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WorksheetsAlgorithm Design and Analysis Quiz
Total questions: 45
Worksheet time: 23mins
Scenario: You are asked to create a sorting algorithm for a system that handles millions of transactions per second. Which design paradigm is most appropriate for such scenarios?
Divide and Conquer
Brute Force
Randomized Algorithms
Greedy Algorithms
Scenario: A company needs an algorithm to verify user credentials against a database with billions of entries. Which factor is most critical to evaluate the algorithm?
Accuracy
Space complexity
Time complexity
Input constraints
Scenario: An algorithm consistently outputs the wrong results for certain inputs. What property of the algorithm is being violated?
Efficiency
Correctness
Simplicity
Stability
Scenario: Your algorithm processes T(n)=4T(n/2)+n2. Using Master’s Theorem, identify the time complexity.
O(n2logn)
O(n3)
O(n2)
O(logn)
Scenario: A function f(n)=5n3+3n2. As nn grows large, what is the asymptotic upper bound?
O(n2)
O(n3)
O(5n3)
O(n4)
Scenario: An algorithm's time complexity is O(log n). What scenario best fits its application?
Searching for an element in a sorted array
Sorting an array
Finding the shortest path in a graph
Traversing a linked list
Scenario: A recursive algorithm divides a problem into 3 subproblems, each half the size of the original. The recurrence is T(n)=3T(n/2)+n. What is the time complexity?
O(n2)
O(nlogn)
O(nlog23)
O(n)
Scenario: For the recurrence T(n)=2T(n/4)+√n, , what is the asymptotic complexity?
O(logn)
O(n1/2)
O(n0.5 logn)
O(nlogn)
Scenario: A binary tree is used to represent a decision-making process. Which traversal gives the sequence of decisions in increasing order of priority?
Preorder
Postorder
Inorder
Level order
Scenario: You implement a queue in a ticket booking system where the first customer to arrive gets served first. Which principle does the queue follow?
FIFO
LIFO
Priority-based
Random access
Scenario: In a text editor, the undo operation is implemented using which data structure?
Queue
Stack
Binary tree
Graph
Scenario: A balanced binary search tree (BST) is used for searching. What is the worst-case time complexity?
O(1)
O(n)
O(logn)
O(nlogn)
Scenario: Your task is to design a network of roads with minimal total cost. Which algorithm would work best for the problem?
Dijkstra’s Algorithm
Kruskal’s Algorithm
Floyd-Warshall Algorithm
Bellman-Ford Algorithm
Scenario: Prim’s algorithm starts from:
The vertex with the minimum degree
Any vertex
The vertex with the maximum degree
The vertex with the smallest edge weight
Scenario: In a graph with negative edge weights, which algorithm would you use to find the Minimum Spanning Tree?
Kruskal’s Algorithm
Prim’s Algorithm
Both
None
Scenario: You are solving a problem where the solution depends on overlapping subproblems. Which approach would you use?
Divide and Conquer
Brute Force
Dynamic Programming
Greedy Algorithms
Scenario: The traveling salesman problem is solved using dynamic programming. What is its time complexity?
O(n2)
O(n22n)
O(2n)
O(n!)
Scenario: You are solving the Longest Common Subsequence problem. Which method will provide the optimal solution?
Backtracking
Greedy Algorithms
Dynamic Programming
Divide and Conquer
Scenario: You need to fill a knapsack to maximize profit, where items can be broken into smaller parts. Which algorithm will give the optimal solution?
Dynamic Programming
Brute Force
Greedy Algorithm
Divide and Conquer
Scenario: In a cash-dispenser system, the machine is programmed to return the fewest coins possible. Which principle is this based on?
Backtracking
Greedy Algorithm
Dynamic Programming
Linear Programming
Scenario: Your database contains sorted records, and you need to find an element quickly. Which search algorithm would you use?
Linear Search
Binary Search
Breadth-First Search
Depth-First Search
Scenario: A hash table is used for fast lookups. What is the average-case time complexity for a successful search?
