To prepare for technical interviews at top tech companies like Google, Microsoft, Amazon, and Meta, you should aim to master the following DSA topics. These companies test problem-solving skills, algorithmic thinking, and system design concepts comprehensively. Here's a complete list:

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1. Arrays and Strings

• Basics: Traversing, Searching, Sorting
• Two Pointers and Sliding Window Techniques
• Prefix Sum, Difference Arrays
• Subarray Problems (Maximum Subarray, Kadane’s Algorithm)
• Merge Intervals
• Matrix (2D Arrays): Spiral Traversal, Rotate Matrix
• Important String Problems: Palindromes, Anagram Checks
• Pattern Matching: KMP, Rabin-Karp, Z Algorithm

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2. Recursion and Backtracking

• Subsets and Subsequence Generation
• Permutations and Combinations
• N-Queens, Sudoku Solver
• Word Search in Grids
• Rat in a Maze
• Backtracking Optimization with Pruning

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3. Searching and Sorting

• Binary Search and Variants:
  • Search in Rotated Sorted Array
  • First/Last Occurrence
  • Median of Two Sorted Arrays
• Sorting Algorithms:
  • QuickSort, MergeSort, HeapSort
  • Counting Sort, Bucket Sort, Radix Sort
• Applications of Sorting:
  • Meeting Rooms, Minimum Platforms

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4. Linked Lists

• Singly and Doubly Linked Lists
• Detect and Remove Cycles (Floyd’s Cycle Detection)
• Merge Two Sorted Linked Lists
• Reverse Linked List (Iterative and Recursive)
• Intersection Point, Flattening Linked List

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5. Stacks and Queues

• Classic Problems:
  • Next Greater Element
  • Largest Rectangle in Histogram
  • Min Stack, Max Stack
• Queue Variants:
  • Circular Queue
  • Deque (Sliding Window Maximum)
  • Priority Queue (Heap)
• Implementations of Stack and Queue

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6. Trees

• Binary Trees:
  • Traversals (Inorder, Preorder, Postorder, Level Order)
  • Diameter, Height of Tree
  • Serialize and Deserialize a Binary Tree
• Binary Search Trees:
  • Insertion, Deletion
  • Lowest Common Ancestor
  • Validate BST
• Tree Views (Top, Bottom, Left, Right)
• Segment Trees and Fenwick Trees
• Trie (Prefix Tree): Insert, Search, Autocomplete

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7. Graphs

• Representations: Adjacency Matrix, List
• Traversal: BFS, DFS
• Shortest Path Algorithms:
  • Dijkstra, Bellman-Ford, Floyd-Warshall
• Minimum Spanning Tree: Kruskal, Prim
• Detect Cycles (Directed/Undirected Graphs)
• Topological Sorting
• Strongly Connected Components (Tarjan, Kosaraju)
• Bipartite Graph Check
• Network Flow: Ford-Fulkerson, Edmonds-Karp

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8. Greedy Algorithms

• Activity Selection Problem
• Huffman Encoding
• Minimum Spanning Tree
• Fractional Knapsack
• Job Scheduling
• Gas Station Problem

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9. Dynamic Programming (DP)

• Basic Problems:
  • Fibonacci, Climbing Stairs
  • Knapsack Problem (0/1, Unbounded)
• Intermediate Problems:
  • Longest Common Subsequence, Longest Palindromic Substring
  • Longest Increasing Subsequence
  • Matrix Chain Multiplication
  • DP on Grids (Unique Paths, Minimum Path Sum)
• Advanced Problems:
  • DP on Trees
  • DP with Bitmasks
  • Egg Dropping Problem

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10. Divide and Conquer

• Sorting Algorithms: MergeSort, QuickSort
• Binary Search Applications
• Closest Pair of Points
• Maximum Subarray (Kadane's Variant)

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11. Bit Manipulation

• Basics: AND, OR, XOR, NOT, Left/Right Shift
• Applications:
  • Count Set Bits
  • Check Power of Two
  • Subsets Using Bits
  • XOR Problems (Single Number, Missing Number)

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12. Disjoint Set Union (Union-Find)

• Basics:
  • Path Compression, Union by Rank
• Applications:
  • Cycle Detection
  • Kruskal’s Algorithm
  • Connected Components in Graphs

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13. Advanced Data Structures

• Heap (Min-Heap, Max-Heap)
• Hash Tables and Hash Maps
• Bloom Filters
• Suffix Arrays and Trees
• LRU Cache Implementation
• Persistent Data Structures

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14. String Algorithms

• Pattern Matching: KMP, Rabin-Karp
• Z Algorithm
• Manacher’s Algorithm (Longest Palindromic Substring)
• Suffix Tree and Suffix Array

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15. Mathematical Algorithms

• Modular Arithmetic (Modular Exponentiation, Modular Inverse)
• Euclidean Algorithm (GCD/LCM)
• Sieve of Eratosthenes (Prime Numbers)
• Combinatorics (nCr, Permutations)
• Fast Fourier Transform (FFT)

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16. Game Theory

• Grundy Numbers
• Nim Game
• Minimax Algorithm

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17. Miscellaneous

• Sliding Window Problems
• Two Pointers Technique
• Interval Problems
• Design Problems (LRU Cache, Rate Limiter)
• Randomized Algorithms (Reservoir Sampling)

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System Design (Optional but Important for Senior Roles)

• Basics of Distributed Systems
• Caching, Load Balancing, Database Sharding
• Consistent Hashing, CAP Theorem
• Designing Scalable Systems (Rate Limiter, URL Shortener, Chat Application)

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Prioritization:

1. Master the Foundational Topics: Arrays, Strings, Recursion, Searching/Sorting, Linked Lists.
2. Focus on Graphs, Trees, and DP, as they are heavily tested.
3. Practice String Algorithms, Sliding Window, and Backtracking for edge-case scenarios.

Let me know if you'd like a structured roadmap to cover these topics!