Iterative Quick Sort in Java

// Iterative Quick Sort in Java
//
// PURPOSE
// Quick sort partitions around a pivot and sorts the two resulting regions. This iterative
// version stores pending intervals explicitly instead of using recursion.
//
// METHOD
// Choose a median-of-three pivot and partition into less-than, equal-to, and greater-than
// regions. Process the smaller region immediately and defer the larger one to keep the
// explicit stack bounded.
//
// COMPLEXITY
// O(n log n) average time, O(n squared) adversarial worst case. Equal-key input takes O(n).
// O(log n) pending intervals; 64 stack slots cover the supported bounded input lengths. Not
// stable.
//
// CONTRACT
// Sorts ascending in place and returns 0. Three-way partition handles repeated keys
// efficiently. Median-of-three reduces common fixed-endpoint pivot problems but does not
// provide introsort's worst-case guarantee.
// 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 quick_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[] lefts = new int[alg_size(64)];
        int[] rights = new int[alg_size(64)];
        int top = 0;
        int low = 0;
        int high = Math.subtractExact(n, 1);
        int left = 0;
        int right = 0;
        int mid = 0;
        int pivot = 0;
        int temp = 0;
        while (((low < high) || (top > 0))) {
            if ((low >= high)) {
                top = Math.subtractExact(top, 1);
                low = lefts[top];
                high = rights[top];
            }
            mid = Math.addExact(low, (Math.subtractExact(high, low) / 2));
            pivot = Math.max(Math.min(a[low], a[mid]), Math.min(Math.max(a[low], a[mid]), a[high]));
            left = low;
            mid = low;
            right = high;
            while ((mid <= right)) {
                if ((a[mid] < pivot)) {
                    temp = a[left];
                    a[left] = a[mid];
                    a[mid] = temp;
                    left = Math.addExact(left, 1);
                    mid = Math.addExact(mid, 1);
                } else {
                    if ((a[mid] > pivot)) {
                        temp = a[mid];
                        a[mid] = a[right];
                        a[right] = temp;
                        right = Math.subtractExact(right, 1);
                    } else {
                        mid = Math.addExact(mid, 1);
                    }
                }
            }
            if ((Math.subtractExact(left, low) < Math.subtractExact(high, right))) {
                if ((Math.addExact(right, 1) < high)) {
                    lefts[top] = Math.addExact(right, 1);
                    rights[top] = high;
                    top = Math.addExact(top, 1);
                }
                high = Math.subtractExact(left, 1);
            } else {
                if ((low < Math.subtractExact(left, 1))) {
                    lefts[top] = low;
                    rights[top] = Math.subtractExact(left, 1);
                    top = Math.addExact(top, 1);
                }
                low = Math.addExact(right, 1);
            }
        }
        return 0;
    }

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