Design And Analysis Of Algorithm (BCS503) - AKTU Question Paper 2025-26
B.Tech · Semester 5 · Free PDF Download
This is the official AKTU Design And Analysis Of Algorithm Previous Year Question Paper for B.Tech Semester 5, academic session 2025-26. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.
Course:B.Tech
Semester:Semester 5
Session:2025-26
University:AKTU / UPTU
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Questions Asked in 2025-26
Design And Analysis Of Algorithm (BCS503) — extracted question text · 70 marks · 3 Hours
Section AAttempt all questions in brief. 02 x 7 = 14
- aDefine algorithm and its characteristics
- b1. Compute the time complexity of the following recurrence relation
- cFind the total number of comparisons after using the Insertion sort on the following array. Array A= {23, 32, 40, 44, 54, 63, 72, 89}
- dWhat is a Persistent Data Structure?
- eDefine growth of functions
- fIn a Red -Black Tree, how many black nodes are there on any path from the root to the leaf if the black height is 3?
- gDefine Polynomial-time Verifiability
Section BAttempt any three of the following: 07 x 3 = 21
- aCompute the time complexity of the following recurrence relation
- bLet P be a Quick Sort Program to sort numbers in ascending order using the first element as pivot. Let 𝑡1 and 𝑡2 be the number of comparisons made by P for the inputs {1, 2, 3, 4, 5} and {4, 1, 5, 3, 2} respectively. Find the number of 𝑡1 and 𝑡2
- cProvides the decreasing order of asymptotic complexity of functions 𝑓1, 𝑓2, and 𝑓3? Justify your answer. 𝑓1 (n) = 𝑛𝑘𝑙𝑜𝑔𝑛 , 𝑓2 (n) = 𝑛1000, and 𝑓3 (n) = 𝑘𝑛𝑙𝑜𝑔𝑘 . Here, k is a very large constant
- dExplain Merge Sort with example and also compute time complexity
- eExplain Fibonacci Heap with suitable example
Section CAttempt any one part of the following: 07 x 1 = 07
- aConsider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. 𝑊𝑖𝑗 in the matrix W below is the weight of the edge {i, j}. What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?
- bConsider a matrix multiplication chain F 1F2F3F4F5, where matrices F 1, F2, F3, F 4, and F 5 are of dimensions 2×25, 25×3, 3×16, 16×1 and 1×1000, respectively. Find the optimal parenthesis and total number of scalar multiplications
- aIn a Skip List, if the probability of a node being promoted to the next level is 1/2, what is the expected number of nodes at the second level if there are 100 nodes at the base level?
- bExplain Kruskal’s algorithm for MST and also discuss the time complexity
- aSolve a 0/1 Knapsack problem with given profits [60, 100, 120 , 90, 75, 45], weights [5, 10, 15, 2 0, 35, 40 ] and capacity = 50 using Dynamic Programming
- bExplain Dijkstra’s Algorithm. Prove that it may fail if the graph contains negative edge weights
- aExplain the Branch and Bound approach for the Travelling Salesman Problem (TSP) using the "Reduced Cost Matrix" method
- bGiven a 3 X 3 cost matrix, calculate the initial "Lower Bound" using the row-reduction method
- aUsing Rabin-Karp algorithm, how many hash computations are needed to search for a pattern of length 4 in a text of length 15?
- bDescribe the Boyer -Moore string matching algorithm. How do the "bad character" and "good suffix" heuristics work?
Question text is extracted from the official AKTU question paper PDF above. Check the original PDF for equations, diagrams and complete wording. Extracted: 2026-08-23.
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