Algorithms

Intermediate Practice - Algorithms

Practice merge sort, quicksort, hash tables, binary search trees, recursion, and BFS and DFS traversal through worked problems.

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 Practice

Deepen your skills with guided intermediate problems

These intermediate exercises cover divide-and-conquer techniques, basic graph traversal, and introductory dynamic programming, each with a worked explanation.

The problems are untimed and designed for learning, so you can trace each solution and understand why it works.

Complete the set to prepare for the advanced practice exercises.

What You Will Practice at Intermediate Level

Implementing Efficient Sorts

Exercises guide you through merge sort's divide and merge steps and quicksort's partitioning, both averaging O(n log n) time.

Building Hash Tables

You will practice designing hash functions, resolving collisions with chaining or probing, and reasoning about average O(1) operations.

Binary Search Tree Operations

Guided problems let you insert, search, and traverse a BST in order, and observe how imbalance pushes operations toward O(n).

Recursion and Graph Search

You will write recursive solutions with clear base cases and trace BFS with a queue and DFS with a stack across sample graphs.

Sample Questions

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

What is the average-case time complexity of Quick Sort?

Answer: O(n log n)

Quick Sort has an average-case time complexity of O(n log n). It achieves this by partitioning the array around a pivot, with each level of recursion doing O(n) work across O(log n) levels.

Which sorting algorithm is stable, meaning equal elements maintain their relative order?

Answer: Merge Sort

Merge Sort is stable because when merging two sorted halves, if elements are equal, the one from the left half is placed first, preserving original order.

What happens if a recursive function has no base case?

Answer: It causes a stack overflow

Without a base case, the function calls itself indefinitely. Each call adds a frame to the call stack, eventually exceeding the stack size limit and causing a stack overflow error.

What is the time complexity of Binary Search?

Answer: O(log n)

Binary Search halves the search space with each comparison. For an array of n elements, it takes at most log2(n) comparisons. Doubling the array size only adds one more step.

A nested loop where both loops run n times has what time complexity?

Answer: O(n^2)

When an inner loop of n iterations runs inside an outer loop of n iterations, the total operations are n * n = n^2, giving O(n^2) quadratic time complexity.

Frequently Asked Questions

Find answers to common questions about this assessment

Start with the partition step: choose a pivot, then move smaller elements left and larger ones right. Recurse on each side. Practice with a randomized or median pivot to avoid the O(n^2) worst case. Tracing small arrays first helps you get the index boundaries right before scaling up.

Begin by clearly stating the base case that stops recursion and the recursive case that shrinks the problem. Trace the call stack for small inputs on paper. Classic drills include factorial, Fibonacci, and tree traversals. Watching how calls unwind builds confidence and prevents infinite recursion or stack overflow errors.

Practice by asking what the problem needs. If it wants the shortest path in an unweighted graph or nearest neighbors, drill breadth-first search with a queue. If it wants to explore full paths, detect cycles, or order dependencies, drill depth-first search with recursion or a stack. Repetition makes the choice quick.

A plain binary search tree teaches the core insert, search, and traversal logic and shows how sorted input degrades it to O(n). Mastering that motivates why balancing matters. Once the basic operations feel automatic, the rotations of AVL and red-black trees at the advanced level are much easier to learn.

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.

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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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