Think you've mastered every sorting trick and logic pattern? Our Ultimate Algorithm Test: Programming Algorithms Quiz challenges your skills with an interactive algorithm test online covering pseudocode challenges, flowchart puzzles and core coding concepts. Start with an intro to programming algorithms, then dive into the algorithm pseudocode quiz to sharpen your logic. Measure your problem-solving prowess, boost algorithmic intuition and build confidence for coding interviews. This free programming algorithms quiz delivers instant feedback and clear explanations. Take the algorithm quiz or explore the algorithm flowchart quiz now!
What is the time complexity of binary search on a sorted array of n elements?
O(n)
O(log n)
O(n log n)
O(1)
Binary search splits the search interval in half on each comparison, leading to logarithmic behavior. It eliminates half of the remaining elements every step, resulting in O(log n) time for worst, average, and best cases on a sorted array. This efficiency makes it ideal for large datasets. More on binary search.
Which data structure uses the Last-In-First-Out (LIFO) principle?
Queue
Stack
Tree
Graph
A stack follows the Last-In-First-Out principle, meaning the most recently added element is the first one to be removed. This is useful in function call management and backtracking algorithms. Queues, trees, and graphs follow different organizational schemes. Stack ADT details.
Which algorithm is commonly used to find the minimum spanning tree of a weighted undirected graph?
Dijkstra's algorithm
Prim's algorithm
Breadth-first search
Depth-first search
Prim's algorithm constructs a minimum spanning tree by starting from an arbitrary node and repeatedly adding the smallest weight edge connecting the growing tree to a new vertex. It guarantees a tree with minimal total edge weight. Dijkstra's solves shortest paths, not spanning trees. Learn about Prim's algorithm.
What is the worst-case time complexity of Bubble Sort on an array of size n?
O(n)
O(n log n)
O(n^2)
O(n^3)
Bubble Sort repeatedly swaps adjacent elements if they are in the wrong order, leading to roughly n*(n-1)/2 comparisons and swaps in the worst case. This quadratic behavior yields O(n^2) time complexity. It's inefficient for large lists but useful for teaching sorting concepts. Bubble Sort details.
In pseudocode, what does a 'for i from 1 to n' loop typically represent?
A loop that runs indefinitely
A counting loop that executes a fixed number of times
A conditional statement
A recursive function call
The 'for i from 1 to n' construct denotes a loop that iterates exactly n times, incrementing i by one each time. It's a fixed-count loop used for array traversal and repetitive operations. It is not indefinite or conditional beyond its specified range. For loop explained.
Which graph traversal algorithm explores nodes level by level starting from the source?
Depth-first search
Breadth-first search
Dijkstra's algorithm
Bellman-Ford algorithm
Breadth-first search (BFS) visits all neighbors of the source before moving on to the next level, effectively traversing the graph level by level. It uses a queue to manage the frontier. DFS, by contrast, goes as deep as possible before backtracking. BFS details.
What does Big O notation describe in algorithm analysis?
Exact runtime in seconds
Upper bound on growth rate of algorithm's running time
Average number of errors in code
Memory consumption in bytes
Big O notation provides an upper bound on the growth rate of an algorithm's running time or space usage as the input size approaches infinity. It abstracts away constant factors and lower-order terms. This helps compare algorithmic efficiency at scale. Big O notation.
Which sorting algorithm is stable and guarantees O(n log n) time in the worst case?
Quick Sort
Heap Sort
Merge Sort
Insertion Sort
Merge Sort divides the array into halves, sorts each recursively, and then merges them, guaranteeing O(n log n) time even in the worst case. It is also stable because it preserves the order of equal elements during merging. Quick Sort and Heap Sort are not stable by default. Merge Sort.
What is the space complexity of Merge Sort on an array of size n?
O(1)
O(log n)
O(n)
O(n log n)
Merge Sort requires additional space proportional to the size of the array for the temporary arrays used in merging. This leads to O(n) auxiliary space complexity. In-place variants exist but are more complex. Merge Sort space complexity.
In dynamic programming, which technique helps avoid redundant computations?
Divide and conquer
Memoization
Greedy choice
Backtracking
Memoization stores the results of expensive function calls and returns the cached result when the same inputs occur again. This avoids redundant calculations and reduces the time complexity. It is a core technique in top-down dynamic programming. Memoization.
What is the height of a balanced binary search tree with n nodes?
O(1)
O(n)
O(log n)
O(n log n)
A balanced binary search tree maintains its height proportional to the logarithm of the number of nodes, i.e., O(log n). This balance ensures efficient search, insertion, and deletion operations. Trees like AVL and Red-Black adhere to this property. Balanced BSTs.
