B.TechSemester 52025-26Design And Analysis Of AlgorithmBCS503
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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) — complete question paper · 70 marks · 3 Hours

Section AAttempt all questions in brief. 02 x 7 = 14
  • a
    Define algorithm and its characteristics
  • b
    1. Compute the time complexity of the following recurrence relation
  • c
    Find the total number of comparisons after using the Insertion sort on the following array. Array A= {23, 32, 40, 44, 54, 63, 72, 89}
  • d
    What is a Persistent Data Structure?
  • e
    Define growth of functions
  • f
    In 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?
  • g
    Define Polynomial-time Verifiability
Section BAttempt any three of the following: 07 x 3 = 21
  • a
    Compute the time complexity of the following recurrence relation
  • b
    Let 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
  • c
    Provides 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
  • d
    Explain Merge Sort with example and also compute time complexity
  • e
    Explain Fibonacci Heap with suitable example
Section CAttempt any one part of the following: 07 x 1 = 07
  • a
    Consider 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?
  • b
    Consider 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
  • a
    In 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?
  • b
    Explain Kruskal’s algorithm for MST and also discuss the time complexity
  • a
    Solve 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
  • b
    Explain Dijkstra’s Algorithm. Prove that it may fail if the graph contains negative edge weights
  • a
    Explain the Branch and Bound approach for the Travelling Salesman Problem (TSP) using the "Reduced Cost Matrix" method
  • b
    Given a 3 X 3 cost matrix, calculate the initial "Lower Bound" using the row-reduction method
  • a
    Using Rabin-Karp algorithm, how many hash computations are needed to search for a pattern of length 4 in a text of length 15?
  • b
    Describe 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. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.

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