Directed Cycle Detection by DFS in Java

// Directed Cycle Detection by DFS in Java
//
// PURPOSE
// DFS detects a directed cycle when an edge points to a vertex still active in the current
// search path.
//
// METHOD
// Use an explicit stack and per-vertex next-neighbor positions. Mark vertices active on
// entry and finished on exit. An edge to an active vertex is a back edge.
//
// COMPLEXITY
// O(n squared) matrix traversal time and O(n) auxiliary space.
//
// CONTRACT
// Flattened n by n 0/1 directed adjacency matrix; returns 1 if a cycle exists, otherwise 0.
// 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 directed_cycle(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[] color = new int[alg_size(Math.addExact(n, 1))];
        int[] stack = new int[alg_size(Math.addExact(n, 1))];
        int[] next_vertex = new int[alg_size(Math.addExact(n, 1))];
        int source = 0;
        int top = 0;
        int u = 0;
        int v = 0;
        while ((source < n)) {
            if ((color[source] == 0)) {
                top = 1;
                stack[0] = source;
                color[source] = 1;
                while ((top > 0)) {
                    u = stack[Math.subtractExact(top, 1)];
                    if ((next_vertex[u] == n)) {
                        color[u] = 2;
                        top = Math.subtractExact(top, 1);
                    } else {
                        v = next_vertex[u];
                        next_vertex[u] = Math.addExact(next_vertex[u], 1);
                        if ((graph[Math.addExact(Math.multiplyExact(u, n), v)] != 0)) {
                            if ((color[v] == 1)) {
                                return 1;
                            }
                            if ((color[v] == 0)) {
                                color[v] = 1;
                                stack[top] = v;
                                top = Math.addExact(top, 1);
                            }
                        }
                    }
                }
            }
            source = Math.addExact(source, 1);
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] graph = new int[] {0, 1, 1, 0};
        int n = 2;
        int result = directed_cycle(graph, n);
        System.out.println(result);
    }
}