https://ad25aderram.github.io/my-portfolio/tags/data-structures/Data StructuresHugoBlox Kit (https://hugoblox.com)en-usSat, 01 Nov 2025 00:00:00 +0000https://ad25aderram.github.io/my-portfolio/media/icon_hu_b93c5070c370bd46.pnghttps://ad25aderram.github.io/my-portfolio/tags/data-structures/https://ad25aderram.github.io/my-portfolio/projects/advanced-algorithms/Sat, 01 Nov 2025 00:00:00 +0000https://ad25aderram.github.io/my-portfolio/projects/advanced-algorithms/<p>A series of algorithm implementations focused on understanding performance trade-offs through experimental analysis. Rather than relying on theoretical Big-O alone, every implementation is benchmarked and visualised against real data.</p> <h2 id="sorting--search-complexity">Sorting &amp; search complexity</h2> <p>Seven sorting algorithms benchmarked across four data distributions — random, ascending, descending, and identical values:</p> <table> <thead> <tr> <th>Algorithm</th> <th>Complexity</th> <th>Best case</th> </tr> </thead> <tbody> <tr> <td>Quick sort (dual-pivot)</td> <td>O(n log n) avg</td> <td>Random data</td> </tr> <tr> <td>Merge sort</td> <td>O(n log n)</td> <td>Consistent</td> </tr> <tr> <td>Heap sort</td> <td>O(n log n)</td> <td>Consistent</td> </tr> <tr> <td>Insertion sort</td> <td>O(n²)</td> <td>Nearly-sorted data</td> </tr> <tr> <td>Selection sort</td> <td>O(n²)</td> <td>—</td> </tr> <tr> <td>Bubble sort</td> <td>O(n²)</td> <td>—</td> </tr> <tr> <td>Binary search</td> <td>O(log n)</td> <td>—</td> </tr> </tbody> </table> <p>Runtime was normalised against T(n)/n, T(n)/(n log n), and T(n)/n² to empirically verify complexity classes. Key finding: insertion sort consistently outperforms O(n log n) algorithms on nearly-sorted data — a result that only becomes intuitive when you see it in a plot.</p> <h2 id="hash-tables">Hash tables</h2> <ul> <li>Chaining with linked lists for collision handling</li> <li>Open addressing: linear probing, quadratic probing, double hashing</li> <li>Benchmarked on datasets up to 100,000 elements — collision rates and lookup times compared across all strategies</li> </ul> <h2 id="probabilistic-filters">Probabilistic filters</h2> <ul> <li><strong>Bloom filter</strong> with k = 2, 3, 4 hash functions — false positive rate vs. memory trade-off</li> <li><strong>Count-Min Sketch</strong> for frequency estimation — precision vs. hash function count</li> </ul> <h2 id="string-pattern-matching">String pattern matching</h2> <ul> <li>Naïve search vs. <strong>deterministic finite automaton (DFA)</strong> — transition function computation and pattern recognition on randomly generated text</li> <li>Performance comparison shows DFA&rsquo;s advantage grows with text length</li> </ul> <h2 id="dynamic-programming">Dynamic programming</h2> <ul> <li>Fibonacci: naïve recursion vs. memoisation — exponential-to-linear improvement demonstrated empirically</li> <li>Coin change: minimum coin count with full optimal solution reconstruction</li> </ul> <h2 id="tech-stack">Tech stack</h2> <ul> <li><strong>Language</strong>: Python</li> <li><strong>Libraries</strong>: Matplotlib, NumPy</li> <li><strong>Focus</strong>: Algorithm design, complexity analysis, experimental benchmarking</li> </ul>