instead of < against a length, which reads or writes one past the valid range.
How do you rotate an array by k positions efficiently?
Reverse the whole array, then reverse the first k elements and the remaining n-k elements separately, which rotates it in O(n) time and O(1) extra space.
What is the difference between a singly and a doubly linked list?
A singly linked list stores a pointer to the next node only, while a doubly linked list also stores a pointer to the previous node, allowing traversal in both directions at the cost of extra memory.
How do you detect a cycle in a linked list?
Floyd's tortoise-and-hare algorithm uses two pointers moving at different speeds; if they ever meet, a cycle exists, in O(n) time and O(1) space.
What is the time complexity of inserting a node at the head of a linked list?
O(1), since it only requires updating a couple of pointers, unlike an array where the same operation is O(n).
How do you reverse a singly linked list?
Walk through the list once, reversing each node's next pointer to point at the previous node, tracking the previous, current, and next nodes as you go.
What is a sentinel or dummy node used for?
A placeholder node before the real head that simplifies edge cases like inserting or deleting the first element, avoiding special-case code for an empty list.
How do you find the middle node of a linked list in one pass?
Use a slow and a fast pointer, moving the fast pointer two steps for every one step of the slow pointer; when the fast pointer reaches the end, the slow pointer is at the middle.
Why is random access slower on a linked list than an array?
A linked list has no contiguous memory layout, so reaching the nth node requires walking node by node from the head, giving O(n) access instead of an array's O(1).
How would you merge two sorted linked lists?
Walk both lists with two pointers, repeatedly attaching the smaller current node to the result and advancing that pointer, then attach whatever remains of the longer list.
What is the core property of a stack?
Last in, first out (LIFO). The most recently added element is the first one removed.
What is the core property of a queue?
First in, first out (FIFO). The earliest added element is the first one removed.
How would you implement a queue using two stacks?
Push new elements onto an "in" stack; when dequeuing, if the "out" stack is empty, pop everything from "in" onto "out" and pop from there, giving amortized O(1) operations.
What is a common use case for a stack?
Matching parentheses or brackets, undo functionality, and tracking function calls during recursion (the call stack).
What is a monotonic stack and when is it used?
A stack kept in strictly increasing or decreasing order, used to solve problems like "next greater element" or daily temperatures in O(n) instead of a naive O(n squared).
What is the difference between a queue and a deque?
A queue only allows insertion at one end and removal at the other, while a deque (double-ended queue) allows insertion and removal at both ends.
How is a stack typically implemented in memory?
With a dynamic array or linked list, tracking a "top" pointer or index; push and pop both operate at that end in O(1).
What is a priority queue, and how does it differ from a normal queue?
A priority queue serves elements by priority rather than insertion order, usually backed by a heap, so the highest (or lowest) priority element is always removed first regardless of when it was added.
What are the two essential parts of a correct recursive function?
A base case that stops the recursion, and a recursive case that reduces the problem and calls itself on the smaller version.
What is a stack overflow in the context of recursion?
When recursive calls go too deep without reaching a base case, exhausting the call stack's memory and crashing the program.
What is the difference between backtracking and plain recursion?
Backtracking explores a solution space step by step and explicitly undoes ("backtracks") a choice when it leads to a dead end, while plain recursion just breaks a problem into subproblems without that undo step.
What is memoization and how does it help recursive algorithms?
Caching the results of expensive recursive calls keyed by their inputs, so repeated calls with the same arguments return instantly instead of recomputing, turning exponential recursion into polynomial time.
How does recursion relate to the call stack?
Each recursive call pushes a new frame onto the call stack holding its local variables and return address; frames pop off as calls return, unwinding back to the original call.
What is tail recursion?
A recursive call that is the very last operation in a function, which some languages or compilers can optimize into a loop to avoid growing the call stack.
How would you generate all subsets of a set using backtracking?
At each element, recursively branch into two choices, include it or exclude it, and collect the current subset at the leaves of that recursion tree.
What is the average time complexity of quicksort?
O(n log n) on average, though it degrades to O(n squared) in the worst case on already-sorted or adversarial input without good pivot selection.
What is the time complexity of merge sort, and why is it stable?
O(n log n) in all cases. It is stable because when merging two sorted halves, elements from the left half are taken first whenever values are equal, preserving their original relative order.
What is the difference between a stable and an unstable sort?
A stable sort preserves the relative order of elements that compare as equal; an unstable sort makes no such guarantee.
