RTU Kota B.Tech AI 5th Semester Analysis of Algorithms Question Paper 2025

RTU Artificial Intelligence Analysis of Algorithms 2025 Paper Review

Preparing for the Rajasthan Technical University B.Tech Analysis of Algorithms exam requires a strict understanding of computational complexity and mathematical optimization. For Artificial Intelligence students, this subject forms the direct theoretical basis for searching state spaces, optimizing loss functions, and selecting efficient heuristic approaches. You cannot build scalable machine learning models or fast search agents without mastering the time and space complexity of underlying algorithms. The 2025 paper tests your capability to write recursive equations, trace dynamic programming tables, and prove NP-completeness. Reviewing this specific branch paper shows you exactly how examiners frame mathematical problems and allocate marks across the theoretical modules. This systematic preparation helps you approach your fifth-semester exam confidently.

Understanding the AI Branch Exam Pattern

The RTU theory examination is a three-hour paper worth 70 marks. The paper features three distinct sections designed to evaluate both theoretical definitions and comprehensive algorithmic tracing.

• Part A: This section contains ten compulsory questions worth two marks each. You must define asymptotic notations (Big-O, Omega, Theta), state the principle of optimality, or write the exact time complexity of Strassen's matrix multiplication under 30 words.
• Part B: You will find seven questions here. You must answer five of them. Each question is worth four marks. Your answers require solving recurrence relations using the Master Theorem, tracing the steps of the Rabin-Karp string matching algorithm, or explaining the functional difference between Las Vegas and Monte Carlo randomized algorithms.
• Part C: This section offers five major questions. You need to answer three. Each question carries ten marks. These require you to fill out a complete 0/1 Knapsack dynamic programming table, draw the full state-space tree for the N-Queens backtracking problem, or execute Dijkstra's algorithm step-by-step to find the shortest path.

Core Topics Evaluated in the AI Paper

The 2025 question paper covers several critical modules that establish the mathematical rules for algorithmic efficiency. Focus your study time on these specific areas to maximize your score.

Divide and Conquer Method

This module evaluates your understanding of recursive problem-solving. You must master the execution and time complexity derivation for Binary Search, Merge Sort, and Quick Sort. Practice writing the exact recurrence relations for these algorithms. The 2025 paper frequently tests Strassen's matrix multiplication; you must know the seven specific multiplication formulas and how they reduce the standard time complexity from O(n3

) to O(n2.81

).

Greedy Method and Dynamic Programming

These two optimization strategies form the heavy computational core of the syllabus. For the Greedy Method, study Job Sequencing with deadlines, Optimal Merge Patterns, and Minimal Spanning Trees (Kruskal and Prim). For Dynamic Programming, you must understand how overlapping subproblems are solved using memoization or tabulation. Practice calculating the exact scalar multiplications for Matrix Chain Multiplication and tracing the two-dimensional grids for the Longest Common Subsequence and the 0/1 Knapsack Problem.

Backtracking and Branch and Bound

This section focuses on searching state spaces for optimal solutions. You must understand how backtracking builds candidates iteratively and abandons them upon detecting a failure. Practice drawing the exact state-space tree for the 8-Queens problem. For Branch and Bound, study the Traveling Salesman Problem and understand how to calculate and apply lower bounds to prune the search tree effectively.

Pattern Matching and Randomized Algorithms

String matching is tested for precise logical execution. You must understand the Naive approach and the optimized mechanics of the Knuth-Morris-Pratt (KMP) and Boyer-Moore algorithms. Practice calculating the prefix function (pi table) for KMP. For randomized algorithms, study the definitions and applications of Min-Cut and 2-SAT problems, and differentiate clearly between algorithms that guarantee correctness (Las Vegas) versus those that guarantee a fixed runtime limit (Monte Carlo).

NP-Hard and NP-Complete Problem Classes

This theoretical module categorizes algorithms based on their tractability. You must master the formal definitions of the P, NP, NP-Hard, and NP-Complete complexity classes. Expect questions asking you to explain polynomial-time reduction or prove that a specific problem belongs to the NP-Complete class.

Answer Writing Strategy for High Marks

RTU evaluators look for clean mathematical steps, explicitly drawn arrays, and clear tabular traces. Use a blue pen for your general text and mathematical derivations, and use a black pen and ruler for drawing state-space trees, dynamic programming grids, and algorithm trace tables.

In Part A, answer directly. If a question asks for the definition of the Big-O notation, write the exact mathematical inequality (f(n)≤c⋅g(n) for all n≥n0

​) and define the constants explicitly.

In Part B, use clear structural steps. When solving a recurrence relation using the Master Theorem, explicitly state the values of a, b, and f(n), compare f(n) with nlogb

​a

, and state the specific case applied before writing the final time complexity.

In Part C, precision in calculation is critical. When solving a ten-mark Longest Common Subsequence problem, do not just write the final string output. Draw the complete two-dimensional matrix, fill in the numerical lengths explicitly, draw the directional arrows for the traceback path, and write down the final matched characters. Draw a clean box around your final time complexities and derived scalar values.

Time Management During the Exam

Allocate 20 minutes to Part A. Spend 40 minutes on Part B. Reserve the remaining 120 minutes for the three long-answer questions in Part C. Drawing multi-level state-space trees, computing multi-cell DP tables, and executing matrix multiplication formulas requires steady focus and significant time to prevent tracking mistakes. This plan guarantees you 40 minutes per major question, giving you time to cross-verify your array indices and recursive boundary limits. Use the final 10 minutes to verify your question numbering, ensure all matrix axes are labeled correctly, and check that you have not skipped any intermediate recursive calls in your trace tables.