TheAlgorithms/Java · error · IllegalArgumentException

Capacities must be non-negative

Error message

Capacities must be non-negative

What it means

Thrown by Dinic.maxFlow when any capacity[i][j] < 0. Flow capacities are non-negative by definition; negative values break the residual-graph invariants. Message: 'Capacities must be non-negative'.

Source

Thrown at src/main/java/com/thealgorithms/graph/Dinic.java:48

     * @param capacity square capacity matrix (n x n); entries must be >= 0
     * @param source source vertex index in [0, n)
     * @param sink sink vertex index in [0, n)
     * @return the maximum flow value
     * @throws IllegalArgumentException if the input matrix is null/non-square/has negatives or
     *     indices invalid
     */
    public static int maxFlow(int[][] capacity, int source, int sink) {
        if (capacity == null || capacity.length == 0) {
            throw new IllegalArgumentException("Capacity matrix must not be null or empty");
        }
        final int n = capacity.length;
        for (int i = 0; i < n; i++) {
            if (capacity[i] == null || capacity[i].length != n) {
                throw new IllegalArgumentException("Capacity matrix must be square");
            }
            for (int j = 0; j < n; j++) {
                if (capacity[i][j] < 0) {
                    throw new IllegalArgumentException("Capacities must be non-negative");
                }
            }
        }
        if (source < 0 || sink < 0 || source >= n || sink >= n) {
            throw new IllegalArgumentException("Source and sink must be valid vertex indices");
        }
        if (source == sink) {
            return 0;
        }

        // residual capacities
        int[][] residual = new int[n][n];
        for (int i = 0; i < n; i++) {
            residual[i] = Arrays.copyOf(capacity[i], n);
        }

        int[] level = new int[n];
        int flow = 0;

View on GitHub (pinned to fdfb9a395b)

Solutions

1. Use 0 to represent 'no edge' between two vertices, never a negative sentinel.
2. Validate every entry >= 0 at the boundary.
3. Sanitize parsed numeric input to reject negatives.

Example fix

// before
cap[0][1] = -1; // intended 'no edge'

// after
cap[0][1] = 0; // no edge

for (int[] row : capacity) {
    for (int c : row) {
        if (c < 0) throw new IllegalArgumentException("negative capacity: " + c);
    }
}

When it happens

Trigger: A negative entry in the capacity matrix; using -1 as a 'no edge' sentinel instead of 0; signed parsing of an unsigned source.

Common situations: Sentinel values for 'no edge'; a subtraction that underflowed into a negative capacity; typo'd config with a minus sign.

Related errors

• Capacity matrix must not be null or empty
• Capacity matrix must be square
• Number of vertices must be positive
• Edges list must not be null or empty
• Edge vertex out of range

AI-assisted analysis of TheAlgorithms/Java@fdfb9a395b (2026-08-13). Data as JSON: /api/errors/3bd3e0aa7dba60aa. Report an issue: GitHub.