EntCSExplore. Visualise. Understand.

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Big-O notationAlgorithms · Count the steps in real loops, then compare n, n log n, n² and 2ⁿ on a live chart.RecursionAlgorithms · Watch frames push and pop on the call stack for factorial and Fibonacci.BFS vs DFSAlgorithms · A queue against a stack: draw a graph and see which order each search visits it in.Sorting algorithmsAlgorithms · Seven sorts on the same input, with comparison, swap and write counts side by side.Binary searchAlgorithms · Halve the range, probe the middle, repeat: with lo, mid and hi drawn on the array.Sets, relations and functionsDiscrete maths · Shade any set expression on a Venn diagram and test a relation for its properties.Proof by inductionDiscrete maths · Four worked proofs revealed one step at a time, and a broken one to diagnose.CombinatoricsDiscrete maths · An exact nPr and nCr calculator, and a Pascal’s triangle that shows its own addition rule.Boolean algebraDiscrete maths · The laws, De Morgan, and normal forms, with a truth-table generator built in.Finite-state machinesTheory · Build a DFA in a table, see it drawn, and run strings through it one symbol at a time.Domain theoryTheory · Why recursion needs least fixed points, and how CPOs, Scott continuity and powerdomains supply them.Truth table generatorTools · Expression in, truth table out: with DNF, CNF, a minimal form and LaTeX.Graph traversal visualiserTools · Draw a graph, then animate BFS, DFS and Dijkstra with the frontier shown.Recursion tree visualiserTools · Paste a recursive function or a recurrence and see its call tree and call count.Gradient descentML maths · Drag the starting point, set the learning rate, and watch it converge or blow up.Vectors and embeddingsML maths · Bend the plane with a 2×2 matrix and measure how close toy word vectors are.Softmax and cross-entropyML maths · Edit the logits and watch the probabilities, the loss and the gradient update live.Attention mechanismML maths · Q, K and V for three tokens, a live score heatmap, and the weighted sum of values.Formatting a CS paper in LaTeXLaTeX · Page limits, \documentclass, front matter, theorem environments and the bibliography.Camera-ready checklistLaTeX · Fonts embedded, PDF/A, copyright form, source bundle, and why final versions get rejected.LaTeX templatesLaTeX · Where the official classes live, plus a minimal article template you can copy.Boolean algebra calculatorTools · A Boolean expression simplifier that names the law used at every step.K-map solverTools · Fill in a Karnaugh map and see the groups, the minimal SOP and POS, and the essential terms.Logic gate simulatorTools · Wire up gates, flip the switches, and get the truth table and expression of your circuit.Regex to NFA converterTools · Type a regular expression and watch Thompson’s construction build its NFA, fragment by fragment.NFA to DFA converterTools · Enter an NFA or a regex and step through the subset construction, then minimise the DFA.DFA simulatorTools · Edit a DFA, run strings through it step by step, batch-test them and share the machine as a link.Regular expressions to automataTheory · Regex to NFA to DFA to minimal DFA, worked through on one example with every set shown.The halting problemTheory · Why no program can tell whether every program halts, with the paradox program played out.Pigeonhole principleDiscrete maths · n pigeons, k holes: why some hole gets ⌈n/k⌉, and the surprising things that follows from it.Dijkstra’s algorithmAlgorithms · Shortest paths with a priority queue: a worked table, a proof, and a graph you can redraw.Hash functionsAlgorithms · Keys in, buckets out: hash a word four ways, then watch chaining and probing handle collisions.Sorting algorithm visualizerTools · Up to seven sorts race on the same data, then step through any one of them line by line.LaTeX table generatorTools · Type or paste a table, merge cells, pick booktabs, and copy clean tabular code.Combination calculatorTools · Exact nCr with the cancelling shown, combinations with repetition, and a full list for small n.Permutation calculatorTools · nPr, nʳ, anagrams like MISSISSIPPI and round-table seatings, with exact working.AlgorithmsSection · Step-through visualisations of sorting, searching, recursion, graph traversal, Dijkstra’s algorithm, hash functions and Big-O growth, with pseudocode that follows along.Discrete mathsSection · Sets, relations and functions, proof by induction, counting, the pigeonhole principle and Boolean algebra, explained with worked examples and interactive checkers.TheorySection · Finite-state machines, regular expressions and automata, the halting problem, and the mathematical semantics of programming languages, explained from first principles.ML mathsSection · Gradient descent, vectors and embeddings, softmax and cross-entropy, and attention, each with a formula, a worked numeric example and a live version.ToolsSection · Free browser tools: truth tables, Boolean simplification, K-maps, logic gates, nCr and nPr, regex to NFA to DFA, sorting and graph visualisers, and LaTeX tables.LaTeXSection · How to format a CS conference or workshop paper in LaTeX, a camera-ready checklist, and a minimal template you can adapt.
Algorithms

Algorithms, visualised step by step

Each page pairs a careful written explanation with a visualiser you can drive yourself: change the input, step forwards and backwards, and watch the pseudocode follow along.

How to use these pages

Every visualiser works the same way. Edit the input at the top, then press play or step one move at a time with the arrow keys. The highlighted line of pseudocode is the one being executed, and the narration underneath says what just happened and why. Step backwards as often as you like: the whole run is computed in advance, so rewinding is instant.

A good order for a first pass is Big-O notation, which gives you the vocabulary for comparing algorithms, then binary search and sorting. Recursion explains the call stack that merge sort, quicksort and depth-first search rely on, and BFS vs DFS moves from arrays to graphs. From there, Dijkstra’s algorithm finds shortest paths in weighted graphs, and hash functions explain how hash tables find a key in constant expected time.

Related tools

The graph traversal visualiser adds Dijkstra’s algorithm to BFS and DFS, and the recursion tree visualiser draws the call tree of any small recursive function you write, or solves a divide-and-conquer recurrence. The sorting algorithm visualiser races up to seven sorts side by side on the same input.