📊 Algorithms & Data Structures

"An algorithm must be seen to be believed." — Donald Knuth

Mastering algorithms is about recognizing patterns, not memorizing solutions. This section organizes problems by solving patterns to build transferable problem-solving skills.

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🎯 Pattern-Based Learning

Array & String Patterns

Pattern	Key Technique	Example Problems
Two Pointers	Start/End convergence	Valid Palindrome, 3Sum
Sliding Window	Dynamic window sizing	Longest Substring, Max Subarray
Prefix Sum	Cumulative computation	Range Sum Query, Subarray Sum

Linked List Patterns

Pattern	Key Technique	Example Problems
Fast & Slow	Cycle detection	Linked List Cycle, Find Middle
Reversal	In-place modification	Reverse List, Reverse K Group
Merge	Combine sorted lists	Merge Two Lists, Merge K Lists

Tree & Graph Patterns

Pattern	Key Technique	Example Problems
DFS	Recursion, Stack	Path Sum, Tree Diameter
BFS	Queue, Level Order	Level Order Traversal, Shortest Path
Union Find	Disjoint sets	Number of Islands, Graph Connectivity

Dynamic Programming Patterns

Pattern	Key Technique	Example Problems
1D DP	Single state array	Climbing Stairs, House Robber
2D DP	Matrix state	Unique Paths, Edit Distance
Knapsack	Weight/Value optimization	0/1 Knapsack, Coin Change

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🏗️ Core Data Structure Implementations

Essential Structures

// HashMap Implementation Concept
public class SimpleHashMap<K, V> {
    private static final int INITIAL_CAPACITY = 16;
    private Node<K, V>[] buckets;
    
    // Key insight: hash(key) % capacity -> bucket index
    // Collision handling: Separate chaining (linked list)
}

Structure Complexity Reference

Structure	Access	Search	Insert	Delete
Array	O(1)	O(n)	O(n)	O(n)
LinkedList	O(n)	O(n)	O(1)	O(1)
HashMap	-	O(1)*	O(1)*	O(1)*
TreeMap	-	O(log n)	O(log n)	O(log n)
Heap	-	O(n)	O(log n)	O(log n)

*Average case, worst case O(n) for hash collisions

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📝 Detailed Notes

Explore specific algorithm categories:

• Two Pointers Pattern
• Sliding Window Pattern
• Dynamic Programming
• Graph Algorithms
• Tree Traversals

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🧠 Problem-Solving Framework

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Interview Strategy

1. Clarify - Ask about constraints, edge cases
2. Plan - Discuss approach before coding
3. Execute - Write clean, modular code
4. Verify - Walk through with examples
5. Optimize - Discuss potential improvements