Discrete maths & graphs
Graphs, logic and set theory: shortest paths, spanning trees, network flow, truth tables and the counting that goes with them. 19 tools, including Bitwise Calculator, Delaunay triangulation generator, Dijkstra shortest path calculator and Graph coloring calculator. All free, with no account and nothing to install.
Bitwise CalculatorAND, OR, XOR, NOT and shifts in binary, decimal or hex, at 8, 16, 32 or 64 bits, with the bit-by-bit diagram and the result in all three bases. Computed with BigInt, so the 64-bit answers are right where JavaScript's own 32-bit operators would silently truncate.Delaunay triangulation generatorPaste a set of 2D points and it triangulates them the Delaunay way — the triangulation that avoids thin sliver triangles, where no point lies inside another triangle's circumcircle. It runs the Bowyer-Watson algorithm in your browser and draws the mesh, with point, triangle and edge counts.Dijkstra shortest path calculatorEnter a weighted graph as edges ("A, B, 4" per line) and a source node: Dijkstra's algorithm returns the shortest distance and the exact path from the source to every reachable vertex. Works for directed or undirected graphs, accepts many edge formats, and flags unreachable vertices — ideal for routing, networks and pathfinding.Graph coloring calculatorColor a graph so that no two adjacent vertices share a color. Enter an edge list and the DSATUR (or greedy) heuristic assigns a color to every vertex, shows the color classes, and reports an upper bound on the chromatic number χ. K4 needs 4 colors, an even cycle 2, an odd cycle 3 — see it instantly.Group theory order calculatorAnalyse the classic finite groups — cyclic Zₙ, direct products Zₘ×Zₙ, dihedral Dₙ and symmetric Sₙ. It gives the group order, whether it is abelian, its structure, the number of generators for cyclic groups, and the order of any element you enter, including a permutation in cycle notation for Sₙ.Hamiltonian path & cycle checkerCheck whether a graph has a Hamiltonian path (visits every vertex once) or a Hamiltonian cycle (also returns to the start). Enter an edge list, pick directed or undirected, and an exhaustive backtracking search either returns a concrete path and cycle or proves that none exists. Capped at 12 vertices for speed.Karnaugh Map (K-Map) SolverMinimize a boolean function with the Quine–McCluskey algorithm: enter minterms, maxterms or a truth table and get the minimal SOP or POS, prime implicants and literal count.Logic Gate SimulatorDraws the gate diagram for a boolean expression and lets you flip each input to watch the signal travel through. Half-adder, multiplexer, parity and majority circuits are one click away.Markov chain steady state calculatorThe long-run distribution of a Markov chain: the probabilities the system settles into no matter where it starts. Enter the transition matrix (each row a state's outgoing probabilities) and it solves π·P = π by power iteration, showing the steady-state probability of each state.Minimum spanning tree calculatorThe cheapest way to connect every node of a weighted graph with no cycles — the classic problem behind laying cable, roads or pipes. List the edges as “A B weight” and Kruskal's algorithm finds the minimum spanning tree, its total weight, and draws it, highlighting the chosen edges.Network flow (max flow) calculatorCompute the maximum flow through a capacitated network. Enter directed arcs with capacities ("S -> A : 10"), a source and a sink, and the Edmonds-Karp algorithm returns the maximum flow value plus the flow on every arc, highlighting the saturated arcs that form the minimum cut (max-flow equals min-cut).Planar graph checkerTest whether a graph is likely planar. Enter an edge list and the tool applies Euler's necessary inequalities (E ≤ 3V−6, and E ≤ 2V−4 when triangle-free) and searches for K5 and K3,3 subgraphs from Kuratowski's theorem. It is an honest heuristic, not a full planarity algorithm: "non-planar" is certain, "likely planar" is not a proof. Capped at 16 vertices.Ring and field calculatorDo abstract-algebra arithmetic in two structures: the modular ring ℤₙ — add, subtract, multiply, divide, power, inverse and the multiplicative order — and the finite field GF(pᵏ), where elements are polynomials over F_p reduced modulo an irreducible polynomial. Enter the modulus or the prime and degree, and it computes exactly, auto-suggesting an irreducible polynomial when you don't supply one.Set theory calculatorCompute every core set operation at once from two, three or four sets: union, intersection, both differences, symmetric difference, complement, Cartesian product and power set. It also checks subset, equality and disjointness, and reports all the cardinalities — numbers, letters or words all work.Shannon entropy calculatorPaste a probability distribution and get its Shannon entropy H = −Σ p·log p in bits — the average information per outcome. It also shows the maximum possible entropy (a uniform distribution) and the redundancy, how far below that maximum you are.Topological sort calculatorOrder the vertices of a directed graph so every arc points forward. Enter directed arcs ("A -> B") and the tool runs Kahn's algorithm with lexicographic tie-breaking and a DFS post-order, returning both valid orderings. If the graph contains a cycle it is not a DAG — the tool detects it and shows the offending cycle.Traveling Salesman SolverSolve the Traveling Salesman Problem from coordinates or a distance matrix: exact Held–Karp for up to 12 cities, nearest-neighbor + 2-opt beyond, with the tour order, total distance and a plot.Truth Table GeneratorBuilds the full truth table for up to 8 variables, with a column per sub-expression so you can see where a row turns. Classifies the formula as tautology, contradiction or contingency, lists the minterms and maxterms, and copies out as CSV, LaTeX or Markdown.Venn diagram generator (3 sets)Build a three-set Venn diagram from your own elements. Enter the members of sets A, B and C and it sorts every element into one of the seven regions, draws the classic overlapping circles with per-region counts, and lists exactly what falls in each zone — only-A, A∩B, A∩B∩C and the rest.