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| <title>Computer Science Batch 01 - Algorithms & Data Structures - Programming Framework Analysis</title> | |
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| <h1>Computer Science Batch 01 - Algorithms & Data Structures - 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. Sorting Algorithms Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| graph TD | |
| A1[Input Array] --> B1[Algorithm Selection] | |
| C1[Array Analysis] --> D1[Complexity Analysis] | |
| E1[Memory Constraints] --> F1[Optimization Strategy] | |
| B1 --> G1[Comparison Based Sorting] | |
| D1 --> H1[Time Complexity O n squared] | |
| F1 --> I1[Space Complexity Analysis] | |
| G1 --> J1[Bubble Sort Algorithm] | |
| H1 --> K1[Quick Sort Algorithm] | |
| I1 --> L1[Merge Sort Algorithm] | |
| J1 --> M1[Adjacent Element Comparison] | |
| K1 --> L1 | |
| L1 --> N1[Divide and Conquer] | |
| M1 --> O1[Element Swapping] | |
| N1 --> P1[Pivot Selection] | |
| O1 --> Q1[Sorting Process] | |
| P1 --> R1[Partitioning Strategy] | |
| Q1 --> S1[Recursive Sorting] | |
| R1 --> T1[Sorting Algorithm Result] | |
| S1 --> U1[Algorithm Validation] | |
| T1 --> V1[Sorted Array Output] | |
| U1 --> W1[Sorting Algorithm Output] | |
| V1 --> X1[Sorting Algorithm Analysis] | |
| W1 --> Y1[Sorting Algorithm Final Result] | |
| X1 --> Z1[Sorting Algorithm Analysis Complete] | |
| style A1 fill:#ff6b6b,color:#fff | |
| style C1 fill:#ff6b6b,color:#fff | |
| style E1 fill:#ff6b6b,color:#fff | |
| style B1 fill:#ffd43b,color:#000 | |
| style D1 fill:#ffd43b,color:#000 | |
| style F1 fill:#ffd43b,color:#000 | |
| style G1 fill:#ffd43b,color:#000 | |
| style H1 fill:#ffd43b,color:#000 | |
| style I1 fill:#ffd43b,color:#000 | |
| style J1 fill:#ffd43b,color:#000 | |
| style K1 fill:#ffd43b,color:#000 | |
| style L1 fill:#ffd43b,color:#000 | |
| style M1 fill:#ffd43b,color:#000 | |
| style N1 fill:#ffd43b,color:#000 | |
| style O1 fill:#ffd43b,color:#000 | |
| style P1 fill:#ffd43b,color:#000 | |
| style Q1 fill:#ffd43b,color:#000 | |
| style R1 fill:#ffd43b,color:#000 | |
| style S1 fill:#ffd43b,color:#000 | |
| style T1 fill:#ffd43b,color:#000 | |
| style U1 fill:#ffd43b,color:#000 | |
| style V1 fill:#ffd43b,color:#000 | |
| style W1 fill:#ffd43b,color:#000 | |
| style X1 fill:#ffd43b,color:#000 | |
| style Y1 fill:#ffd43b,color:#000 | |
| style Z1 fill:#ffd43b,color:#000 | |
| style M1 fill:#51cf66,color:#fff | |
| style N1 fill:#51cf66,color:#fff | |
| style O1 fill:#51cf66,color:#fff | |
| style P1 fill:#51cf66,color:#fff | |
| style Q1 fill:#51cf66,color:#fff | |
| style R1 fill:#51cf66,color:#fff | |
| style S1 fill:#51cf66,color:#fff | |
| style T1 fill:#51cf66,color:#fff | |
| style U1 fill:#51cf66,color:#fff | |
| style V1 fill:#51cf66,color:#fff | |
| style W1 fill:#51cf66,color:#fff | |
| style X1 fill:#51cf66,color:#fff | |
| style Y1 fill:#51cf66,color:#fff | |
| style Z1 fill:#51cf66,color:#fff | |
| style Z1 fill:#b197fc,color:#fff | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Algorithm Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Sorting Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 1.</strong> Sorting Algorithms Process. This computer science process visualization demonstrates comparison-based sorting algorithms. The flowchart shows input array and complexity analysis, algorithm methods and selection, sorting operations and comparisons, intermediate results, and final sorted array outputs. | |
| </div> | |
| </div> | |
| <h2>2. Graph Algorithms Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| graph TD | |
| A2[Graph Representation] --> B2[Graph Type Analysis] | |
