Algorithm Design and Analysis Quiz

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(n^log₂3)

• O(n)

Scenario: For the recurrence T(n)=2T(n/4)+√n, , what is the asymptotic complexity?

• O(logn)

• O(n^1/2)

• O(n^0.5 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