Euclidean GCD in Java

// Euclidean GCD in Java
//
// PURPOSE
// The Euclidean algorithm finds the greatest common divisor by replacing a pair with the
// smaller number and the remainder. Common divisors are preserved by this replacement.
//
// METHOD
// Repeatedly compute a modulo b, move b into a, and put the remainder into b. Stop when b is
// zero; the last nonzero value divides both original inputs.
//
// COMPLEXITY
// O(log(min(a,b))) arithmetic steps for positive inputs, O(1) auxiliary space.
//
// CONTRACT
// a and b are nonnegative integers. Defines gcd(0,0) as 0. Avoid negative values because
// remainder conventions vary by language.
// 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: 6.
// 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 gcd(int a, int b) {
        alg_require(((a >= 0) && (b >= 0)));
        int remainder = 0;
        while ((b != 0)) {
            remainder = (a % b);
            a = b;
            b = remainder;
        }
        return a;
    }

    public static void main(String[] args) {
        int a = 48;
        int b = 18;
        int result = gcd(a, b);
        System.out.println(result);
    }
}