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        <h1>Computer Science Processes - Programming Framework Analysis</h1>
        
        <p>This document presents computer science processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.</p>

        <h2>1. QuickSort Algorithm Process</h2>
        <div class="figure">
            <div class="mermaid">
graph TD
    A[Input Array] --> B[Choose Pivot]
    B --> C[Partition Array]
    C --> D[Recursive Sort Left]
    C --> E[Recursive Sort Right]
    D --> F[Merge Results]
    E --> F
    F --> G[Sorted Array]
    
    style A fill:#ff6b6b,color:#fff
    style B fill:#ffd43b,color:#000
    style C fill:#51cf66,color:#fff
    style D fill:#74c0fc,color:#fff
    style E fill:#74c0fc,color:#fff
    style F fill:#51cf66,color:#fff
    style G fill:#b197fc,color:#fff

            </div>
            <div class="color-legend">
                <span><span class="color-box" style="background:#ff6b6b;"></span>Inputs & Data</span>
                <span><span class="color-box" style="background:#ffd43b;"></span>Data Structures & Arrays</span>
                <span><span class="color-box" style="background:#51cf66;"></span>Operations & Algorithms</span>
                <span><span class="color-box" style="background:#74c0fc;"></span>States & Variables</span>
                <span><span class="color-box" style="background:#b197fc;"></span>Output & Results</span>
            </div>
            <div class="figure-caption">
                <strong>Figure 1.</strong> QuickSort Algorithm Process. This computer science process visualization demonstrates the computational logic of the QuickSort algorithm. The flowchart shows input data and parameters, data structures and arrays, algorithmic operations and comparisons, intermediate states and recursive calls, and final sorted output.
            </div>
        </div>

        <h2>2. Binary Search Tree Process</h2>
        <div class="figure">
            <div class="mermaid">
graph TD
    A[Search Key] --> B[Compare with Root]
    B --> C[Key less than Root Question]
    C -->|Yes| D[Search Left Subtree]
    C -->|No| E[Search Right Subtree]
    D --> F[Recursive Search]
    E --> G[Recursive Search]
    F --> H[Key Found Question]
    G --> I[Key Found Question]
    H -->|Yes| J[Return Node]
    H -->|No| K[Return Null]
    I -->|Yes| L[Return Node]
    I -->|No| M[Return Null]
    J --> N[Search Successful]
    L --> N
    K --> O[Search Unsuccessful]
    M --> O
    
    style A fill:#ff6b6b,color:#fff
    style B fill:#ffd43b,color:#000
    style C fill:#51cf66,color:#fff
    style D fill:#74c0fc,color:#fff
    style E fill:#74c0fc,color:#fff
    style F fill:#51cf66,color:#fff
    style G fill:#51cf66,color:#fff
    style H fill:#51cf66,color:#fff
    style I fill:#51cf66,color:#fff
    style J fill:#74c0fc,color:#fff
    style K fill:#74c0fc,color:#fff
    style L fill:#74c0fc,color:#fff
    style M fill:#74c0fc,color:#fff
    style N fill:#b197fc,color:#fff
    style O fill:#b197fc,color:#fff
            </div>
            <div class="color-legend">
                <span><span class="color-box" style="background:#ff6b6b;"></span>Inputs & Data</span>
                <span><span class="color-box" style="background:#ffd43b;"></span>Data Structures & Arrays</span>
                <span><span class="color-box" style="background:#51cf66;"></span>Operations & Algorithms</span>
                <span><span class="color-box" style="background:#74c0fc;"></span>States & Variables</span>
                <span><span class="color-box" style="background:#b197fc;"></span>Output & Results</span>
            </div>
            <div class="figure-caption">
                <strong>Figure 2.</strong> Binary Search Tree Process. This computer science process visualization demonstrates the computational logic of binary search tree operations. The flowchart shows search key validation, tree structure analysis, binary search strategy, recursive traversal, and search result determination.
            </div>
        </div>

        <h2>3. Dynamic Programming Process</h2>
        <div class="figure">
            <div class="mermaid">
graph TD
    %% Problem Definition
    A[Problem Statement] --> B[Problem Analysis]
    C[Input Parameters] --> D[Parameter Validation]
    E[Constraints] --> F[Constraint Analysis]
    
    %% Dynamic Programming Setup
    B --> G[Subproblem Identification]
    D --> H[State Space Definition]
    F --> I[Memory Requirements]
    
    %% Algorithm Design
    G --> J[Recursive Relation]
    H --> K[DP Table Structure]
    I --> L[Memory Allocation]
    
    %% Implementation
    J --> M[Base Case Definition]
    K --> N[Table Initialization]
    L --> O[Array Creation]
    
    %% Computation
    M --> P[Fill Base Cases]
    N --> Q[Iterative Computation]
    O --> R[State Transitions]
    
    %% Solution Construction
    P --> S[DP Table Population]
    Q --> T[Optimal Value Calculation]
    R --> U[Path Reconstruction]
    
