What causes "At least two cities are required." in TheAlgorithms/C-Sharp?

Ensure at least two cities exist before solving; handle 0/1-city cases as trivial (empty or zero-distance route) at the call site.

TheAlgorithms/C-Sharp · error

At least two cities are required.

Error message

At least two cities are required.

What it means

This ArgumentException is the input-size guard in TravelingSalesmanSolver.SolveBruteForce (TravelingSalesmanSolver.cs:25), after the square-matrix check. The brute-force route construction fixes city 0 as start and end and permutes the remaining cities; with fewer than 2 cities there is no round trip to optimize. It fires when distanceMatrix has dimension n < 2.

Solutions

Ensure at least two cities exist before solving; handle 0/1-city cases as trivial (empty or zero-distance route) at the call site.
Validate matrix dimension >= 2 before calling.
Fix upstream filtering that removed all but one city.

Example fix

// before
var r = TravelingSalesmanSolver.SolveBruteForce(m);
// after
var r = n >= 2 ? TravelingSalesmanSolver.SolveBruteForce(m) : (new[] { 0 }, 0.0);

Defensive patterns

Strategy: validation

Validate before calling

if (m.GetLength(0) < 2) throw new InvalidOperationException("TSP needs at least two cities");

Try / catch

try { var r = TravelingSalesmanSolver.SolveBruteForce(m); }
catch (ArgumentException ex) { return (Array.Empty<int>(), 0.0); }

Prevention

Handle 0/1-city datasets as trivial cases upstream
Check dataset cardinality after filtering
Document minimum input size in calling code

When it happens

Trigger: Calling SolveBruteForce with a 0x0 or 1x1 distance matrix, e.g. a single-city dataset or an empty matrix.

Common situations: Dataset filtered down to one row; empty input file producing a 0x0 matrix; caller not guarding the trivial single-city case.

Understand the failure class

Background: "value must be between 0 and 1" / "out of range" / "must not be negative" errors: fixing range-validation failures across open-source libraries — this error's family across 42 libraries.

Related errors

AI-assisted analysis of TheAlgorithms/C-Sharp@96e2905cab (2026-09-13). Data as JSON: /api/errors/e1bb7244058bfc6e. Report an issue: GitHub.

Appendix: source

Thrown at Algorithms/Problems/TravelingSalesman/TravelingSalesmanSolver.cs:25

public static class TravelingSalesmanSolver
{
    /// <summary>
    /// Solves the TSP using brute-force search. This method checks all possible permutations of cities to find the shortest possible route.
    /// WARNING: This approach is only feasible for small numbers of cities due to factorial time complexity.
    /// </summary>
    /// <param name="distanceMatrix">A square matrix where element [i, j] represents the distance from city i to city j.</param>
    /// <returns>A tuple containing the minimal route (as an array of city indices) and the minimal total distance.</returns>
    public static (int[] Route, double Distance) SolveBruteForce(double[,] distanceMatrix)
    {
        int n = distanceMatrix.GetLength(0);
        if (n != distanceMatrix.GetLength(1))
        {
            throw new ArgumentException("Distance matrix must be square.");
        }

        if (n < 2)
        {
            throw new ArgumentException("At least two cities are required.");
        }

        var cities = Enumerable.Range(0, n).ToArray();
        double minDistance = double.MaxValue;
        int[]? bestRoute = null;

        foreach (var perm in Permute(cities.Skip(1).ToArray()))
        {
            var route = new int[n + 1];
            route[0] = 0;
            for (int i = 0; i < perm.Length; i++)
            {
                route[i + 1] = perm[i];
            }

            // Ensure route ends at city 0
            route[n] = 0;

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