Complexity Analysis

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Big O notation  
Time and space complexity  
Best, average, and worst-case scenarios  

Fundamental Data Structures

  • Arrays and Strings

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Insertion, deletion, traversal  
String manipulation techniques  

  • Linked Lists

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Singly Linked List  
Doubly Linked List  
Circular Linked List  
Common operations and use cases  

  • Stacks and Queues

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LIFO vs. FIFO principles  
Implementation using arrays and linked lists  

Trees

  • Binary Trees

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Tree terminology (nodes, edges, height, depth)  
Traversals methods (pre-order, in-order, post-order)  

  • Binary Search Trees

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Properties of BST  
Operations on BST (insertion, deletion, search)  

  • Balanced Binary Trees

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AVL Trees  
Red-Black Trees  
Importance of tree balancing  

Advanced Data Structures

  • Heaps

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Min-heaps and max-heaps  
Heap operations  
Priority queues  

  • Hash Tables

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Hash functions  
Collision resolution strategies (chaining, open addressing)  
Load factor and resizing  

Graphs

  • Graph Theory Basics

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Definitions (vertices, edges, adjacency)  
Directed vs. undirected graphs  

  • Graph Representation

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Adjacency matrix  
Adjacency list  

  • Graph Traversal Algorithms

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Depth-first search (DFS)  
Breadth-first search (BFS)  

  • Shortest Path Algorithms

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Dijkstra’s algorithm  
Bellman-Ford algorithm  

Sorting and Searching Algorithms

  • Sorting Algorithms

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Bubble Sort  
Selection Sort  
Insertion Sort  
Merge Sort  
Quick Sort  
Heap Sort  
Radix Sort  

  • Searching Algorithms

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Linear Search  
Binary Search  
Search in trees and graphs  

Algorithm Design Techniques

  • Recursion

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Understanding recursive functions  
Tail recursion  

  • Divide and Conquer

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Concept and applications  
Master theorem for complexity  

  • Dynamic Programming

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Principles and memoization  
Classic problems (Fibonacci sequence, knapsack problem)  

  • Greedy Algorithms

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Strategy and examples  
When to use greedy vs. dynamic programming  

Advanced Topics

  • Backtracking Algorithms

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Concept and problem-solving  
N-Queens problem, sudoku solver  

  • Advanced Data Structures

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Tries  
Segment trees  
Disjoint sets (Union-Find)  

  • Algorithm Complexity Classes

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P vs. NP  
NP-Complete problems