Kahn Topological Cycle Detection in Java

// Kahn Topological Cycle Detection in Java
//
// PURPOSE
// Kahn algorithm repeatedly removes vertices with no incoming edges. A directed graph has a
// topological ordering exactly when all vertices can be removed this way.
//
// METHOD
// Compute indegrees, queue every zero-indegree vertex, then remove its outgoing edges.
// Enqueue a neighbor when its indegree becomes zero. Compare the number removed with n.
//
// COMPLEXITY
// O(n squared) time with an adjacency matrix and O(n) auxiliary space. Adjacency lists give
// O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 directed matrix. Returns 1 for a DAG and 0 for a cycle. Empty graph
// is a DAG. This variant reports existence rather than returning an ordering.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 1.
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int is_dag(int[] graph, int n) {
        java.util.Objects.requireNonNull(graph, "graph");
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((graph.length == Math.multiplyExact(n, n)));
        int[] indegree = new int[alg_size(Math.addExact(n, 1))];
        int[] queue = new int[alg_size(Math.addExact(n, 1))];
        int u = 0;
        int v = 0;
        int head = 0;
        int tail = 0;
        while ((u < n)) {
            v = 0;
            while ((v < n)) {
                if ((graph[Math.addExact(Math.multiplyExact(u, n), v)] != 0)) {
                    indegree[v] = Math.addExact(indegree[v], 1);
                }
                v = Math.addExact(v, 1);
            }
            u = Math.addExact(u, 1);
        }
        v = 0;
        while ((v < n)) {
            if ((indegree[v] == 0)) {
                queue[tail] = v;
                tail = Math.addExact(tail, 1);
            }
            v = Math.addExact(v, 1);
        }
        while ((head < tail)) {
            u = queue[head];
            head = Math.addExact(head, 1);
            v = 0;
            while ((v < n)) {
                if ((graph[Math.addExact(Math.multiplyExact(u, n), v)] != 0)) {
                    indegree[v] = Math.subtractExact(indegree[v], 1);
                    if ((indegree[v] == 0)) {
                        queue[tail] = v;
                        tail = Math.addExact(tail, 1);
                    }
                }
                v = Math.addExact(v, 1);
            }
        }
        if ((tail == n)) {
            return 1;
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] graph = new int[] {0, 1, 0, 0, 0, 1, 0, 0, 0};
        int n = 3;
        int result = is_dag(graph, n);
        System.out.println(result);
    }
}