Pattern Library - Master Algorithmic Thinking Through Internal Monologue

Reverse-engineering expertise: Learning by observing how senior engineers think through patterns

The 4-Stage Mental Pipeline

Every pattern follows the same cognitive progression:

Problem → Pattern (Recognition): What triggers map problem keywords to this pattern?
Pattern → Structure (What do I need?): What data structures, pointers, state variables?
Structure → Behavior (How does it move?): What are the movement rules, invariants, termination conditions?
Behavior → Code (Expression): Verbose form first (proof of understanding), then terse form (interview ready)

📚 Pattern Files (29 Total)

NEW: Each pattern now includes a code-to-visual mapping companion file following the CODE_MAPPING_GUIDE methodology for sticky learning.

📏 LINEAR STRUCTURES (8 patterns)

#	Pattern	Description	Files	Status
01	Sliding Window	Contiguous subsequence optimization	Pattern · Code Map	✅ COMPLETE
02	Two Pointers	Sorted input, pairs/triplets	Pattern · Code Map	✅ COMPLETE
03	Fast & Slow Pointers	Cycle detection	Pattern · Code Map	✅ COMPLETE
04	Merge Intervals	Overlapping ranges	Pattern · Code Map	✅ COMPLETE
05	Cyclic Sort	[1..n] in-place sorting	Pattern · Code Map	✅ COMPLETE
06	Monotonic Stack	Next greater/smaller	Pattern · Code Map	✅ COMPLETE
07	Prefix Sum	Static range queries	Pattern · Code Map	✅ COMPLETE
08	Line Sweep	Event-based intervals	Pattern · Code Map	✅ COMPLETE

🌳 TREES & GRAPHS (7 patterns)

#	Pattern	Description	Files	Status
09	Tree Traversals	Pre/In/Post-Order DFS	Pattern · Code Map	✅ COMPLETE
10	BFS	Level-order, shortest path	Pattern · Code Map	✅ COMPLETE
11	DFS	Exhaustive search	Pattern · Code Map	✅ COMPLETE
12	Topological Sort	DAG ordering	Pattern · Code Map	✅ COMPLETE
13	Union Find	Connected components	Pattern · Code Map	✅ COMPLETE
14	Trie	Prefix matching	Pattern · Code Map	✅ COMPLETE
15	Shortest Path	Dijkstra, Bellman-Ford	Pattern · Code Map	✅ COMPLETE

🎯 SELECTION & SEARCH (3 patterns)

#	Pattern	Description	Files	Status
16	Binary Search	Sorted data O(log n)	Pattern · Code Map	✅ COMPLETE
17	Top K / Heap	Priority, streaming	Pattern · Code Map	✅ COMPLETE
18	K-way Merge	Sorted lists merge	Pattern · Code Map	✅ COMPLETE

🔀 COMBINATORIAL & OPTIMIZATION (6 patterns)

#	Pattern	Description	Files	Status
19	Backtracking	Exhaustive + pruning	Pattern · Code Map	✅ COMPLETE
20	Dynamic Programming	Overlapping subproblems	Pattern · Code Map	✅ COMPLETE
21	Greedy	Local → global optimal	Pattern · Code Map	✅ COMPLETE
22	Branch & Bound	Optimization + pruning	Pattern · Code Map	✅ COMPLETE
23	Constraint Satisfaction	Variables + domains	Pattern · Code Map	✅ COMPLETE
24	Partitions	Equal sum splits	Pattern · Code Map	✅ COMPLETE

🔧 ADVANCED TECHNIQUES (2 patterns)

#	Pattern	Description	Files	Status
25	Bit Manipulation	Bitwise operations	Pattern · Code Map	✅ COMPLETE
26	String Matching	KMP, Rabin-Karp	Pattern · Code Map	✅ COMPLETE

📊 ADVANCED DATA STRUCTURES (3 patterns)

