JNTU ananthapur R23 btech 2nd year -1sem ADSA questions papers answers
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ADSA Exam Preparation
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7 marks Long answer
Write an algorithm for finding maximum element of an array perform best, worst and average case complexity with appropriate order notations.
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Algorithm iterates through the array, returning the maximum value.
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7 marks Long answer
Construct a B+ Tree of order 3 for the keys: 10, 20, 5, 6, 12, 30, 7, 17. Show the final tree.
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Insert keys while maintaining B+ Tree properties.
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6 marks Long answer
Perform insertion and deletion operations on a Splay Tree for the elements: 10, 20, 30, 40, 50. Show tree after each step.
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Insert and delete elements while maintaining tree structure.
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6 marks Long answer
Given a Red-Black Tree, insert 18, 11, 14, 15 and show how properties are preserved during insertion.
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Insert while ensuring red-black properties are maintained.
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6 marks Long answer
Insert the values 12, 44, 13, 88, 23, 94, 11, 39 into a hash table of size 13 using division method. Show the final table.
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Use modulo operation to place values in the table.
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6 marks Long answer
Sort the array [9, 4, 7, 3, 1, 6] using Heap Sort. Show the heap construction and sorting steps.
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Build heap, then sort by repeatedly extracting max.
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6 marks Long answer
Use Divide and Conquer to perform Matrix Multiplication for two 2x2 matrices using Strassen's algorithm. Show all 7 multiplications.
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Apply Strassen's algorithm to compute matrix product.
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6 marks Long answer
Solve the Travelling Salesman Problem using Dynamic Programming for 4 cities with given cost matrix. Show the steps and minimum cost.
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Use DP to find minimum cost path visiting all cities.
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6 marks Long answer
Solve the Fractional Knapsack problem using Greedy method: Weights = [10, 20, 30], Values = [60, 100, 120], Capacity = 50. Show steps.
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Select items based on value-to-weight ratio until capacity is reached.
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4 marks Medium answer
Explain the method of solving recurrence equations with suitable example.
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Use substitution or iteration to simplify and solve the equation.
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4 marks Medium answer
Explain the necessary steps for analyzing the efficiency of recursive algorithms.
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Identify base cases, recursive cases, and use recurrence relations.
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4 marks Medium answer
Compare Splay Trees with AVL Trees based on operations and efficiency.
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Splay Trees are self-adjusting; AVL Trees maintain strict balancing.
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4 marks Medium answer
Discuss how clustering affects hash performance in open addressing.
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Clustering can lead to longer search times due to increased collision.
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4 marks Medium answer
Write the time complexity of Heap Sort with three cases and compare with Merge Sort.
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Heap Sort: O(n log n); Merge Sort: O(n log n) with stable sorting.
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4 marks Medium answer
Compare Strassen's algorithm with the standard approach.
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Strassen's is faster than standard O(n^3) method.
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4 marks Medium answer
Mention the challenges in solving TSP using brute force.
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Exponential time complexity makes it impractical for large datasets.
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4 marks Medium answer
Why is Greedy method not suitable for 0/1 Knapsack?
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It may not yield the optimal solution due to indivisibility of items.
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3 marks Medium answer
Write the asymptotic notations used for best case, average case and worst case analysis of algorithms.
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Best case: O(1), Average case: O(n), Worst case: O(n^2).
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3 marks Medium answer
Explain how leaf node chaining helps in range queries in B+ Trees.
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Leaf node chaining allows efficient traversal for range queries.
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2 marks Short answer
What are the key steps involved in designing an algorithm?
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Define the problem, analyze requirements, design, implement, test.
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2 marks Short answer
Define asymptotic notation. Mention any two types.
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Asymptotic notation describes algorithm efficiency; types include Big-O and Big-Ω.
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2 marks Short answer
Mention any two applications of AVL Trees.
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Used in databases and memory management.
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2 marks Short answer
What is a B-Tree? Mention one operation performed on B-Trees.
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A B-Tree is a self-balancing tree; operations include insertion.
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2 marks Short answer
List any two properties of Red-Black Trees.
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Each node is red or black; the root is black.
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2 marks Short answer
Define Hash Function and its significance in Hash Tables.
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A hash function maps data to a fixed size; it ensures efficient data retrieval.
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2 marks Short answer
What is the purpose of Strassen's Matrix Multiplication in Divide and Conquer?
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To reduce the time complexity of matrix multiplication.
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2 marks Short answer
Define the term 'Greedy Method' with one example application.
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A problem-solving method that makes the locally optimal choice; e.g., Kruskal's algorithm.
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2 marks Short answer
State the principle of Dynamic Programming.
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Breaks problems into simpler subproblems and stores results.
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2 marks Short answer
What is meant by NP-Complete problem?
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A problem for which no efficient solution is known, but solutions can be verified quickly.
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2 marks Short answer
List any four properties of Red-Black Trees.
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Each node is red or black; no two red nodes in a row.
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