Data Structures and Algorithms (DSA) Syllabus

1. Introduction to DSA (done)

• Importance of Data Structures and Algorithms (done)
• Time and Space Complexity Analysis (Asymptotic Notations, Big-O) (done)
• Types of Algorithmic Paradigms
  • Divide and Conquer
  • Greedy Algorithms
  • Dynamic Programming
  • Backtracking
  • Branch and Bound

2. Linear Data Structures

2.1 Arrays (done)

• Definition and Types of Arrays (1D, 2D, Multi-dimensional)
• Array Operations: Insertion, Deletion, Access, Update
• Dynamic Arrays (ArrayList in Java, Vectors in C++)

2.2 Strings (need to revise!)

• Definition and Basics of String
• String Operations: Concatenation, Substring, Length, 搜索, Comparison
• String Algorithms: String Reversal, Palindrome, Anagram Detection, Character Frequency Count, String Matching

2.3 Linked Lists (done)

• Singly Linked List: Insertion, Deletion, Traversal
• Doubly Linked List: Insertion, Deletion, Traversal
• Circular Linked List
• Applications of Linked Lists (Queue Implementation, Polynomial Representation)

2.4 Stacks (done)

• Definition and Operations: Push, Pop, Peek
• Stack Implementation: STL(Standard Template Library)/Collection Framework, Array-based, Linked List-based
• Applications (Expression Evaluation, Balancing Parentheses, Recursion)

2.5 Queues (in progress...)

• Definition and Operations: Enqueue, Dequeue, Front, Rear
• Types of Queues: Simple Queue, Circular Queue, Double Ended Queue (Deque)
• Applications (Scheduling, Resource Management)

3. Non-Linear Data Structures

3.1 Trees

• Binary Tree: Structure, Operations (Insertion, Deletion, Traversal)
• Binary 搜索 Tree (BST): Insertion, Deletion, 搜索
• Balanced Trees: AVL Tree, Red-Black Tree
• Heap Trees: Min-Heap, Max-Heap, Heap Operations (Insert, Delete)
• Tree Traversals: Pre-order, In-order, Post-order, Level-order
• Applications (Expression Trees, Decision Trees, Priority Queues)

3.2 Graphs

• Graph Representation: Adjacency Matrix, Adjacency List
• Graph Traversals: Depth-First 搜索 (DFS), Breadth-First 搜索 (BFS)
• Shortest Path Algorithms: Dijkstra’s, Bellman-Ford, Floyd-Warshall
• Minimum Spanning Tree: Prim’s, Kruskal’s Algorithms
• Topological Sort and Cycle Detection
• Applications (网络 Routing, Social 网络s, GPS Navigation)

3.3 Hash-based Data Structures

• Hashing: Hash Functions, Collision Resolution
• Hash Table: Chaining, Open Addressing (Linear Probing, Quadratic Probing, Double Hashing)
• Applications (Dictionary, Database Indexing)

4. Advanced Data Structures

4.1 Trie (Prefix Tree)

• Structure and Operations (Insert, 搜索, Delete)
• Applications (Autocomplete, IP Routing, Dictionary)

4.2 Segment Tree

• Structure and Operations
• Range Queries and Updates
• Applications (Range Sum Queries, Range Minimum Queries)

4.3 Fenwick Tree (Binary Indexed Tree)

• Structure and Operations
• Applications (Prefix Sum Queries)

4.4 Disjoint Set Union (Union-Find)

• Operations: Union, Find
• Applications (网络 Connectivity, Kruskal’s Algorithm)

5. Algorithms

5.1 Sorting Algorithms

• Basic Sorting: Bubble Sort, Selection Sort, Insertion Sort
• Efficient Sorting: Merge Sort, Quick Sort, Heap Sort
• Linear Sorting: Radix Sort, Counting Sort, Bucket Sort
• Applications (Sorting Large Data, External Sorting)

5.2 搜索ing Algorithms

• Linear 搜索
• Binary 搜索
• Interpolation 搜索
• Exponential 搜索
• Applications (Finding Elements in Sorted Arrays)

5.3 Graph Algorithms

• DFS (Depth-First 搜索)
• BFS (Breadth-First 搜索)
• Dijkstra’s Algorithm for Shortest Path
• Bellman-Ford Algorithm
• Floyd-Warshall Algorithm for All-Pairs Shortest Paths
• Prim’s Algorithm and Kruskal’s Algorithm for Minimum Spanning Tree

5.4 Dynamic Programming

• Knapsack Problem (0/1 Knapsack, Fractional Knapsack)
• Longest Common Subsequence (LCS)
• Longest Increasing Subsequence (LIS)
• Matrix Chain Multiplication
• Fibonacci Series (Recursive, Iterative, DP)
• Applications (Optimal Substructure, Overlapping Subproblems)

5.5 Greedy Algorithms

• 动态 Selection
• Huffman Encoding
• Fractional Knapsack
• Job Sequencing with Deadlines
• Applications (Optimal Solutions with Local Choices)

5.6 Backtracking

• N-Queens Problem
• Sudoku Solver
• Subset Sum Problem
• Hamiltonian Path and Cycle
• Graph Coloring
• Applications (Puzzles, Optimized 搜索 Problems)

5.7 Divide and Conquer

• Merge Sort
• Quick Sort
• Strassen’s Matrix Multiplication
• Applications (Divide Large Problems into Simpler Subproblems)

5.8 Bit Manipulation

• Basic Bitwise Operations (AND, OR, XOR, NOT, Left/Right Shift)
• Applications (Checking Odd/Even, Counting Set Bits, Bit Masking)

5.9 Sliding Window Technique

• Fixed Size Window: Max/Min Sum, Subarray Problems
• Variable Size Window: Longest Substring Problems

5.10 Two Pointer Technique

• Pair Problems (Find Pair with Given Sum, Triplet Sum)
• Sorted Array Problems (Find Specific Elements)

6. Applications of Data Structures and Algorithms

• File Systems
• Databases
• 网络 Routing Algorithms
• Operating Systems (Memory Management, Process Scheduling)
• Compilers (Syntax Tree, Parsing)
• Web Crawling
• Machine Learning (Data Preprocessing, Decision Trees)

7. I'm Preparing from (recommended):

• YouTube Channel:
  • Kunal Kushwaha: https://www.youtube.com/playlist?list=PL9gnSGHSqcnr_DxHsP7AW9ftq0AtAyYqJ
  • College Wallah: https://www.youtube.com/playlist?list=PLxgZQoSe9cg00xyG5gzb5BMkOClkch7Gr
• Online Platforms:
  • GeeksforGeeks
  • Javatpoint
  • LeetCode