| C2[Vertex Edge Analysis] --> D2[Traversal Strategy] | |
| E2[Path Finding] --> F2[Algorithm Selection] | |
| B2 --> G2[Directed Graph] | |
| D2 --> H2[Undirected Graph] | |
| F2 --> I2[Weighted Graph] | |
| G2 --> J2[Depth First Search] | |
| H2 --> K2[Breadth First Search] | |
| I2 --> L2[Dijkstra Algorithm] | |
| J2 --> M2[Stack Based Traversal] | |
| K2 --> L2 | |
| L2 --> N2[Queue Based Traversal] | |
| M2 --> O2[Priority Queue] | |
| N2 --> P2[Shortest Path] | |
| O2 --> Q2[Graph Algorithm Process] | |
| P2 --> R2[Minimum Spanning Tree] | |
| Q2 --> S2[Topological Sorting] | |
| R2 --> T2[Graph Algorithm Result] | |
| S2 --> U2[Algorithm Validation] | |
| T2 --> V2[Graph Analysis Output] | |
| U2 --> W2[Graph Algorithm Output] | |
| V2 --> X2[Graph Algorithm Analysis] | |
| W2 --> Y2[Graph Algorithm Final Result] | |
| X2 --> Z2[Graph Algorithm Analysis Complete] | |
| style A2 fill:#ff6b6b,color:#fff | |
| style C2 fill:#ff6b6b,color:#fff | |
| style E2 fill:#ff6b6b,color:#fff | |
| style B2 fill:#ffd43b,color:#000 | |
| style D2 fill:#ffd43b,color:#000 | |
| style F2 fill:#ffd43b,color:#000 | |
| style G2 fill:#ffd43b,color:#000 | |
| style H2 fill:#ffd43b,color:#000 | |
| style I2 fill:#ffd43b,color:#000 | |
| style J2 fill:#ffd43b,color:#000 | |
| style K2 fill:#ffd43b,color:#000 | |
| style L2 fill:#ffd43b,color:#000 | |
| style M2 fill:#ffd43b,color:#000 | |
| style N2 fill:#ffd43b,color:#000 | |
| style O2 fill:#ffd43b,color:#000 | |
| style P2 fill:#ffd43b,color:#000 | |
| style Q2 fill:#ffd43b,color:#000 | |
| style R2 fill:#ffd43b,color:#000 | |
| style S2 fill:#ffd43b,color:#000 | |
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| style U2 fill:#ffd43b,color:#000 | |
| style V2 fill:#ffd43b,color:#000 | |
| style W2 fill:#ffd43b,color:#000 | |
| style X2 fill:#ffd43b,color:#000 | |
| style Y2 fill:#ffd43b,color:#000 | |
| style Z2 fill:#ffd43b,color:#000 | |
| style M2 fill:#51cf66,color:#fff | |
| style N2 fill:#51cf66,color:#fff | |
| style O2 fill:#51cf66,color:#fff | |
| style P2 fill:#51cf66,color:#fff | |
| style Q2 fill:#51cf66,color:#fff | |
| style R2 fill:#51cf66,color:#fff | |
| style S2 fill:#51cf66,color:#fff | |
| style T2 fill:#51cf66,color:#fff | |
| style U2 fill:#51cf66,color:#fff | |
| style V2 fill:#51cf66,color:#fff | |
| style W2 fill:#51cf66,color:#fff | |
| style X2 fill:#51cf66,color:#fff | |
| style Y2 fill:#51cf66,color:#fff | |
| style Z2 fill:#51cf66,color:#fff | |
| style Z2 fill:#b197fc,color:#fff | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Graph Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Traversal Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 2.</strong> Graph Algorithms Process. This computer science process visualization demonstrates graph traversal and path finding algorithms. The flowchart shows graph representation and vertex analysis, graph methods and traversal strategies, traversal operations and path finding, intermediate results, and final graph algorithm outputs. | |
| </div> | |
| </div> | |
| <h2>3. Dynamic Programming Process</h2> | |
| <div class="figure"> | |
| <div class="mermaid"> | |
| graph TD | |
| A3[Problem Analysis] --> B3[Optimal Substructure] | |
| C3[Overlapping Subproblems] --> D3[Recursive Formulation] | |
| E3[Memoization Strategy] --> F3[Tabulation Method] | |
| B3 --> G3[Subproblem Identification] | |
| D3 --> H3[Recursive Solution] | |
| F3 --> I3[Bottom Up Approach] | |
| G3 --> J3[State Definition] | |
| H3 --> K3[Top Down Approach] | |
| I3 --> L3[Table Construction] | |
| J3 --> M3[Transition Function] | |
| K3 --> L3 | |
| L3 --> N3[Space Optimization] | |
| M3 --> O3[Base Case Definition] | |
