Counting Sort in Java

// Counting Sort in Java
//
// PURPOSE
// Counting sort counts each possible key instead of comparing pairs. It is efficient when
// nonnegative integer keys occupy a small range.
//
// METHOD
// Count occurrences in a frequency array, then write each key the recorded number of times.
// The output prefix is sorted throughout reconstruction.
//
// COMPLEXITY
// O(n + k) time and O(k) auxiliary space, where k = maximum + 1. This key-only version does
// not demonstrate stable sorting of records.
//
// CONTRACT
// All n values must be between 0 and maximum inclusive. Sorts in place and returns 0. A huge
// maximum makes this approach unsuitable.
// 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: [1, 1, 3, 5].
// 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 counting_sort(int[] a, int maximum) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require(((maximum >= 0) && (maximum <= 1000000)));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require(((alg_value >= 0) && (alg_value <= maximum)));
        }
        int[] counts = new int[alg_size(Math.addExact(maximum, 1))];
        int i = 0;
        int value = 0;
        int out = 0;
        while ((i < n)) {
            counts[a[i]] = Math.addExact(counts[a[i]], 1);
            i = Math.addExact(i, 1);
        }
        while ((value <= maximum)) {
            while ((counts[value] > 0)) {
                a[out] = value;
                out = Math.addExact(out, 1);
                counts[value] = Math.subtractExact(counts[value], 1);
            }
            value = Math.addExact(value, 1);
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {5, 1, 3, 1};
        int maximum = 5;
        int result = counting_sort(a, maximum);
        System.out.println(result);
        System.out.println(java.util.Arrays.toString(a));
        // Expected a: [1, 1, 3, 5]
    }
}