LSD Radix Sort in Java

// LSD Radix Sort in Java
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// 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 a after call: [0, 1, 255, 256, 65536].
// 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 radix_sort(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require((alg_value >= 0));
        }
        int[] output = new int[alg_size(Math.addExact(n, 1))];
        int[] count = new int[alg_size(256)];
        int divisor = 1;
        int digit = 0;
        int pass_index = 0;
        int i = 0;
        while ((pass_index < 4)) {
            i = 0;
            while ((i < 256)) {
                count[i] = 0;
                i = Math.addExact(i, 1);
            }
            i = 0;
            while ((i < n)) {
                digit = ((a[i] / divisor) % 256);
                count[digit] = Math.addExact(count[digit], 1);
                i = Math.addExact(i, 1);
            }
            i = 1;
            while ((i < 256)) {
                count[i] = Math.addExact(count[i], count[Math.subtractExact(i, 1)]);
                i = Math.addExact(i, 1);
            }
            i = Math.subtractExact(n, 1);
            while ((i >= 0)) {
                digit = ((a[i] / divisor) % 256);
                count[digit] = Math.subtractExact(count[digit], 1);
                output[count[digit]] = a[i];
                i = Math.subtractExact(i, 1);
            }
            i = 0;
            while ((i < n)) {
                a[i] = output[i];
                i = Math.addExact(i, 1);
            }
            pass_index = Math.addExact(pass_index, 1);
            if ((pass_index < 4)) {
                divisor = Math.multiplyExact(divisor, 256);
            }
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {256, 1, 65536, 0, 255};
        int result = radix_sort(a);
        System.out.println(result);
        // Expected a: [0, 1, 255, 256, 65536]
        System.out.println(java.util.Arrays.toString(a));
    }
}