Algorithms_Extended_Intro_Presentation.pptx
- 2. Introduction to Algorithms • Algorithms are step-by-step procedures for solving problems: • - Used in computer science, mathematics, and daily tasks. • - Essential for programming and software development. • - Examples: sorting, searching, optimization algorithms.
- 3. Characteristics of an Algorithm • - **Input**: Accepts inputs. • - **Output**: Produces outputs. • - **Definiteness**: Clear and unambiguous steps. • - **Finiteness**: Terminates after a finite number of steps. • - **Effectiveness**: Steps are simple and executable.
- 4. Types of Algorithms • - **Sorting Algorithms**: Arrange data (e.g., QuickSort, MergeSort). • - **Searching Algorithms**: Locate items (e.g., Binary Search, Linear Search). • - **Optimization Algorithms**: Find best solutions (e.g., Dijkstra's, A*). • - **Divide and Conquer Algorithms**: Break problems into sub-problems.
- 5. Sorting Algorithms • - **Bubble Sort**: Repeatedly swaps adjacent elements. • - **Selection Sort**: Selects the smallest element repeatedly. • - **MergeSort**: Divides and merges sorted subarrays. • - **QuickSort**: Uses a pivot to partition arrays.
- 6. Searching Algorithms • - **Linear Search**: Sequentially checks elements. • - **Binary Search**: Efficient search on sorted arrays. • - **Depth-First Search (DFS)**: Explores all paths in a graph. • - **Breadth-First Search (BFS)**: Explores neighbors first in a graph.
- 7. Divide and Conquer Technique • - Breaks a problem into smaller sub-problems. • - Solves each sub-problem recursively. • - Combines solutions for the final result. • - Examples: MergeSort, QuickSort, Binary Search.
- 8. Greedy Algorithms • - Builds solutions step-by-step by choosing optimal sub-solutions. • - Works for problems with optimal substructure. • - Examples: • - Huffman Coding for data compression. • - Kruskal's Algorithm for Minimum Spanning Trees.
- 9. Dynamic Programming • - Solves problems by breaking them into overlapping sub-problems. • - Stores intermediate results to avoid redundant calculations. • - Examples: • - Fibonacci sequence. • - Longest Common Subsequence (LCS).
- 10. Graph Algorithms • - Solve problems related to graph structures. • - Examples: • - Dijkstra's Algorithm: Shortest path in weighted graphs. • - Prim's Algorithm: Minimum Spanning Tree. • - Floyd-Warshall: All-pairs shortest paths.
- 11. Backtracking • - Tries all possible solutions and backtracks upon failure. • - Suitable for constraint satisfaction problems. • - Examples: • - N-Queens Problem. • - Sudoku Solver.
- 12. Complexity Analysis • - **Time Complexity**: Time taken as a function of input size. • - **Space Complexity**: Memory used as a function of input size. • - Notations: • - O(n): Worst-case. • - Ω(n): Best-case. • - Θ(n): Average-case.
- 13. Recursion vs Iteration • - **Recursion**: Function calls itself until base condition is met. • - **Iteration**: Loops until a condition is satisfied. • - Recursion often simplifies problems, but uses more stack space.
- 14. Applications of Algorithms • - **Data Compression**: Huffman Coding. • - **Cryptography**: RSA algorithm. • - **Pathfinding**: Dijkstra's and A* algorithms. • - **Machine Learning**: Gradient Descent.
- 15. Emerging Trends in Algorithms • - Quantum Algorithms: Shor's and Grover's algorithms. • - AI Algorithms: Reinforcement learning, deep learning. • - Bioinformatics Algorithms: Genome sequencing. • - Real-Time Algorithms: Used in robotics and IoT.
- 16. Challenges in Algorithm Design • - Balancing time and space complexity. • - Handling large data efficiently. • - Ensuring scalability for distributed systems. • - Dealing with NP-complete problems.
- 17. Conclusion • - Algorithms are fundamental to problem- solving in computing. • - Essential for efficient and scalable solutions. • - Evolving with advances in technology and applications.