Advanced Algorithms: Trees, Graphs, and Dynamic Programming

Description

In this course, you will learn:

• Improve your computational skills with a thorough examination of key data structures and algorithms. Explore binary and M-Way search trees, as well as AVL and red-black trees, and learn about their insertions, deletions, and balancing procedures.
• Learn graph theory, from basic ideas to advanced traversals like breadth-first and depth-first searches, as well as algorithms like Prim's and Kruskal's.
• Learn dynamic programming using real-world examples like as factorial, Fibonacci, and the coin change problem. The course closes with actual Bloom Filter applications, which provide insights into efficient data processing and optimization strategies.

Syllabus:

1. Binary Search Trees

• Binary Search Tree Overview
• Traversals
• Deletions & Insertions

2. AVL & Red-Black Trees

• Balance Factor
• AVL Complexity
• Red-Black Trees

3. M-Way & B-Trees

• M-Way Tree Structure
• B-Trees
• B-Tree Insertions
• B-Tree Leaf Deletion
• B-Tree Internal Deletion

4. Graphs

• Graphs Overview
• Adjacency Lists & Matrices
• Breadth-First Search
• Depth-First Search
• Spanning Trees & Prim's Algorithm
• Priority Queues
• Kruskal Algorithm
• Ford-Fulkerson: Max Flow
• Ford-Fulkerson: Min Cut

5. Dynamic Programming

• Factorials & Fibonacci
• Max Subarray
• Coin Change Problem
• Bloom Filter

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