Kosaraju Strongly Connected Components in Java

// Kosaraju Strongly Connected Components in Java
//
// PURPOSE
// Strongly connected components group vertices that can reach each other in both directions.
//
// METHOD
// First perform iterative DFS to record finishing order. Traverse vertices in reverse
// finishing order using incoming edges, counting each newly discovered component.
//
// COMPLEXITY
// O(n squared) time for the dense matrix and O(n) auxiliary space.
//
// CONTRACT
// Flattened n by n directed 0/1 matrix. Returns number of components; empty graph returns
// zero.
// 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: 2.
// 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 scc_count(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[] seen = 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[] order = new int[alg_size(Math.addExact(n, 1))];
        int source = 0;
        int top = 0;
        int finished = 0;
        int u = 0;
        int v = 0;
        int count = 0;
        while ((source < n)) {
            if ((seen[source] == 0)) {
                stack[0] = source;
                top = 1;
                seen[source] = 1;
                while ((top > 0)) {
                    u = stack[Math.subtractExact(top, 1)];
                    if ((next_vertex[u] == n)) {
                        order[finished] = u;
                        finished = Math.addExact(finished, 1);
                        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) && (seen[v] == 0))) {
                            seen[v] = 1;
                            stack[top] = v;
                            top = Math.addExact(top, 1);
                        }
                    }
                }
            }
            source = Math.addExact(source, 1);
        }
        source = 0;
        while ((source < n)) {
            seen[source] = 0;
            source = Math.addExact(source, 1);
        }
        while ((finished > 0)) {
            finished = Math.subtractExact(finished, 1);
            source = order[finished];
            if ((seen[source] == 0)) {
                count = Math.addExact(count, 1);
                stack[0] = source;
                top = 1;
                seen[source] = 1;
                while ((top > 0)) {
                    top = Math.subtractExact(top, 1);
                    u = stack[top];
                    v = 0;
                    while ((v < n)) {
                        if (((graph[Math.addExact(Math.multiplyExact(v, n), u)] != 0) && (seen[v] == 0))) {
                            seen[v] = 1;
                            stack[top] = v;
                            top = Math.addExact(top, 1);
                        }
                        v = Math.addExact(v, 1);
                    }
                }
            }
        }
        return count;
    }

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