Which algorithm finds the shortest path from a single source to all other vertices in a graph with non-negative weights?
Bellman-Ford
Dijkstra's algorithm
Floyd-Warshall
Prim's algorithm
Dijkstra's algorithm picks the unvisited vertex with the smallest tentative distance, updates its neighbors, and repeats until all nodes are visited. It only works correctly with non-negative edge weights. Bellman-Ford handles negative weights but is slower. Dijkstra's algorithm.
What is the worst-case time complexity of Insertion Sort on an array of size n?
O(n)
O(n log n)
O(n^2)
O(log n)
Insertion Sort builds the sorted array one element at a time by shifting larger elements to the right. In the worst case (reverse-sorted input), each insertion requires shifting all prior elements, resulting in about n(n-1)/2 comparisons and shifts, i.e., O(n^2). Insertion Sort.
What is the main idea behind the divide and conquer paradigm?
Make a greedy choice at each step
Break the problem into independent subproblems, solve them, and combine results
Store and reuse overlapping subproblems
Search exhaustively through all possibilities
Divide and conquer divides the original problem into smaller, independent subproblems, solves each recursively, and then combines their solutions to form the final answer. Examples include Merge Sort and Quick Sort. It differs from dynamic programming, which reuses overlapping subproblem results. Divide and conquer.
What is the worst-case time complexity of Quick Sort, and under what input condition does it occur?
O(n log n) when pivot divides arrays equally
O(n^2) when the pivot is always the smallest or largest element
O(n) when the pivot is the median
O(n^3) for random pivots
Quick Sort degrades to O(n^2) when the chosen pivot is consistently the smallest or largest element, such as in already sorted or reverse-sorted arrays. In this scenario, the partitioning is unbalanced, causing recursive calls on subarrays of size n?1. Average performance remains O(n log n) with good pivot choices. Quick Sort worst case.
What is the average-case time complexity for search operations in a balanced skip list?
O(1)
O(log n)
O(n)
O(n log n)
A skip list uses multiple levels of linked lists to skip over elements, reducing search paths. On average, it achieves O(log n) time for search, insertion, and deletion. The worst case can degrade to O(n) if levels are unbalanced, but probabilistic balancing keeps average costs logarithmic. Skip list.
Which algorithm solves the all-pairs shortest path problem in O(n^3) time?
Dijkstra's algorithm repeated for each source
Bellman-Ford algorithm
Floyd–Warshall algorithm
Johnson's algorithm
The Floyd–Warshall algorithm computes shortest paths between all pairs of vertices by iteratively improving path estimates in a triple-nested loop, resulting in O(n^3) time. It handles negative weights but no negative cycles. Johnson's algorithm can be faster for sparse graphs. Floyd–Warshall.
What is the space complexity of a depth-first search implemented recursively on a graph with n vertices?
O(1)
O(log n)
O(n)
O(n^2)
Recursive depth-first search uses the call stack to keep track of the recursion, which in the worst case grows proportional to the number of vertices (O(n)). Additionally, storing visited markers and adjacency lists contributes to O(n + m), but the recursion stack dominates in worst-case. DFS complexity.
How does the Bellman-Ford algorithm detect the presence of a negative-weight cycle reachable from the source?
It checks if any distance can be reduced after n-1 iterations
It uses a priority queue to look for negative edges
It performs a DFS to find back edges
It relies on greedy selection of edges
Bellman-Ford relaxes all edges n-1 times to compute shortest paths. After these iterations, if any edge can still be relaxed (i.e., distance reduced), it indicates a reachable negative-weight cycle. This extra check is the standard method for cycle detection. Bellman-Ford detection.
What is the amortized time complexity of append (push) operation in a dynamic array that doubles its size when full?
O(1) amortized
O(n)
O(log n)
O(n log n)
In a dynamic array that doubles its capacity when full, most append operations take O(1) time, with occasional O(n) reallocations. The cost of these reallocations is spread out over many inserts, leading to an amortized time of O(1). Amortized analysis.
In the A* pathfinding algorithm, what property must the heuristic function h(n) satisfy to guarantee optimality?
h(n) must be negative
h(n) must never overestimate the true cost to reach the goal (admissible)
h(n) must be non-deterministic
h(n) must be exactly zero
For A* to guarantee the shortest path, the heuristic must be admissible—i.e., it never overestimates the actual minimal cost from node n to the goal. If it overestimates, A* can miss the optimal path. Consistency (monotonicity) is a stronger condition that also ensures optimality. A* heuristic.