#	Pattern	Description	Files	Status
27	Segment Tree	Range queries + updates	Pattern · Code Map	✅ COMPLETE
28	Fenwick Tree	Prefix sums + updates	Pattern · Code Map	✅ COMPLETE
29	Suffix Array	Substring matching	Pattern · Code Map	✅ COMPLETE

🎓 How to Use This Library

For Learning a New Pattern

Read the pattern file (01-29) to activate the mental model
Study the code-map file - connect visual metaphors to actual code (sticky learning!)
Focus on Internal Monologue section - how to think through problems
Study Thought Narratives - solving problems as if first time
Practice LeetCode problems from the pattern file (organized by difficulty)

For Deep Understanding (Code-to-Visual Mapping)

Start with the visual - Read pattern file's mermaid diagrams
Read the code - Study implementation examples in pattern file
Use the code-map - See exact line-by-line visual-to-code correspondence
Test yourself - Can you explain code using visual metaphor?
Trace an example - Step through execution with both visual and code side-by-side

For Interview Prep

Review Self-Check questions at top of each pattern
Study Interview Communication Template - what to say in interviews
Practice Decision Trees - 5-second pattern recognition
Solve Medium → Hard problems from LeetCode tables

For Review

Check Self-Check questions only - if all checked, skip to next pattern
If any unchecked - re-read relevant sections
Test yourself: Can you explain structure + behavior in plain language?

When Stuck on a Problem

Read pattern keywords in problem description
Use Decision Trees to identify the right pattern
Open that pattern file and read Thought Narratives
Apply the 4-Stage Pipeline to think through the solution

🧠 Philosophy

"Code is just the expression of structure and behavior. If I can't articulate the structure (what exists) and behavior (how it moves) in plain language, I don't understand the pattern—I'm just copying syntax."

The goal: Internalize the thinking process, not just code templates.

What makes this different:

❌ Not just code templates
❌ Not just problem lists
✅ Thought narratives - how senior engineers think
✅ Internal monologue - the self-talk during problem-solving
✅ Pattern recognition - 5-second trigger mapping
✅ Interview communication - what to say out loud

🗺️ Pattern Concept Tree

A visual mental model of how patterns relate:

graph TB
    Root["Algorithmic Patterns<br/>(29 patterns)"]

    subgraph Linear["📏 LINEAR STRUCTURES (8)"]
        SW["01. Sliding Window"]
        TP["02. Two Pointers"]
        FSP["03. Fast & Slow"]
        MI["04. Merge Intervals"]
        CS["05. Cyclic Sort"]
        MS["06. Monotonic Stack"]
        PS["07. Prefix Sum"]
        LS["08. Line Sweep"]
    end

    subgraph TreesGraphs["🌳 TREES & GRAPHS (7)"]
        TT["09. Tree Traversals"]
        BFS["10. BFS"]
        DFS["11. DFS"]
        Topo["12. Topological Sort"]
        UF["13. Union Find"]
        Trie["14. Trie"]
        SP["15. Shortest Path"]
    end

    subgraph Selection["🎯 SELECTION & SEARCH (3)"]
        BS["16. Binary Search"]
        Heap["17. Top K / Heap"]
        KM["18. K-way Merge"]
    end

    subgraph Combo["🔀 COMBINATORIAL (6)"]
        Back["19. Backtracking"]
        DP["20. Dynamic Programming"]
        Greedy["21. Greedy"]
        BB["22. Branch & Bound"]
        CSP["23. Constraint Satisfaction"]
        Part["24. Partitions"]
    end

    subgraph Advanced["🔧 ADVANCED (5)"]
        Bit["25. Bit Manipulation"]
        SM["26. String Matching"]
        SegTree["27. Segment Tree"]
        Fenwick["28. Fenwick Tree"]
        Suffix["29. Suffix Array"]
    end

    Root --> Linear
    Root --> TreesGraphs
    Root --> Selection
    Root --> Combo
    Root --> Advanced

    style Root fill:#4a1942,stroke:#f472b6,stroke-width:3px,color:#e0e0e0
    style SW fill:#1e3a5f,stroke:#22d3ee,stroke-width:2px,color:#e0e0e0
    style TP fill:#1e3a5f,stroke:#22d3ee,stroke-width:2px,color:#e0e0e0
    style SegTree fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0
    style Fenwick fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0
    style Suffix fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0

🔍 Decision Tree: Which Pattern to Use?