O(n)
O(1)
O(logn)
O(nlogn)
Scenario: A company wants to implement a scheduling system where tasks need to be prioritized and executed quickly. Which algorithmic design technique is most appropriate?
Divide and Conquer
Greedy Algorithm
Dynamic Programming
Backtracking
Scenario: You have been given a problem where there is no efficient solution, and the exact solution is required only for small instances. What approach is most suitable?
Brute Force
Approximation Algorithms
Randomized Algorithms
Divide and Conquer
Scenario: A sorting algorithm has a time complexity of O(n2). Which input size is feasible for this algorithm to run within a few seconds?
n=104
n=102
n=106
n=103
Scenario: Given an algorithm with a time complexity of O(2n), for what input size does it become impractical?
n=10
n=20
n=50
n=100
Scenario: Which of the following is an example of Ω(n) performance in the best case?
Searching for an element in a sorted array using linear search
Sorting an array using quicksort
Searching for an element using binary search
Traversing a graph with DFS
Scenario: A recursive function solves T(n)=T(n/2)+n2. What is the time complexity?
O(n log n)
O(n2)
O(n3)
O(nlog23)
Scenario: You analyze an algorithm with T(n)=2T(n−1)+1. What is its complexity?
O(n2)
O(2n)
O(n log n)
O(n)
Scenario: An algorithm with recurrence T(n)=2T(n/2)+n fits into which category using the Master Theorem?
Divide and Conquer with O(n log n)
Linear time O(n)
Quadratic time O(n2)
Exponential time O(2n)
Scenario: You need to store hierarchical data like a company’s organizational structure. Which data structure is best suited?
Queue
Binary Tree
Stack
Graph
Scenario: A web browser maintains user navigation history for the back button. What data structure is most appropriate?
Queue
Stack
Binary Tree
Graph
Scenario: A queue is implemented to manage jobs in a printer. Which operation is most efficient in this setup?
Enqueue at the front
Dequeue at the rear
Dequeue at the front
Enqueue at both ends
Scenario: A graph has 1000 vertices and 2000 edges. Which algorithm will likely run faster to find a Minimum Spanning Tree?
Prim’s Algorithm
Kruskal’s Algorithm
Both perform equally
Neither is suitable
Scenario: You have a weighted, connected graph. Which property ensures that Prim’s and Kruskal’s algorithms produce the same MST?
Negative weights
Unique weights
Equal edge weights
Directed graph
Scenario: You are tasked to determine the number of ways to make change for an amount using given coin denominations. Which algorithm design is appropriate?
Backtracking
Greedy Algorithm
Dynamic Programming
Divide and Conquer
Scenario: Solving the matrix chain multiplication problem requires:
Divide and Conquer
Brute Force
Dynamic Programming
Greedy Algorithm
Scenario: The problem of finding the edit distance between two strings can be solved using:
Greedy Algorithm
Dynamic Programming
Divide and Conquer
Brute Force
Scenario: You want to schedule jobs on a single machine to minimize total completion time. Which algorithm type will yield the optimal solution?
Dynamic Programming
Greedy Algorithm
Backtracking
Divide and Conquer
Scenario: A problem requires minimizing the number of platforms needed at a railway station. Which approach should you use?
Brute Force
Dynamic Programming
Greedy Algorithm
Divide and Conquer
Scenario: The Huffman encoding problem can be solved using:
Dynamic Programming
Divide and Conquer
Backtracking
Greedy Algorithm
Scenario: A sorted array is used for searching a number. If the array size doubles, how does the number of comparisons in binary search change?
Doubles
Increases linearly
Increases logarithmically
Remains constant
Scenario: A graph needs to be traversed to find if two nodes are connected. Which search algorithm is more suitable for this?
Binary Search
Linear Search
Depth-First Search
Sorting and Searching
Scenario: In a social network graph, you want to find all people connected to a specific person. Which search algorithm works best?
Binary Search
Breadth-First Search
Depth-First Search
Linear Search
Scenario: You need to sort a nearly sorted array with minimal swaps. Which sorting algorithm will be most efficient?
Quick Sort
Bubble Sort
Insertion Sort
Merge Sort