Which optimization technique specifically transforms tail-recursive function calls into iterative loops?
Loop unrolling
Tail call elimination (optimization)
Memoization
Inline expansion
Tail call elimination (or tail call optimization) allows a compiler or interpreter to reuse the current function's stack frame for a tail-recursive call, effectively turning recursion into iteration. This prevents stack overflow and reduces overhead. Tail call optimization.
According to the Master Theorem, if a recurrence is T(n) = aT(n/b) + ?(n^{log_b(a)} · log^k(n)), what is its solution?
?(n^{log_b(a)})
?(n^{log_b(a)} · log^{k+1}(n))
?(n^{log_b(a)} · log^k(n))
?(n^{log_b(a)+?}) for some ?>0
This matches case 2 of the Master Theorem, where f(n) = ?(n^{log_b(a)} · log^k(n)). The solution is T(n) = ?(n^{log_b(a)} · log^{k+1}(n)). The extra log factor arises from combining subproblem solutions. Master Theorem.
In NP-completeness theory, what does it mean for problem A to be reducible to problem B in polynomial time?
Solutions of A can be checked by solving B's instances in constant time
Instances of A can be transformed into instances of B using a polynomial-time algorithm
A and B have the same input size
B can be solved in exponential time whenever A can
Polynomial-time reducibility means there exists a polynomial-time computable function that maps instances of A to instances of B such that the answer is preserved. If A reduces to B and B is in P, then A is also in P. This concept underpins NP-completeness. Problem reduction.
Which linear-time algorithm constructs the suffix array of a string in O(n) time?
Suffix tree construction followed by DFS
SA-IS (Suffix Array Induced Sorting)
Radix sort on all suffixes directly
Suffix automaton method
The SA-IS algorithm constructs the suffix array in O(n) time by induced sorting of suffixes. It classifies characters into types and induces the order of suffixes efficiently without explicit comparisons. This advances over O(n log n) approaches. SA-IS algorithm.
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Study Outcomes
Understand core programming algorithm concepts -
Grasp key ideas behind common algorithms covered in this programming algorithms quiz, including sorting, searching, and recursion techniques.
Interpret pseudocode effectively -
Learn to read and write algorithm pseudocode by recognizing standard formats and translating problem statements into clear, step-by-step logic.
Apply problem-solving strategies -
Use proven methods such as divide-and-conquer, greedy approaches, and dynamic programming to tackle algorithm test questions with confidence.
Evaluate algorithm efficiency -
Assess time and space complexity to compare different solutions and optimize performance during your algorithm test online.
Reinforce concepts through interactive challenges -
Engage with fun, scenario-based questions that solidify your understanding of intro to programming algorithms in a practical context.
Self-assess and track progress -
Use immediate feedback from this algorithm test to identify strengths and areas for improvement as you advance your coding skills.
Cheat Sheet
Time Complexity & Big-O Notation -
Understanding how to classify an algorithm's performance is crucial for any algorithm test, whether it's an algorithm test online or a programming algorithms quiz. Big-O notation gives an upper bound on runtime (e.g., O(n log n) for merge sort), and a handy mnemonic is "Worst-case worries." According to CLRS (2009), analyzing best, average, and worst cases ensures comprehensive coverage.
Pseudocode Conventions -
Clear pseudocode helps you ace an algorithm pseudocode quiz by communicating logic without language syntax errors. Follow CLRS style: use indentation for blocks, uppercase keywords (IF, WHILE), and clear function names like Merge(A, B). As per MIT's OpenCourseWare, consistent naming and comments boost readability.
Divide-and-Conquer Strategies -
Divide-and-conquer breaks a problem into subproblems, solves them recursively, then merges results, exemplified by merge sort (T(n)=2T(n/2)+Θ(n)). A simple phrase to remember: "Divide, conquer, combine." Stanford's CS161 course highlights this pattern as fundamental for many efficient algorithms.
Dynamic Programming vs. Greedy -
Dynamic programming (DP) stores subproblem results in a table (e.g., optimal coin-change), while greedy picks the best local choice (e.g., Kruskal's MST). Use DP when choices overlap, greedy when the greedy-choice property holds. As noted by University of California, Berkeley, distinguishing these strategies is key for problem-solving quizzes.
Recurrence Relations & Master Theorem -
Many algorithms yield recurrence relations like T(n)=aT(n/b)+f(n); the Master Theorem gives three cases to solve these quickly. For instance, T(n)=2T(n/2)+n falls into Case 2, yielding Θ(n log n). This theorem is widely taught in academic institutions such as Carnegie Mellon University for fast analysis.
