72Laboratories

Complete DSA Patterns Guide for LeetCode Mastery

Table of Contents

1. Graph Algorithms
2. Binary Search
3. Greedy Algorithms
4. String Algorithms
5. Dynamic Programming (DP)
6. Binary Search Patterns
7. Sliding Window Patterns
8. Greedy Algorithm Patterns
9. Tree Traversal Techniques
10. System Design
11. Math and Number Theory
12. Bit Manipulation

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1. Graph Algorithms

Core Concepts

• Graph Representation: Adjacency List, Adjacency Matrix, Edge List
• Graph Types: Directed, Undirected, Weighted, Unweighted
• Traversal Methods: DFS, BFS
• Advanced Algorithms: Dijkstra’s, Floyd-Warshall, Topological Sort

Key Patterns

1. DFS Traversal
   • Connected Components
   • Cycle Detection
   • Path Finding
2. BFS Traversal
   • Shortest Path in Unweighted Graph
   • Level Order Processing
   • Minimum Steps Problems
3. Union-Find (Disjoint Set)
   • Connected Components
   • Cycle Detection in Undirected Graph
   • Kruskal’s MST
4. Topological Sort
   • Course Schedule Problems
   • Dependency Resolution
   • Build Order

Practice Strategy

• Start with basic DFS/BFS traversals
• Master cycle detection techniques
• Practice shortest path algorithms
• Learn MST algorithms (Kruskal’s, Prim’s)

Resource: Graph Patterns

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2. Binary Search

Core Concepts

• Search Space: Sorted arrays, Answer space
• Template: Left, Right, Mid calculations
• Boundary Conditions: Lower bound, Upper bound

Key Patterns

1. Standard Binary Search
   • Finding exact element
   • First/Last occurrence
2. Search in Rotated Array
   • Rotated sorted array variations
   • Finding pivot point
3. Binary Search on Answer
   • Minimizing maximum or maximizing minimum
   • Feasibility function approach

Practice Strategy

• Master the basic template
• Practice boundary condition handling
• Focus on “search on answer” problems
• Understand when to use binary search

Resource: Binary Search Patterns

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3. Greedy Algorithms

Core Concepts

• Greedy Choice Property: Local optimal leads to global optimal
• Proof Techniques: Exchange argument, Greedy stays ahead
• Common Applications: Scheduling, Interval problems

Key Patterns

1. Interval Scheduling
   • Meeting rooms
   • Non-overlapping intervals
   • Merge intervals
2. Fractional/0-1 Problems
   • Knapsack variations
   • Job scheduling
3. Graph Greedy
   • Minimum Spanning Tree
   • Shortest path (Dijkstra’s)

Practice Strategy

• Identify greedy choice property
• Practice interval-based problems
• Learn to prove greedy correctness
• Understand when greedy fails

Resource: Greedy Algorithms

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4. String Algorithms

Core Concepts

• Pattern Matching: KMP, Rabin-Karp
• String Processing: Parsing, Validation
• Advanced: Trie, Suffix arrays

Key Patterns

1. Two Pointers
   • Palindrome checking
   • String reversal
   • Valid strings
2. Sliding Window
   • Longest substring problems
   • Character frequency
3. Pattern Matching
   • Substring search
   • Regular expression
   • Wildcard matching
4. String DP
   • Edit distance
   • Longest common subsequence
   • Palindromic subsequences

Practice Strategy

• Master basic string manipulation
• Learn KMP algorithm for pattern matching
• Practice substring problems with sliding window
• Focus on DP with strings

Resource: String Patterns

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5. Dynamic Programming (DP)

Core Concepts

• Optimal Substructure: Problem can be broken into subproblems
• Overlapping Subproblems: Same subproblems solved multiple times
• Memoization vs Tabulation: Top-down vs Bottom-up

Key Patterns

1. Linear DP
   • House robber
   • Climbing stairs
   • Maximum subarray
2. 2D DP
   • Unique paths
   • Longest common subsequence
   • Edit distance
3. Interval DP
   • Matrix chain multiplication
   • Palindrome partitioning
4. Tree DP
   • Binary tree maximum path sum
   • House robber III
5. Bitmask DP
   • Traveling salesman
   • Subset problems with states

Practice Strategy

• Start with 1D DP problems
• Master state definition and transitions
• Practice 2D grid problems
• Learn advanced patterns (bitmask, tree DP)

Resource: DP Patterns

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6. Binary Search Patterns

Advanced Binary Search Techniques

1. Template Variations
   • Left boundary search
   • Right boundary search
   • Exact match search
2. Search Space Types
   • Array indices
   • Value ranges
   • Answer spaces
3. Complex Applications
   • 2D matrix search
   • Peak finding
   • Minimize max or maximize min

Practice Focus

• Master all template variations
• Practice on different search spaces
• Focus on binary search on answers
• Handle edge cases properly

Resource: Binary Search Patterns

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7. Sliding Window Patterns

Core Concepts

• Fixed Size Window: K-sized problems
• Variable Size Window: Condition-based expansion/contraction
• Two Pointers: Fast and slow pointer technique

Key Patterns

1. Fixed Window Size
   • Maximum sum of K elements
   • Average of subarrays
2. Variable Window Size
   • Longest substring without repeating characters
   • Minimum window substring
   • Longest subarray with condition
3. Shrinking Window
   • Minimum size subarray sum
   • Smallest window containing all characters

