Warshall Transitive Closure in Java

// Warshall Transitive Closure in Java
//
// PURPOSE
// Transitive closure records whether every vertex can reach every other vertex. Warshall is
// the Boolean counterpart of Floyd-Warshall.
//
// METHOD
// Mark each vertex reachable from itself. For every intermediate k, mark i-to-j reachable
// whenever i reaches k and k reaches j. The matrix accumulates reachability through the
// processed intermediates.
//
// COMPLEXITY
// O(n cubed) time and O(1) auxiliary space beyond the caller-owned matrix.
//
// CONTRACT
// Mutates a flattened n by n 0/1 adjacency matrix to reflexive transitive closure. Returns
// 0. A vertex reaches itself via a path of zero edges.
// 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: 0.
// Expected graph after call: [1, 1, 1, 0, 1, 1, 0, 0, 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 transitive_closure(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 i = 0;
        int j = 0;
        int k = 0;
        while ((i < n)) {
            graph[Math.addExact(Math.multiplyExact(i, n), i)] = 1;
            i = Math.addExact(i, 1);
        }
        while ((k < n)) {
            i = 0;
            while ((i < n)) {
                j = 0;
                while ((j < n)) {
                    if (((graph[Math.addExact(Math.multiplyExact(i, n), k)] != 0) && (graph[Math.addExact(Math.multiplyExact(k, n), j)] != 0))) {
                        graph[Math.addExact(Math.multiplyExact(i, n), j)] = 1;
                    }
                    j = Math.addExact(j, 1);
                }
                i = Math.addExact(i, 1);
            }
            k = Math.addExact(k, 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 = transitive_closure(graph, n);
        System.out.println(result);
        System.out.println(java.util.Arrays.toString(graph));
        // Expected graph: [1, 1, 1, 0, 1, 1, 0, 0, 1]
    }
}