What is binary search and what does it require?
An O(log n) algorithm that repeatedly halves a search range by comparing the target to the middle element. It requires the data to be sorted.
What is the time complexity of binary search?
O(log n), since each comparison eliminates half of the remaining elements.
When would you choose insertion sort over quicksort?
For small or nearly-sorted inputs, where insertion sort's low overhead and O(n) best case on nearly sorted data beat quicksort's higher constant factor.
What is the difference between comparison-based sorting and counting/radix sort?
Comparison-based sorts (like quicksort, merge sort) are bounded by O(n log n) because they compare elements pairwise; counting and radix sort avoid comparisons entirely and can reach O(n) for suitable data like bounded-range integers.
What is heap sort and what is its time complexity?
An in-place sort that builds a max-heap and repeatedly extracts the maximum element, running in O(n log n) time with O(1) extra space.
How does binary search adapt to finding the first or last occurrence of a value in a sorted array with duplicates?
Instead of stopping at the first match, keep narrowing the search range further in one direction after a match to find the boundary, still in O(log n).
What is the time complexity of building a hash-based frequency count for search purposes?
O(n) to build the map, then O(1) average-case lookup per query afterward.
What is a binary search tree?
A binary tree where every node's left subtree contains only smaller values and its right subtree contains only larger values, enabling O(log n) average search, insert, and delete when balanced.
What is the difference between preorder, inorder, and postorder traversal?
Preorder visits root then left then right; inorder visits left then root then right (which yields sorted order for a BST); postorder visits left then right then root.
What is the difference between depth-first and breadth-first tree traversal?
Depth-first goes as deep as possible down one branch before backtracking (using a stack or recursion); breadth-first visits level by level (using a queue).
How do you check if a binary tree is balanced?
Recursively compute each subtree's height, and at every node confirm the height difference between left and right subtrees is at most 1, failing fast if any subtree is already unbalanced.
What is the worst-case time complexity of search in an unbalanced BST?
O(n), because a degenerate BST can devolve into a linked list, for example when values are inserted in sorted order.
What is a self-balancing binary search tree?
A BST that automatically maintains a bounded height through rotations after insertions and deletions, such as an AVL tree or a red-black tree, keeping operations at O(log n).
How do you find the lowest common ancestor of two nodes in a BST?
Starting at the root, move left if both target values are smaller than the current node, right if both are larger, and stop at the first node where the values split, since that node is the LCA.
What is a trie used for?
Storing and searching strings efficiently by sharing common prefixes across branches, which makes prefix search, autocomplete, and dictionary lookups fast.
What is the height of a balanced binary tree with n nodes?
O(log n), since each level roughly doubles the number of nodes it can hold.
How do you serialize and deserialize a binary tree?
Traverse the tree (commonly preorder), recording each node's value and using a sentinel marker for null children, then rebuild the tree by reading that same sequence back recursively.
What is a complete binary tree?
A binary tree where every level is fully filled except possibly the last, which is filled from left to right, a property heaps rely on.
What distinguishes a binary tree from a general tree?
A binary tree restricts every node to at most two children (left and right); a general tree allows any number of children per node.
What is a heap?
A complete binary tree stored in an array where every parent satisfies the heap property relative to its children, either always greater (max-heap) or always smaller (min-heap).
What is the time complexity of inserting into a heap?
O(log n), since the new element bubbles up to its correct position through at most the tree's height.
What is the time complexity of extracting the minimum (or maximum) from a heap?
O(log n): the root is removed, the last element takes its place, and it sifts down to restore the heap property.
How is a binary heap typically stored?
In a plain array, where a node at index i has children at indices 2i+1 and 2i+2, avoiding the overhead of explicit pointers.
When would you use a heap instead of sorting the whole array?
When you only need the k smallest or largest elements repeatedly, a heap gives O(n log k) instead of paying O(n log n) to fully sort everything.
What is the time complexity of building a heap from an unsorted array?
O(n), which is faster than it looks because most nodes near the bottom need very little sifting.
How does a hash map achieve average O(1) lookup?
A hash function converts a key into an array index, so lookup, insert, and delete jump straight to (roughly) the right bucket instead of scanning.
What is a hash collision and how is it handled?
Two different keys mapping to the same bucket. Common fixes are chaining (storing a list of entries per bucket) or open addressing (probing for the next free slot).
Why is the worst-case time complexity of a hash map operation O(n)?
