Josephus Survivor in Java

// Josephus Survivor in Java
//
// PURPOSE
// The Josephus recurrence finds the last survivor when every kth person in a circle is
// eliminated.
//
// METHOD
// Start with survivor index zero for a one-person circle. Grow the circle one person at a
// time using survivor=(survivor+k) modulo size.
//
// COMPLEXITY
// O(n) time, O(1) space.
//
// CONTRACT
// 1 <= n <= 1000000, 1 <= k <= 1000000. Returns a zero-based survivor index.
// 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 josephus(int n, int k) {
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require(((n >= 1) && (n <= 1000000) && (k >= 1) && (k <= 1000000)));
        int survivor = 0;
        int size = 2;
        while ((size <= n)) {
            survivor = (Math.addExact(survivor, k) % size);
            size = Math.addExact(size, 1);
        }
        return survivor;
    }

    public static void main(String[] args) {
        int n = 7;
        int k = 3;
        int result = josephus(n, k);
        System.out.println(result);
    }
}