TheAlgorithms/Java · error · IllegalArgumentException

Capacities must be non-negative

Error message

Capacities must be non-negative

What it means

PushRelabel.validate throws this IllegalArgumentException when any capacity cell is negative. Push-relabel's preflow and relabel operations assume non-negative capacities; negative values break the excess invariant and can produce incorrect flow values.

Source

Thrown at src/main/java/com/thealgorithms/graph/PushRelabel.java:154

            }
        }
        if (minHeight < Integer.MAX_VALUE) {
            height[u] = minHeight + 1;
        }
    }

    private static void validate(int[][] capacity, int source, int sink) {
        if (capacity == null || capacity.length == 0) {
            throw new IllegalArgumentException("Capacity matrix must not be null or empty");
        }
        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");
        }
    }
}

View on GitHub (pinned to fdfb9a395b)

Solutions

1. Use 0 for no-edge representation.
2. Clamp parsed values with Math.max(0, val).
3. Unit-test the matrix for non-negativity before calling.

Example fix

// before
cap[u][v] = hasEdge ? w : -1;

// after
cap[u][v] = hasEdge ? w : 0;

for (int i = 0; i < capacity.length; i++)
    for (int j = 0; j < capacity[i].length; j++)
        if (capacity[i][j] < 0) capacity[i][j] = 0;

boolean allNonNegative(int[][] cap) {
    for (int[] row : cap) for (int v : row) if (v < 0) return false;
    return true;
}

When it happens

Trigger: Passing a matrix with any cell < 0, including -1 sentinels for 'no edge'.

Common situations: Using -1 for no-edge. Signed weights not clamped. Buggy in-place residual mutation before calling validate.

Related errors

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

AI-assisted analysis of TheAlgorithms/Java@fdfb9a395b (2026-08-13). Data as JSON: /api/errors/f5becd93569f4928. Report an issue: GitHub.