If many keys collide into the same bucket, that bucket degenerates into a list that must be scanned linearly, though a good hash function makes this rare in practice.
What makes a good hash function?
It distributes keys uniformly across buckets, is fast to compute, and produces very different outputs for similar inputs to minimize clustering.
What is the difference between a HashMap and a HashSet?
A HashMap stores key-value pairs; a HashSet stores unique keys only, effectively a HashMap where the values are ignored.
Why do hash maps typically resize (rehash) as they grow?
To keep the load factor (entries per bucket) low, which keeps collisions rare and lookups close to O(1); resizing reallocates a larger bucket array and reinserts every entry.
How would you use a hash map to find the first non-repeating character in a string?
Count character frequencies in one pass with a hash map, then scan the string again in order and return the first character whose count is 1.
What is the difference between a directed and an undirected graph?
In a directed graph, edges have a direction (A to B does not imply B to A); in an undirected graph, an edge connects both nodes symmetrically.
What is the difference between an adjacency list and an adjacency matrix?
An adjacency list stores each node's neighbors in a list, using O(V+E) space and fast iteration over neighbors; an adjacency matrix uses a V by V grid, giving O(1) edge lookup but O(V squared) space.
What is the difference between BFS and DFS on a graph?
BFS explores level by level using a queue and finds the shortest path in an unweighted graph; DFS explores as deep as possible down one path using a stack or recursion before backtracking.
What is the time complexity of BFS and DFS?
Both run in O(V+E), visiting every vertex and edge once.
How do you detect a cycle in a directed graph?
Run DFS while tracking nodes currently on the recursion stack; if a DFS edge points to a node still on that stack, a cycle exists.
What is topological sorting and when does it apply?
An ordering of a directed acyclic graph's nodes so that every edge points from an earlier node to a later one, used for scheduling tasks with dependencies.
What algorithm finds the shortest path in a weighted graph with non-negative edges?
Dijkstra's algorithm, which greedily expands the closest unvisited node using a priority queue, in roughly O((V+E) log V).
When would you use Bellman-Ford instead of Dijkstra?
When the graph can have negative edge weights, since Bellman-Ford correctly handles them (and can detect negative cycles), at the cost of a slower O(V times E) runtime.
What is a minimum spanning tree?
A subset of a weighted, connected, undirected graph's edges that connects all vertices with the minimum total edge weight and no cycles.
What is the difference between Kruskal's and Prim's algorithm for minimum spanning trees?
Kruskal's sorts all edges and greedily adds the smallest one that does not form a cycle, using a union-find structure; Prim's grows a single tree outward, always adding the cheapest edge connecting the tree to a new vertex.
What is a connected component?
A maximal set of vertices in an undirected graph that are all reachable from one another, found by running BFS or DFS from each unvisited node.
How would you detect a cycle in an undirected graph?
Run DFS or BFS, and if you reach an already-visited vertex that is not the immediate parent of the current vertex, a cycle exists; union-find flags a cycle when an edge connects two vertices already in the same set.
What is dynamic programming?
A technique for solving problems by breaking them into overlapping subproblems, solving each subproblem once, and reusing the stored result instead of recomputing it.
What are the two main approaches to implementing dynamic programming?
Top-down with memoization (recursion plus a cache) and bottom-up with tabulation (iteratively filling a table from the smallest subproblems up).
What two properties must a problem have to be solved with dynamic programming?
Optimal substructure (an optimal solution can be built from optimal solutions to subproblems) and overlapping subproblems (the same subproblems recur many times).
How does dynamic programming differ from plain divide and conquer?
Divide and conquer splits a problem into independent subproblems solved separately (like merge sort); dynamic programming targets subproblems that overlap and reuses cached results to avoid redundant work.
What is the classic example of overlapping subproblems?
Computing Fibonacci numbers naively with recursion, where fib(n-2) gets recomputed many times across different branches unless the result is cached.
How would you solve the coin change (minimum coins) problem with DP?
Build a table where entry i holds the minimum coins needed to make amount i, computed from the best of (1 plus table[i minus coin]) over every coin denomination, working up from 0.
What is the 0/1 knapsack problem?
Given items with weights and values and a weight capacity, choose a subset (each item used at most once) that maximizes total value without exceeding capacity, typically solved with a 2D DP table over items and capacity.
How do you find the longest common subsequence of two strings with DP?
Build a 2D table where entry (i, j) holds the LCS length of the first i and j characters of each string, extending by 1 on a character match or taking the best of skipping a character from either string otherwise.