| N3 --> P3[Time Complexity] | |
| O3 --> Q3[Dynamic Programming Process] | |
| P3 --> R3[Algorithm Validation] | |
| Q3 --> S3[Solution Construction] | |
| R3 --> T3[Dynamic Programming Result] | |
| S3 --> U3[Dynamic Programming Validation] | |
| T3 --> V3[Dynamic Programming Parameters] | |
| U3 --> W3[Dynamic Programming Output] | |
| V3 --> X3[Dynamic Programming Analysis] | |
| W3 --> Y3[Dynamic Programming Final Result] | |
| X3 --> Z3[Dynamic Programming Analysis Complete] | |
| style A3 fill:#ff6b6b,color:#fff | |
| style C3 fill:#ff6b6b,color:#fff | |
| style E3 fill:#ff6b6b,color:#fff | |
| style B3 fill:#ffd43b,color:#000 | |
| style D3 fill:#ffd43b,color:#000 | |
| style F3 fill:#ffd43b,color:#000 | |
| style G3 fill:#ffd43b,color:#000 | |
| style H3 fill:#ffd43b,color:#000 | |
| style I3 fill:#ffd43b,color:#000 | |
| style J3 fill:#ffd43b,color:#000 | |
| style K3 fill:#ffd43b,color:#000 | |
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| style M3 fill:#ffd43b,color:#000 | |
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| style U3 fill:#ffd43b,color:#000 | |
| style V3 fill:#ffd43b,color:#000 | |
| style W3 fill:#ffd43b,color:#000 | |
| style X3 fill:#ffd43b,color:#000 | |
| style Y3 fill:#ffd43b,color:#000 | |
| style Z3 fill:#ffd43b,color:#000 | |
| style M3 fill:#51cf66,color:#fff | |
| style N3 fill:#51cf66,color:#fff | |
| style O3 fill:#51cf66,color:#fff | |
| style P3 fill:#51cf66,color:#fff | |
| style Q3 fill:#51cf66,color:#fff | |
| style R3 fill:#51cf66,color:#fff | |
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| style U3 fill:#51cf66,color:#fff | |
| style V3 fill:#51cf66,color:#fff | |
| style W3 fill:#51cf66,color:#fff | |
| style X3 fill:#51cf66,color:#fff | |
| style Y3 fill:#51cf66,color:#fff | |
| style Z3 fill:#51cf66,color:#fff | |
| style Z3 fill:#b197fc,color:#fff | |
| </div> | |
| <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;"> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Dynamic Programming Methods | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Optimization Operations | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates | |
| </div> | |
| <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;"> | |
| <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products | |
| </div> | |
| </div> | |
| <div class="figure-caption"> | |
| <strong>Figure 3.</strong> Dynamic Programming Process. This computer science process visualization demonstrates optimal substructure and overlapping subproblems. The flowchart shows problem analysis and subproblem identification, dynamic programming methods and strategies, optimization operations and solution construction, intermediate results, and final dynamic programming outputs. | |
| </div> | |
| </div> | |
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| <h3>Navigation</h3> | |
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| <a href="computer_science_index.html" class="nav-link">← Back to Computer Science Index</a> | |
| <a href="computer_science_batch_02.html" class="nav-link">Next: Software Engineering →</a> | |
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| <p><strong>Generated using the Programming Framework methodology</strong></p> | |
| <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p> | |
| <div class="contact-info"> | |
| <p><strong>Gary Welz</strong></p> | |
| <p>Retired Faculty Member</p> | |
| <p>John Jay College, CUNY (Department of Mathematics and Computer Science)</p> | |
| <p>Borough of Manhattan Community College, CUNY</p> | |
| <p>CUNY Graduate Center (New Media Lab)</p> | |
| <p>Email: gwelz@jjay.cuny.edu</p> | |
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