    %% Final Result
    S --> V[Optimal Solution]
    T --> W[Performance Analysis]
    U --> X[Solution Verification]
    
    %% Styling - Computer Science Color Scheme
    %% Red: Inputs & Triggers
    style A fill:#ff6b6b,color:#fff
    style C fill:#ff6b6b,color:#fff
    style E fill:#ff6b6b,color:#fff
    
    %% Yellow: Structures & Objects
    style B fill:#ffd43b,color:#000
    style D fill:#ffd43b,color:#000
    style F fill:#ffd43b,color:#000
    style G fill:#ffd43b,color:#000
    style H fill:#ffd43b,color:#000
    style I fill:#ffd43b,color:#000
    style J fill:#ffd43b,color:#000
    style K fill:#ffd43b,color:#000
    style L fill:#ffd43b,color:#000
    style M fill:#ffd43b,color:#000
    style N fill:#ffd43b,color:#000
    style O fill:#ffd43b,color:#000
    
    %% Green: Processing & Operations
    style P fill:#51cf66,color:#fff
    style Q fill:#51cf66,color:#fff
    style R fill:#51cf66,color:#fff
    style S fill:#51cf66,color:#fff
    style T fill:#51cf66,color:#fff
    style U fill:#51cf66,color:#fff
    
    %% Blue: Intermediates & States
    style V fill:#74c0fc,color:#fff
    style W fill:#74c0fc,color:#fff
    style X fill:#74c0fc,color:#fff
            </div>
            <div class="color-legend">
                <span><span class="color-box" style="background:#ff6b6b;"></span>Inputs & Data</span>
                <span><span class="color-box" style="background:#ffd43b;"></span>Data Structures & Arrays</span>
                <span><span class="color-box" style="background:#51cf66;"></span>Operations & Algorithms</span>
                <span><span class="color-box" style="background:#74c0fc;"></span>States & Variables</span>
                <span><span class="color-box" style="background:#b197fc;"></span>Output & Results</span>
            </div>
            <div class="figure-caption">
                <strong>Figure 3.</strong> Dynamic Programming Process. This computer science process visualization demonstrates the computational logic of dynamic programming algorithms. The flowchart shows problem analysis, subproblem identification, recursive relation formulation, table-based computation, and optimal solution construction.
            </div>
        </div>

        <h2>4. Graph Traversal Process</h2>
        <div class="figure">
            <div class="mermaid">
graph TD
    %% Graph Representation
    A[Graph Structure] --> B[Graph Analysis]
    C[Starting Vertex] --> D[Vertex Validation]
    E[Traversal Type] --> F[Algorithm Selection]
    
    %% Data Structure Setup
    B --> G[Adjacency List/Matrix]
    D --> H[Vertex Initialization]
    F --> I[Queue/Stack Selection]
    
    %% Traversal Initialization
    G --> J[Graph Representation]
    H --> K[Visited Array]
    I --> L[Data Structure Creation]
    
    %% Traversal Process
    J --> M[Neighbor Discovery]
    K --> N[Visit Tracking]
    L --> O[Element Management]
    
    %% Algorithm Execution
    M --> P[Neighbor Processing]
    N --> Q[Visit Marking]
    O --> R[Element Removal]
    
    %% Completion
    P --> S[Traversal Complete]
    Q --> T[All Vertices Visited]
    R --> U[Data Structure Empty]
    
    %% Final Result
    S --> V[Traversal Order]
    T --> W[Connected Components]
    U --> X[Algorithm Termination]
    
    %% Styling - Computer Science Color Scheme
    %% Red: Inputs & Triggers
    style A fill:#ff6b6b,color:#fff
    style C fill:#ff6b6b,color:#fff
    style E fill:#ff6b6b,color:#fff
    
    %% Yellow: Structures & Objects
    style B fill:#ffd43b,color:#000
    style D fill:#ffd43b,color:#000
    style F fill:#ffd43b,color:#000
    style G fill:#ffd43b,color:#000
    style H fill:#ffd43b,color:#000
    style I fill:#ffd43b,color:#000
    style J fill:#ffd43b,color:#000
    style K fill:#ffd43b,color:#000
    style L fill:#ffd43b,color:#000
    
    %% Green: Processing & Operations
    style M fill:#51cf66,color:#fff
    style N fill:#51cf66,color:#fff
    style O fill:#51cf66,color:#fff
    style P fill:#51cf66,color:#fff
    style Q fill:#51cf66,color:#fff
    style R fill:#51cf66,color:#fff
    style S fill:#51cf66,color:#fff
    style T fill:#51cf66,color:#fff
    style U fill:#51cf66,color:#fff
    
