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Traveling Salesman Solver

Solve 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.

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Open Traveling Salesman Solver and you get an answer straight away, with no account to create. It covers exact Held–Karp for up to 12 cities, nearest-neighbor + 2-opt beyond, with the tour order, total distance and a plot — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Traveling Salesman Solver do?

Solve 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.

What does it take into account?

It factors in exact Held–Karp for up to 12 cities, nearest-neighbor + 2-opt beyond, with the tour order, total distance and a plot. Change any of them and the output follows immediately.

When would I actually use this?

Anything modelled as points and connections: a shortest route, a network's capacity, a schedule with dependencies, or a circuit reduced to its logic.

What is the most common mistake?

Assuming a shortest path stays shortest when a weight changes sign. Negative edges break the greedy argument Dijkstra rests on, and the algorithm returns a confident wrong answer rather than an error.

How is Traveling Salesman Solver different from Karnaugh Map (K-Map) Solver?

They sit next to each other but answer different questions: Karnaugh Map (K-Map) Solver is the one to open when you need it to minimize 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. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Absolute Value Equation Solver is the closest one after this: Solve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.

What else is worth having open alongside it?

Absolute Value Inequality Solver and Bernoulli ODE Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algorithms are the textbook ones and their results are exact for the graph you enter. What varies is cost: several of these problems have no known efficient solution, so large inputs are answered by heuristic and the tool says when that is the case.

Further reading

All guides →
ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.