What space optimization is commonly used in DP problems that use a 2D table?
If a row only depends on the previous row, keep just two rows (or one, updated carefully) instead of the full table, cutting space from O(n times m) to O(m) or O(1).
What is the difference between the longest increasing subsequence problem and the longest common subsequence problem?
LIS finds the longest subsequence of one array that is strictly increasing; LCS finds the longest subsequence shared between two different sequences, regardless of order.
How do you check if a number is even or odd using bitwise operations?
Check the least significant bit with n & 1; if it is 0 the number is even, if it is 1 the number is odd.
How do you check if a number is a power of two?
A power of two has exactly one set bit, so n > 0 and (n & (n - 1)) == 0 is true only for powers of two.
What does the XOR operator do, and why is it useful for finding a single non-duplicate in an array of pairs?
XOR returns 1 only where bits differ; XOR-ing every number together cancels out all pairs (since x XOR x is 0), leaving only the one number without a pair.
What is the effect of a left shift and a right shift?
A left shift moves bits toward the higher end, equivalent to multiplying by 2 per shift; a right shift moves bits toward the lower end, equivalent to integer division by 2 per shift.
How would you count the number of set bits (1s) in an integer?
Repeatedly clear the lowest set bit with n & (n - 1) and count how many times this can be done before n becomes 0, which takes time proportional to the number of set bits.
What is two's complement and why do computers use it to represent negative numbers?
A binary representation where negating a number is done by inverting all bits and adding 1; it lets addition and subtraction use the same hardware circuit for both positive and negative numbers.
What are the four pillars of object-oriented programming?
Encapsulation, abstraction, inheritance, and polymorphism.
What is encapsulation?
Bundling data and the methods that operate on it inside a class, while restricting direct access to internal state from outside code.
What is the difference between abstraction and encapsulation?
Abstraction hides complexity by exposing only the essential behavior through an interface; encapsulation hides the internal data and implementation details behind that interface.
What is inheritance?
A mechanism where a class (subclass) acquires the properties and behavior of another class (superclass), enabling code reuse and a hierarchical relationship between types.
What is polymorphism, and what is the difference between compile-time and runtime polymorphism?
Polymorphism lets the same interface behave differently depending on the object. Compile-time polymorphism is method overloading, resolved at compile time; runtime polymorphism is method overriding, resolved via the actual object type at runtime.
What is the difference between an abstract class and an interface?
An abstract class can hold shared state and partially implemented methods and supports single inheritance; an interface (in most languages) defines only a contract of method signatures, and a class can implement multiple interfaces.
What is method overriding versus method overloading?
Overriding redefines a superclass method in a subclass with the same signature to change its behavior; overloading defines multiple methods in the same class with the same name but different parameters.
What is composition, and why is "favor composition over inheritance" common advice?
Composition builds objects out of other objects rather than through class hierarchies. It is favored because deep inheritance chains get rigid and fragile, while composition keeps relationships flexible and easier to change.
What is a constructor and what is its purpose?
A special method called when an object is created, used to initialize the object's state, often setting required fields or validating input.
What does "programming to an interface, not an implementation" mean?
Writing code that depends on an abstract type's contract rather than a specific concrete class, so implementations can be swapped without changing the code that uses them.
What is the difference between a process and a thread?
A process is an independent program instance with its own memory space; a thread is a unit of execution within a process that shares that process's memory with other threads in it.
What is a deadlock?
A situation where two or more processes or threads are each waiting on a resource the other holds, so none of them can proceed.
What are the four necessary conditions for deadlock?
Mutual exclusion, hold and wait, no preemption, and circular wait; all four must hold simultaneously for a deadlock to occur.
What is the difference between multitasking and multithreading?
Multitasking runs multiple processes concurrently on a system; multithreading runs multiple threads concurrently within a single process, sharing its memory.
What is a context switch?
The operating system saving the state of a currently running process or thread and loading the state of another, allowing the CPU to switch between them.
What is virtual memory?
An abstraction that gives each process the illusion of a large, contiguous private address space, backed by physical memory and disk, managed by the OS through paging.
What is paging?
Dividing memory into fixed-size blocks (pages) so a process's memory can be scattered across non-contiguous physical frames while still appearing contiguous to the process.
What is a race condition?
A bug where the outcome of concurrent operations depends on the unpredictable timing or order of execution, typically arising from unsynchronized access to shared data.
What is a mutex and how does it prevent race conditions?
