Category: Blog
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How to Learn the Nelder–Mead Algorithm: Simplexes, Reflection, Expansion, Contraction, Shrinkage and Derivative-Free Optimisation
Learn Nelder–Mead from geometric intuition to professional optimisation practice: simplexes, reflection, expansion, contraction, shrinkage, stopping rules, failure modes and implementation.
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How to Learn de Boor’s Algorithm: B-Spline Evaluation, Knot Spans, Local Support and Numerically Stable Curve Computation
Quick read: de Boor’s algorithm evaluates a B-spline curve at a chosen parameter value by repeatedly interpolating only the control points that can influence that location. It is the B-spline counterpart of de Casteljau’s method for Bézier curves and is valued for locality, efficiency and numerical stability. One-sentence answer: find the knot span containing the…
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How to Learn the Matula–Beck Algorithm: Smallest-Last Ordering, Graph Degeneracy, k-Cores and Greedy Coloring
Quick read: The Matula–Beck smallest-last algorithm repeatedly removes a currently minimum-degree vertex, records the removal order, and then reads that order backwards. With the right bucket data structure, this reveals graph degeneracy and supports k-core decomposition and strong greedy-coloring orderings in O(|V| + |E|) time. One-sentence answer: peel the graph from its sparsest exposed vertex…
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How to Learn Patience Sorting: Piles, Binary Search, Longest Increasing Subsequences and O(n log n) Reconstruction
Quick read: Patience sorting begins with a simple card-game rule: place each new value on the leftmost pile whose top is at least that value, or start a new pile if none exists. That tiny rule leads to an O(n log n) method for finding the length of a longest increasing subsequence and, with predecessor…
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How to Learn the Dutch National Flag Algorithm: Three-Way Partitioning, Loop Invariants, Duplicate Keys and Production Quicksort
Quick read: The Dutch National Flag algorithm turns an array containing three classes of values into three contiguous regions in one linear scan and constant extra space. The important lesson is not the colours. It is the discipline of maintaining a loop invariant while several boundaries move at once. One-sentence answer: keep a left boundary…
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How to Learn Dynamic Time Warping (DTW): Cost Matrices, Warping Paths, Step Constraints, Sakoe–Chiba Bands and Production Sequence Alignment
A beginner-to-professional guide to Dynamic Time Warping covering cost matrices, warping paths, step constraints, Sakoe–Chiba bands, memory, lower bounds, testing and production sequence alignment.
