Algorithms

Expert Test - Algorithms

Assess your expertise in minimum spanning trees, max flow, topological sort, amortized analysis, NP-completeness, and string algorithms.

Duration

Complete at your own pace or within the time limit

Questions

Multiple choice with one correct answer

Accuracy

Expert-reviewed questions with clear answer keys

Results

Instant detailed breakdown by topic area

Algorithms
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About This Algorithm Test

Challenge your mastery of cutting-edge algorithm theory

This expert assessment covers NP-completeness, network flow, randomized algorithms, approximation algorithms, string matching (KMP, Rabin-Karp), and advanced graph theory.

Questions test deep theoretical reasoning about complexity classes, correctness proofs, and the design of efficient solutions to hard problems.

Results include a detailed breakdown by topic area, helping you pinpoint the advanced concepts to revisit.

What This Expert Test Assesses

Advanced Graph Algorithms

Questions cover minimum spanning trees via Kruskal and Prim, maximum flow with Ford-Fulkerson, and topological sort of directed acyclic graphs.

Amortized Analysis

You will be tested on aggregate, accounting, and potential methods, such as why dynamic array append is amortized O(1) despite occasional resizing.

NP-Completeness and Advanced DP

Items assess reductions, the P versus NP question, classic NP-complete problems, and dynamic programming over bitmasks or intervals.

Range Structures and String Algorithms

This section evaluates segment and Fenwick trees for O(log n) range queries plus KMP pattern matching and suffix arrays.

Sample Questions

A few real questions from this test, with answers and explanations. Take the full test above for the complete set.

Which complexity class contains problems solvable in polynomial time by a non-deterministic Turing machine?

Answer: NP

NP (Non-deterministic Polynomial time) is the class of problems for which a non-deterministic Turing machine can find a solution in polynomial time. Equivalently, a deterministic machine can verify a given solution in polynomial time.

A Monte Carlo algorithm is one that:

Answer: May give incorrect answers but always runs in bounded time

Monte Carlo algorithms have bounded running time but may produce incorrect results with some probability. Las Vegas algorithms are the opposite: always correct but with variable running time (e.g., randomized QuickSort).

A B-tree of order m guarantees that each non-root node has at least:

Answer: m/2 children (ceil)

In a B-tree of order m, each non-root internal node must have at least ceil(m/2) children and at most m children. This guarantees the tree remains balanced with O(log n) height, optimal for disk-based storage systems.

The Vertex Cover problem has a polynomial-time 2-approximation algorithm. This means:

Answer: It finds a cover at most twice the optimal size

The algorithm repeatedly picks an uncovered edge and adds both endpoints to the cover. Since optimal must include at least one endpoint of each edge, and we add both, the cover is at most 2x optimal. No better polynomial-time ratio is known unless P=NP.

The Hopcroft-Karp algorithm finds maximum matching in bipartite graphs in:

Answer: O(E * sqrt(V))

Hopcroft-Karp uses BFS to find shortest augmenting paths and DFS to find vertex-disjoint augmenting paths. It processes O(sqrt(V)) phases, each taking O(E), giving O(E * sqrt(V)) total.

Frequently Asked Questions

Find answers to common questions about this assessment

Kruskal sorts edges and adds the smallest that does not form a cycle, using a union-find structure, running in O(E log E) time. Prim grows a tree from one vertex, always adding the cheapest crossing edge with a priority queue, running in O((V+E) log V). Both yield a minimum spanning tree.

An NP-complete problem is in NP and is at least as hard as every other problem in NP, so any NP problem reduces to it in polynomial time. No polynomial-time algorithm is known for any of them, and finding one would prove P equals NP. Examples include SAT and the traveling salesman decision problem.

The Knuth-Morris-Pratt algorithm precomputes a prefix or failure table that tells it how far to shift the pattern after a mismatch without rechecking matched characters. This avoids re-scanning the text, giving O(n + m) time for a text of length n and pattern of length m, far better than the naive O(n times m).

A Fenwick, or binary indexed, tree supports prefix sums and point updates in O(log n) with less memory and simpler code than a segment tree. Choose it for cumulative frequency and prefix-sum tasks. Prefer a segment tree when you need range minimum, range maximum, or more general range queries and lazy updates.

Scores are based on the number of correct answers divided by total questions, with a breakdown by topic category.

Yes, questions are randomly selected and ordered from our question bank to ensure each attempt is unique.

No account is required. You can take the test immediately. Optionally provide an email to save your results.

There is no pass/fail threshold. The test measures your knowledge level and provides detailed feedback for improvement.

For knowledge tests, we recommend answering without external help to get an accurate assessment. Practice exercises are designed for learning, so references are acceptable.

Our questions are written for structured educational practice and can give a useful snapshot of your current knowledge in the tested topics.

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