DESIGN &ANALYSIS OF ALGORITHMS

Categories: Semester-5
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Introduction of Design & Analysis of Algorithms:- Unit:- 1
Design and Analysis of Algorithms is a field of computer science that focuses on creating efficient and effective methods for solving computational problems. It involves the development of algorithms, the study of their correctness, and the evaluation of their performance in terms of time and space complexity. This discipline helps ensure that algorithms are optimized for speed and resource usage, making them practical for real-world applications.

  • Characteristics of Algorithm
    07:56
  • Analysis of algorithm: Asymptotic Analysis of Complexity Bounds – Best, Average and Worst-Case Behaviour
    14:25
  • Performance Measurements of Algorithm, Time and Space Trade-offs
    11:59
  • Analysis of Recursive Algorithms through Recurrence relations: Substitution method,
    07:40
  • Recursion tree method and Masters’ theorem
    06:34

Fundamental Algorithmic Strategies:- Unit:- 2
Fundamental Algorithmic Strategies in the context of Design and Analysis of Algorithms refer to the basic approaches used to solve computational problems. These strategies include techniques such as divide-and-conquer, dynamic programming, greedy algorithms, and backtracking. Each strategy offers a unique way to approach problem-solving, focusing on efficiency and optimization to handle complex tasks effectively.

Graph and Tree Algorithms:- Unit:- 3
Graph Algorithms: Graph algorithms involve methods for processing and analyzing data structured as graphs, where nodes represent entities and edges represent relationships. These algorithms are used to solve problems like finding the shortest path between nodes, detecting cycles, and determining connectivity within a graph. Tree Algorithms: Tree algorithms focus on operations on tree data structures, where each node has a parent-child relationship. These algorithms handle tasks such as traversing nodes (e.g., in-order, pre-order, post-order), searching for specific values, and balancing trees to optimize performance.

Tractable and Intractable Problems:- Unit:- 4
Tractable Problems are those for which an algorithm can find a solution in polynomial time, meaning the time taken to solve the problem increases at a manageable rate as the input size grows. Intractable Problems, on the other hand, cannot be solved in polynomial time, and their solution requires super-polynomial time, making them impractical to solve for large input sizes due to the excessive time and computational resources needed.

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