Heap Sort in Java

// Heap Sort in Java
//
// PURPOSE
// Heap sort uses a max heap so the largest remaining value can be moved to the end. It gives
// a worst-case time guarantee without a second array.
//
// METHOD
// Build a max heap from the bottom up. Swap its root with the last active element, shrink
// the heap, and sift the new root downward. The suffix is sorted after every extraction.
//
// COMPLEXITY
// O(n log n) time, O(1) auxiliary space; heap construction is O(n). Not stable.
//
// CONTRACT
// Sorts n elements 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: [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 heap_sort(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int start = Math.subtractExact((n / 2), 1);
        int end = Math.subtractExact(n, 1);
        int root = 0;
        int child = 0;
        int temp = 0;
        while ((start >= 0)) {
            root = start;
            while ((Math.addExact(Math.multiplyExact(2, root), 1) < n)) {
                child = Math.addExact(Math.multiplyExact(2, root), 1);
                if (((Math.addExact(child, 1) < n) && (a[child] < a[Math.addExact(child, 1)]))) {
                    child = Math.addExact(child, 1);
                }
                if ((a[root] >= a[child])) {
                    break;
                }
                temp = a[root];
                a[root] = a[child];
                a[child] = temp;
                root = child;
            }
            start = Math.subtractExact(start, 1);
        }
        while ((end > 0)) {
            temp = a[0];
            a[0] = a[end];
            a[end] = temp;
            root = 0;
            while ((Math.addExact(Math.multiplyExact(2, root), 1) < end)) {
                child = Math.addExact(Math.multiplyExact(2, root), 1);
                if (((Math.addExact(child, 1) < end) && (a[child] < a[Math.addExact(child, 1)]))) {
                    child = Math.addExact(child, 1);
                }
                if ((a[root] >= a[child])) {
                    break;
                }
                temp = a[root];
                a[root] = a[child];
                a[child] = temp;
                root = child;
            }
            end = Math.subtractExact(end, 1);
        }
        return 0;
    }

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