1. Introduction to data structures and algorithms
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Understanding the importance of DSA in software development.
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Defining data structures and algorithms.
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Analyzing the efficiency of algorithms using Time and Space Complexity, especially focusing on Big O notation.
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Choosing the best algorithm for a particular problem.
2. Fundamental data structures
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Arrays and Strings: Introduction, types, operations, and problem-solving techniques like Two Pointers and Sliding Window.
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Linked Lists: Concepts, types (singly, doubly, circular), representation, and operations (insertion, deletion, traversal).
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Stacks and Queues: Introduction, operations (push, pop, enqueue, dequeue), implementations using arrays and linked lists, and applications like expression evaluation.
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Trees: Concepts (nodes, edges, root), types (binary, binary search tree, heap), traversals (inorder, preorder, postorder, level order), and heap implementation.
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Graphs: Concepts, representations (adjacency matrix, adjacency list), and basic traversal algorithms like Breadth-First Search (BFS) and Depth-First Search (DFS).
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Hashing: Introduction to hashing techniques and their application in data retrieval.
3. Core algorithms
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Searching: Linear search and Binary search.
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Sorting: Common algorithms like Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, Quick Sort, and Heap Sort, along with their implementations and analysis.
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Recursion: Understanding recursion, recursive functions, base cases, recursion vs. iteration, and solving problems like Fibonacci sequence, Tower of Hanoi, and tree traversals.
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Divide and Conquer: Introduction and application to problems like binary search and merge sort.
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Dynamic Programming (DP): Introduction, key principles (overlapping subproblems, optimal substructure), memoization, tabulation, and solving problems like Fibonacci sequence, Knapsack problem, and Longest Common Subsequence.
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Graph Algorithms: Exploring algorithms like Dijkstra's algorithm for shortest paths.
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Greedy Algorithms: Learning the concept and applying it to relevant problems.
4. Advanced topics (depending on course level)
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Advanced Tree Structures: AVL trees, Red-Black trees, and B-trees.
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String Matching Algorithms: Techniques like KMP algorithm (Knuth-Morris-Pratt).
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Graph Theory Applications: Network flow, minimum spanning trees.
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Bit Manipulation: Techniques for manipulating bits and their applications.
5. Problem-solving and competitive programming
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Solving various problems from competitive programming platforms and interview questions.
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Developing strong logic-building and problem-solving skills.
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Improving coding efficiency and preparing for technical interviews.