Depth First Search Reachability in Java

// Depth First Search Reachability in Java
//
// PURPOSE
// DFS follows a branch deeply before returning to pending branches. An explicit stack avoids
// language recursion limits for reachability exploration.
//
// METHOD
// Push the source and mark it. Pop a vertex, count it, then mark and push each unseen
// neighbor. Marking when pushed bounds stack entries to at most n.
//
// COMPLEXITY
// O(n squared) time with a matrix and O(n) auxiliary space. Adjacency lists reduce traversal
// to O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 matrix, n >= 1, valid source. Returns the number of reachable
// vertices INCLUDING source. Directed edges supported.
// 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: 3.
// 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 dfs_reachable(int[] graph, int n, int source) {
        java.util.Objects.requireNonNull(graph, "graph");
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((graph.length == Math.multiplyExact(n, n)));
        alg_require(((n >= 1) && (source >= 0) && (source < n)));
        int[] seen = new int[alg_size(n)];
        int[] stack = new int[alg_size(n)];
        int top = 1;
        int count = 0;
        int u = 0;
        int v = 0;
        stack[0] = source;
        seen[source] = 1;
        while ((top > 0)) {
            top = Math.subtractExact(top, 1);
            u = stack[top];
            count = Math.addExact(count, 1);
            v = 0;
            while ((v < n)) {
                if (((graph[Math.addExact(Math.multiplyExact(u, n), v)] != 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, 0, 0, 1, 0, 0, 0};
        int n = 3;
        int source = 0;
        int result = dfs_reachable(graph, n, source);
        System.out.println(result);
    }
}