    %% Blue: Intermediates & States
    style V fill:#74c0fc,color:#fff
    style W fill:#74c0fc,color:#fff
    style X fill:#74c0fc,color:#fff
            </div>
            <div class="color-legend">
                <span><span class="color-box" style="background:#ff6b6b;"></span>Inputs & Data</span>
                <span><span class="color-box" style="background:#ffd43b;"></span>Data Structures & Arrays</span>
                <span><span class="color-box" style="background:#51cf66;"></span>Operations & Algorithms</span>
                <span><span class="color-box" style="background:#74c0fc;"></span>States & Variables</span>
                <span><span class="color-box" style="background:#b197fc;"></span>Output & Results</span>
            </div>
            <div class="figure-caption">
                <strong>Figure 4.</strong> Graph Traversal Process. This computer science process visualization demonstrates the computational logic of graph traversal algorithms. The flowchart shows graph representation, vertex initialization, neighbor discovery, visit tracking, and traversal completion.
            </div>
        </div>

        <h2>5. Memory Management Process</h2>
        <div class="figure">
            <div class="mermaid">
graph TD
    %% Memory Request
    A[Memory Request] --> B[Request Analysis]
    C[Size Requirements] --> D[Size Validation]
    E[Memory Type] --> F[Type Selection]
    
    %% Memory Allocation
    B --> G[Free List Search]
    D --> H[Block Size Check]
    F --> I[Allocation Strategy]
    
    %% Block Management
    G --> J[Free Block Identification]
    H --> K[Block Splitting]
    I --> L[Allocation Method]
    
    %% Memory Assignment
    J --> M[Block Assignment]
    K --> N[Remaining Block]
    L --> O[Memory Marking]
    
    %% Deallocation
    M --> P[Memory Usage]
    N --> Q[Free Block Update]
    O --> R[Allocation Complete]
    
    %% Cleanup
    P --> S[Memory Release]
    Q --> T[Free List Update]
    R --> U[Fragmentation Check]
    
    %% Final State
    S --> V[Memory Freed]
    T --> W[Free List Maintained]
    U --> X[Memory Management Complete]
    
    %% Styling - Computer Science Color Scheme
    %% Red: Inputs & Triggers
    style A fill:#ff6b6b,color:#fff
    style C fill:#ff6b6b,color:#fff
    style E fill:#ff6b6b,color:#fff
    
    %% Yellow: Structures & Objects
    style B fill:#ffd43b,color:#000
    style D fill:#ffd43b,color:#000
    style F fill:#ffd43b,color:#000
    style G fill:#ffd43b,color:#000
    style H fill:#ffd43b,color:#000
    style I fill:#ffd43b,color:#000
    style J fill:#ffd43b,color:#000
    style K fill:#ffd43b,color:#000
    style L fill:#ffd43b,color:#000
    style M fill:#ffd43b,color:#000
    style N fill:#ffd43b,color:#000
    style O fill:#ffd43b,color:#000
    
    %% Green: Processing & Operations
    style P fill:#51cf66,color:#fff
    style Q fill:#51cf66,color:#fff
    style R fill:#51cf66,color:#fff
    style S fill:#51cf66,color:#fff
    style T fill:#51cf66,color:#fff
    style U fill:#51cf66,color:#fff
    
    %% Blue: Intermediates & States
    style V fill:#74c0fc,color:#fff
    style W fill:#74c0fc,color:#fff
    style X fill:#74c0fc,color:#fff
            </div>
            <div class="color-legend">
                <span><span class="color-box" style="background:#ff6b6b;"></span>Inputs & Data</span>
                <span><span class="color-box" style="background:#ffd43b;"></span>Data Structures & Arrays</span>
                <span><span class="color-box" style="background:#51cf66;"></span>Operations & Algorithms</span>
                <span><span class="color-box" style="background:#74c0fc;"></span>States & Variables</span>
                <span><span class="color-box" style="background:#b197fc;"></span>Output & Results</span>
            </div>
            <div class="figure-caption">
                <strong>Figure 5.</strong> Memory Management Process. This computer science process visualization demonstrates the computational logic of memory management systems. The flowchart shows memory request analysis, free block search, allocation strategy, block management, and memory cleanup operations.
            </div>
        </div>
        
        <div style="margin-top: 3rem; padding: 2rem; background: #f8f9fa; border-radius: 8px; border-left: 4px solid #007bff;">
            <h3 style="margin-top: 0; color: #007bff;">Contact Information</h3>
            <p style="margin-bottom: 0.5rem;"><strong>Gary Welz</strong></p>
            <p style="margin-bottom: 0.5rem;">Retired Faculty Member</p>
            <p style="margin-bottom: 0.5rem;">John Jay College, CUNY (Department of Mathematics and Computer Science)</p>
            <p style="margin-bottom: 0.5rem;">Borough of Manhattan Community College, CUNY</p>
            <p style="margin-bottom: 0.5rem;">CUNY Graduate Center (New Media Lab)</p>
            <p style="margin-bottom: 0;"><strong>Email:</strong> gwelz@jjay.cuny.edu</p>
        </div>
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