Use this for 5-second pattern recognition:

flowchart TD
    Start{Problem Type?}

    Start -->|Array/String| Array
    Start -->|Tree/Graph| Graph
    Start -->|Optimization| Opt
    Start -->|Range Queries| Range

    Array{Array Pattern?}
    Array -->|Contiguous subarray| SW["01. Sliding Window"]
    Array -->|Two elements, sorted| TP["02. Two Pointers"]
    Array -->|Overlapping intervals| MI["04. Merge Intervals"]
    Array -->|Numbers [1..n]| CS["05. Cyclic Sort"]
    Array -->|Next greater/smaller| MS["06. Monotonic Stack"]
    Array -->|Cumulative sums| PS["07. Prefix Sum"]

    Graph{Graph Pattern?}
    Graph -->|Level-by-level| BFS["10. BFS"]
    Graph -->|All paths| DFS["11. DFS"]
    Graph -->|DAG dependencies| Topo["12. Topological Sort"]
    Graph -->|Connected components| UF["13. Union Find"]
    Graph -->|Shortest path| SP["15. Dijkstra/Bellman-Ford"]
    Graph -->|Prefix strings| Trie["14. Trie"]

    Opt{Optimization Type?}
    Opt -->|Generate all| Back["19. Backtracking"]
    Opt -->|Overlapping subproblems| DP["20. Dynamic Programming"]
    Opt -->|Local → Global optimal| Greedy["21. Greedy"]
    Opt -->|Discrete optimization| BB["22. Branch & Bound"]
    Opt -->|Variables + Constraints| CSP["23. Constraint Satisfaction"]
    Opt -->|Equal sum groups| Part["24. Partitions"]

    Range{Update Pattern?}
    Range -->|Static array| PS["07. Prefix Sum"]
    Range -->|Point updates + range sum| Fenwick["28. Fenwick Tree"]
    Range -->|Range updates + any op| SegTree["27. Segment Tree"]
    Range -->|Pattern matching| Suffix["29. Suffix Array"]

    style Start fill:#4a1942,stroke:#f472b6,stroke-width:3px,color:#e0e0e0
    style SW fill:#1a4a3a,stroke:#4ade80,stroke-width:2px,color:#e0e0e0
    style SegTree fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0
    style Fenwick fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0
    style Suffix fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0

🔗 Pattern Relationships

How patterns build on each other:

graph LR
    subgraph Foundation["Foundation Patterns"]
        TP["02. Two Pointers"]
        BS["16. Binary Search"]
        DFS["11. DFS"]
    end

    subgraph Derived["Derived Patterns"]
        SW["01. Sliding Window<br/>(extends Two Pointers)"]
        Back["19. Backtracking<br/>(extends DFS)"]
        DP["20. DP<br/>(memoized recursion)"]
    end

    subgraph RangeQueries["Range Query Evolution"]
        PS["07. Prefix Sum<br/>(static)"]
        Fenwick["28. Fenwick Tree<br/>(prefix sums + updates)"]
        SegTree["27. Segment Tree<br/>(any operation + updates)"]
    end

    subgraph StringOps["String Pattern Matching"]
        Naive["Naive O(nm)"]
        KMP["26. KMP O(n+m)"]
        Suffix["29. Suffix Array<br/>(multiple patterns)"]
    end

    TP --> SW
    DFS --> Back
    Back --> DP

    PS --> Fenwick
    Fenwick -.->|More general| SegTree
    PS -.->|No updates| SegTree

    Naive --> KMP
    KMP -.->|Many queries| Suffix

    style PS fill:#4a3a0a,stroke:#fbbf24,stroke-width:2px,color:#e0e0e0
    style Fenwick fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0
    style SegTree fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0
    style Suffix fill:#1a4a3a,stroke:#4ade80,stroke-width:3px,color:#e0e0e0