A mutual-exclusion lock that only one thread can hold at a time, used to guard a critical section so only one thread modifies shared state at once.
What is the difference between a mutex and a semaphore?
A mutex allows only one thread to access a resource and is typically owned and released by the same thread; a semaphore maintains a count and can allow a fixed number of threads to access a resource, and can be signaled by a different thread than the one that waited.
What is thrashing?
A state where a system spends more time swapping pages in and out of memory than doing actual work, usually caused by too many processes competing for too little physical memory.
What is the difference between a process's stack and heap memory?
The stack holds function call frames, local variables, and return addresses with automatic, fast allocation and deallocation; the heap holds dynamically allocated memory that persists until explicitly freed (or garbage collected) and is slower to manage.
What does ACID stand for in database transactions?
Atomicity, consistency, isolation, and durability, the guarantees that keep transactions reliable even under failures or concurrent access.
What is the difference between INNER JOIN and LEFT JOIN?
INNER JOIN returns only rows with matches in both tables; LEFT JOIN returns all rows from the left table plus matching rows from the right table, with nulls where there is no match.
What is database normalization and why is it used?
Organizing tables to reduce data redundancy and avoid update anomalies, typically by splitting data into related tables following normal forms (1NF, 2NF, 3NF).
What is a primary key versus a foreign key?
A primary key uniquely identifies each row in its own table; a foreign key is a column referencing a primary key in another table, enforcing a relationship between them.
What is an index, and what is its trade-off?
A separate data structure (commonly a B-tree) that speeds up lookups on a column, at the cost of extra storage and slower writes since every insert or update also has to update the index.
What is the difference between SQL and NoSQL databases?
SQL databases are relational, with fixed schemas and strong consistency, suited to structured data and complex joins; NoSQL databases are typically schema-flexible and built for horizontal scale or specific access patterns like documents, key-value, or graphs.
What is a transaction?
A sequence of database operations treated as a single unit: either every operation succeeds and is committed, or if any fails, all of them are rolled back.
What is the N+1 query problem?
Fetching a list of N items with one query, then running a separate query for each item's related data, resulting in N+1 total queries instead of one efficient join or batched query.
What is the difference between GROUP BY and HAVING in SQL?
GROUP BY groups rows sharing a column value so aggregate functions can be applied to each group; HAVING filters those groups after aggregation, unlike WHERE which filters rows before grouping.
What is database isolation level, and what problem does a lower level risk?
How strictly transactions are kept from seeing each other's uncommitted changes. Lower isolation levels risk anomalies like dirty reads (seeing uncommitted data) or non-repeatable reads (a value changing between two reads in the same transaction).
What is the difference between TCP and UDP?
TCP is connection-oriented and guarantees ordered, reliable delivery with retransmission; UDP is connectionless, faster, and does not guarantee delivery or order, which suits use cases like video streaming or DNS.
What happens during a TCP three-way handshake?
The client sends SYN, the server responds with SYN-ACK, and the client replies with ACK, establishing a reliable connection before any data is sent.
What is the difference between HTTP and HTTPS?
HTTPS is HTTP layered over TLS/SSL encryption, so data in transit is encrypted and the server's identity is verified via a certificate; plain HTTP sends data unencrypted.
What does DNS do?
Translates human-readable domain names into IP addresses so browsers and other clients know which server to connect to.
What is the difference between a 4xx and a 5xx HTTP status code?
A 4xx code means the client made a bad request (like 404 Not Found or 401 Unauthorized); a 5xx code means the server failed while handling an otherwise valid request (like 500 Internal Server Error).
What is the purpose of a load balancer?
Distributing incoming traffic across multiple servers so no single server is overwhelmed, improving reliability and letting a system scale horizontally.
What is the difference between a stateless and a stateful protocol?
A stateless protocol like HTTP treats each request independently with no memory of prior requests; a stateful protocol maintains context across a sequence of interactions, such as an open TCP connection.
What is a REST API?
An architectural style for web APIs built around resources identified by URLs, manipulated through standard HTTP methods (GET, POST, PUT, DELETE), and typically stateless.
What is CORS and why does it exist?
Cross-Origin Resource Sharing is a browser security mechanism that blocks a web page from making requests to a different origin unless that origin's server explicitly allows it via response headers.
What is the OSI model, at a high level?
A conceptual 7-layer model (physical, data link, network, transport, session, presentation, application) describing how network communication is broken into layers, each handling a distinct responsibility.
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