Practice Strategy

• Start with fixed-size windows
• Master the expand-contract technique
• Practice character frequency problems
• Focus on optimization problems

Resource: Sliding Window Patterns

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8. Greedy Algorithm Patterns

Advanced Greedy Strategies

1. Sorting-Based Greedy
   • Activity selection
   • Fractional knapsack
2. Priority Queue Greedy
   • Huffman coding
   • Merge intervals optimally
3. Mathematical Greedy
   • Coin change (when possible)
   • Gas station problem

Key Insights

• When to choose greedy over DP
• Proving greedy correctness
• Common greedy failure cases
• Optimization vs feasibility problems

Resource: Greedy Algorithm Patterns

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9. Tree Traversal Techniques

Core Concepts

• Binary Trees: Structure and properties
• Traversal Methods: Preorder, Inorder, Postorder, Level-order
• Tree Properties: Height, depth, balance

Key Patterns

1. DFS Traversals
   • Preorder: Root → Left → Right
   • Inorder: Left → Root → Right (gives sorted order in BST)
   • Postorder: Left → Right → Root
2. BFS Traversal
   • Level-order traversal
   • Right side view
   • Level-wise processing
3. Tree Construction
   • From traversals
   • From arrays
   • Balanced tree construction
4. Tree Modification
   • Tree flattening
   • Tree mirroring
   • Path sum problems

Practice Strategy

• Master all traversal methods (recursive and iterative)
• Practice tree construction problems
• Focus on path-related problems
• Learn tree DP patterns

Resource: Tree Traversal Techniques

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10. System Design

Core Concepts

• Scalability: Horizontal vs Vertical scaling
• Reliability: Fault tolerance, redundancy
• Consistency: ACID properties, CAP theorem
• Performance: Latency, throughput optimization

Key Patterns

1. Database Design
   • SQL vs NoSQL
   • Sharding strategies
   • Indexing
2. Caching
   • Cache strategies (LRU, LFU)
   • Distributed caching
   • Cache invalidation
3. Load Balancing
   • Load balancer types
   • Load balancing algorithms
   • Health checks
4. Microservices
   • Service decomposition
   • Inter-service communication
   • Data consistency

Practice Strategy

• Study real-world system architectures
• Practice designing scalable systems
• Learn about trade-offs in system design
• Focus on commonly asked systems (URL shortener, chat systems)

Resource: System Design

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11. Math and Number Theory

Core Concepts

• Prime Numbers: Sieve of Eratosthenes, primality testing
• GCD/LCM: Euclidean algorithm
• Modular Arithmetic: Properties and applications
• Combinatorics: Permutations, combinations

Key Patterns

1. Number Properties
   • Even/odd patterns
   • Digit manipulation
   • Number conversion
2. Mathematical Sequences
   • Fibonacci numbers
   • Arithmetic/geometric progressions
   • Pascal’s triangle
3. Optimization Problems
   • Mathematical formulation
   • Constraint satisfaction
   • Proof-based solutions

Practice Strategy

• Review basic number theory
• Practice mathematical proof problems
• Focus on pattern recognition
• Learn common mathematical tricks

Resource: Math and Number Theory

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12. Bit Manipulation

Core Concepts

• Bitwise Operations: AND, OR, XOR, NOT, shifts
• Bit Tricks: Setting, clearing, toggling bits
• Properties: XOR properties, bit counting

Key Patterns

1. Single Number Problems
   • XOR properties
   • Finding unique elements
2. Bit Counting
   • Count set bits
   • Brian Kernighan’s algorithm
   • Bit manipulation DP
3. Subset Generation
   • All subsets using bits
   • Subset sum with bitmask
4. Optimization
   • Space optimization using bits
   • Fast arithmetic operations

Practice Strategy

• Master basic bitwise operations
• Learn common bit tricks
• Practice subset enumeration
• Focus on optimization techniques

Resource: Bit Manipulation

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Study Plan Recommendation

Phase 1 (Weeks 1-4): Foundation

1. Arrays and Two Pointers
2. Basic Recursion and Backtracking
3. Binary Search fundamentals
4. Basic Tree traversals

Phase 2 (Weeks 5-8): Core Patterns

1. Sliding Window techniques
2. Dynamic Programming (1D and 2D)
3. Graph traversals (DFS/BFS)
4. Greedy algorithms

Phase 3 (Weeks 9-12): Advanced Topics

1. Advanced DP patterns
2. Advanced Graph algorithms
3. String algorithms
4. Bit manipulation

Phase 4 (Weeks 13-16): Integration

1. System Design concepts
2. Math and Number Theory
3. Mixed problem solving
4. Mock interviews and practice

Tips for Success

1. Consistency: Solve 2-3 problems daily
2. Understanding over Speed: Focus on understanding patterns
3. Multiple Solutions: Learn different approaches for same problem
4. Time Complexity: Always analyze and optimize
5. Mock Interviews: Practice explaining your solutions
6. Review: Revisit difficult problems after a few days

Remember: The key to mastering DSA is recognizing patterns and knowing which technique to apply when. Focus on understanding the underlying concepts rather than memorizing solutions.

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