📊 Decision Matrices

Range Query Structures: When to Use What

Feature	Prefix Sum	Fenwick Tree	Segment Tree
Point Update	❌ O(n)	✅ O(log n)	✅ O(log n)
Range Update	❌	❌	✅ O(log n) w/ lazy
Range Sum Query	✅ O(1)	✅ O(log n)	✅ O(log n)
Range Min/Max Query	❌	❌	✅ O(log n)
Arbitrary Associative Op	❌	❌	✅ O(log n)
Space Complexity	O(n)	O(n)	O(4n)
Code Complexity	Simple	Medium	Complex
Use When	Read-only	Prefix sums + updates	Any range op + updates
Pattern #	07	28	27

String Pattern Structures: When to Use What

Feature	Trie	Suffix Array	KMP
Multiple Patterns	✅ Prefixes	✅ Substrings	❌ Single
Build Time	O(total chars)	O(n log n)	O(m)
Query Time	O(m)	O(m log n)	O(n)
Space	O(alphabet × nodes)	O(n)	O(m)
Use When	Autocomplete, prefix match	Many substring queries	One-time search
Pattern #	14	29	26

🚀 Quick Reference

Pattern by Number: 01 · 02 · 03 · 04 · 05 · 06 · 07 · 08 · 09 · 10 · 11 · 12 · 13 · 14 · 15 · 16 · 17 · 18 · 19 · 20 · 21 · 22 · 23 · 24 · 25 · 26 · 27 · 28 · 29

By Category:

📏 Linear: 01-08
🌳 Trees & Graphs: 09-15
🎯 Search: 16-18
🔀 Combinatorial: 19-24
🔧 Advanced: 25-29

🧭 Navigation

↑ Back: Library 2025

→ Related:

Learning Methodology - How to study
Visual Shapes - Core algorithm shapes
Applications - Multi-pattern projects

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Pattern Library - Master Algorithmic Thinking Through Internal Monologue

The 4-Stage Mental Pipeline

📚 Pattern Files (29 Total)

📏 LINEAR STRUCTURES (8 patterns)

🌳 TREES & GRAPHS (7 patterns)

🎯 SELECTION & SEARCH (3 patterns)

🔀 COMBINATORIAL & OPTIMIZATION (6 patterns)

🔧 ADVANCED TECHNIQUES (2 patterns)

📊 ADVANCED DATA STRUCTURES (3 patterns)

🎓 How to Use This Library

For Learning a New Pattern

For Deep Understanding (Code-to-Visual Mapping)

For Interview Prep

For Review

When Stuck on a Problem

🧠 Philosophy

🗺️ Pattern Concept Tree

🔍 Decision Tree: Which Pattern to Use?

🔗 Pattern Relationships

📊 Decision Matrices

Range Query Structures: When to Use What

String Pattern Structures: When to Use What

🚀 Quick Reference

🧭 Navigation

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Pattern Library - Master Algorithmic Thinking Through Internal Monologue

The 4-Stage Mental Pipeline

📚 Pattern Files (29 Total)

📏 LINEAR STRUCTURES (8 patterns)

🌳 TREES & GRAPHS (7 patterns)

🎯 SELECTION & SEARCH (3 patterns)

🔀 COMBINATORIAL & OPTIMIZATION (6 patterns)

🔧 ADVANCED TECHNIQUES (2 patterns)

📊 ADVANCED DATA STRUCTURES (3 patterns)

🎓 How to Use This Library

For Learning a New Pattern

For Deep Understanding (Code-to-Visual Mapping)

For Interview Prep

For Review

When Stuck on a Problem

🧠 Philosophy

🗺️ Pattern Concept Tree

🔍 Decision Tree: Which Pattern to Use?

🔗 Pattern Relationships

📊 Decision Matrices

Range Query Structures: When to Use What

String Pattern Structures: When to Use What

🚀 Quick Reference

🧭 Navigation