Q.1
14 Marks(a)
Define Following terms
1Space Complexity
2Universal Quantifier
3Vector
(b)
Explain the characteristics of a good algorithm.
(c)
Explain asymptotic notations (Big-O, Big-Theta, Big-Omega) with graphs and examples.
Gujarat Technological UniversitySummer 2026 examination
GTU BE04000241 Analysis and Design of Algorithms Summer 2026 Question Paper & PDF
B.E. · Computer Engineering · Semester 4 · Subject code BE04000241
- Total
- 70 marks
- To pass
- 23 marks (33%)
- Duration
- 2.5 Hours 10:30 AM – 1:00 PM
- Questions
- 5 with internal choice
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Q.2
14 Marks(a)
Calculate the number of comparisons in linear search when the element is at:
1)first position
2)last position
(b)
Describe time complexity and explain theoretical vs empirical analysis.
(c)
Analyze Bucket Sort and Counting Sort algorithms with example.
OR
(c)
Explain amortized analysis and its techniques in detail.
Q.3
14 Marks(a)
Write general method of recurrence.
(b)
Solve recurrence using Master Theorem:
1)T(n) = 2T(n/2) + n
2)T(n) = 3T(n/2) + n²
(c)
Write and analyze Binary Search algorithm. Demonstrate for: A = {3, 7,8, 10,11,15, 20, 25, 30}, Key = 15
OR
(a)
Explain the Principle of Optimality?
(b)
Solve Making Change problem using Dynamic programming:
Coins = {1, 3, 4}, Amount = 6.
(c)
Explain Matrix Chain Multiplication using Dynamic programming.
Q.4
14 Marks(a)
List characteristics of Greedy Algorithms.
(b)
Solve Fractional Knapsack using greedy method: Weights = {10, 20, 30} Values = {60, 100, 120} Capacity = 50.
(c)
Find the Minimum Spanning Tree using Kruskal’s Algorithm for the given graph:
Consider a graph with vertices edge weights: GH: 8, GI: 2, GJ: 5, GK: 3, HI: 1, HJ: 7, HK: 4, IJ: 5, IK: 9, JK:
OR
(a)
Define Activity Selection problem?
(b)
Find an optimal Huffman code for the following set of frequency. a: 50, b: 20, c: 15, d: 30.
(c)
Find the Minimum Spanning Tree using Prim’s Algorithm starting from vertex A for the graph: Vertices: A, B, C, D, E. Consider a graph with vertices edge weights: AB:2, AC:3, AD:6, BC:1, BD:4, BE:5, CD:2, CE:7, DE:3.
Q.5
14 Marks(a)
Define Following
1Articulation point
2Graph
3Tree
(b)
Compare DFS and BFS.
(c)
Explain topological sorting with algorithm and example.
OR
(a)
Explain polynomial reduction?
(b)
Differentiate NP-Complete and NP-Hard problems.
(c)
Explain Backtracking Method. What is N-Queens Problem? Give solution of 4- Queens Problem using Backtracking Method.
Other Semester 4 subjects
BE Computer
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About this paper
Official Gujarat Technological University (GTU) examination paper for Analysis and Design of Algorithms (Summer 2026, B.E. · Computer Engineering, Sem 4). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.