https://massimo-nocentini.github.io/categories/data-structure/Recent content in Data Structure on Massimo NocentiniHugoen-USThu, 12 Nov 2026 10:30:00 +0100https://massimo-nocentini.github.io/post/bottom-k-sketches/Thu, 12 Nov 2026 10:30:00 +0100Massimo Nocentinihttps://massimo-nocentini.github.io/post/bottom-k-sketches/https://massimo-nocentini.github.io/post/sbral/Fri, 10 Apr 2026 09:58:04 +0100Massimo Nocentinihttps://massimo-nocentini.github.io/post/sbral/<p>We describe a CHICKEN Scheme implementation of <em>skew binary random-access lists</em> (SBRALs), a purely functional data structure that provides <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">O</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span></span></span></span> worst-case <code>cons</code>, <code>car</code>, and <code>cdr</code> at the front while supporting <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(\log n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">O</span><span class="mopen">(</span><span class="mop">lo<span style="margin-right:0.0139em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span> indexed lookup and persistent update. The module <code>(aux fds sbral)</code> realises the structure as a list of weight-annotated complete binary trees whose sizes follow the skew binary number system. We present the representation, walk through every exported definition, give complexity bounds, and illustrate the invariants with a concrete trace drawn from the accompanying test suite.</p>