TheAlgorithms/Java · error · IllegalArgumentException

Invalid number of vertices or root

Error message

Invalid number of vertices or root

What it means

Edmonds.findMinimumSpanningArborescence throws this IllegalArgumentException when the root vertex is outside [0, numVertices). Despite the message mentioning 'number of vertices', the guard only checks root bounds; a numVertices of 0 combined with root 0 is the typical trigger. The method then delegates to the recursive MSA computation only if root is valid and numVertices > 1.

Source

Thrown at src/main/java/com/thealgorithms/graph/Edmonds.java:72

            this.to = to;
            this.weight = weight;
        }
    }

    /**
     * Computes the total weight of the Minimum Spanning Arborescence of a directed,
     * weighted graph from a given root.
     *
     * @param numVertices the number of vertices, labeled {@code 0..numVertices-1}
     * @param edges list of directed edges in the graph
     * @param root the root vertex
     * @return the total weight of the MSA. Returns -1 if not all vertices are reachable
     *         from the root or if a valid arborescence cannot be formed.
     * @throws IllegalArgumentException if {@code numVertices <= 0} or {@code root} is out of range.
     */
    public static long findMinimumSpanningArborescence(int numVertices, List<Edge> edges, int root) {
        if (root < 0 || root >= numVertices) {
            throw new IllegalArgumentException("Invalid number of vertices or root");
        }
        if (numVertices == 1) {
            return 0;
        }

        return findMSARecursive(numVertices, edges, root);
    }

    /**
     * Recursive helper method for finding MSA.
     */
    private static long findMSARecursive(int n, List<Edge> edges, int root) {
        long[] minWeightEdge = new long[n];
        int[] predecessor = new int[n];
        Arrays.fill(minWeightEdge, Long.MAX_VALUE);
        Arrays.fill(predecessor, -1);

        for (Edge edge : edges) {

View on GitHub (pinned to fdfb9a395b)

Solutions

1. Ensure root is in [0, numVertices - 1] and numVertices > 0 before calling.
2. If the graph is empty (numVertices == 0), skip the call or handle it explicitly instead of relying on the algorithm.
3. Convert external 1-based root labels to 0-based.
4. Validate that edge endpoints also fall within [0, numVertices).

Example fix

// before
long w = Edmonds.findMinimumSpanningArborescence(0, edges, 0); // throws

// after
if (numVertices <= 0) {
    return 0;
}
long w = Edmonds.findMinimumSpanningArborescence(numVertices, edges, root);

if (numVertices <= 0 || root < 0 || root >= numVertices) {
    throw new IllegalArgumentException("numVertices must be > 0 and root in [0, numVertices-1]");
}

When it happens

Trigger: Calling findMinimumSpanningArborescence(numVertices, edges, root) with root < 0, root >= numVertices, or numVertices <= 0 (since root 0 >= numVertices 0 triggers the same guard).

Common situations: Passing numVertices = 0 for an empty graph with root 0 (0 >= 0 is true). Off-by-one on vertex count. Using a root id sourced from external 1-based labeling without conversion.

Related errors

• Source and sink must be valid vertex indices
• Source and sink must be valid vertex indices
• Source and sink must be valid vertex indices
• Capacity matrix must not be null or empty
• Capacity matrix must be square

AI-assisted analysis of TheAlgorithms/Java@fdfb9a395b (2026-08-13). Data as JSON: /api/errors/d482d63cd1273154. Report an issue: GitHub.