Quickselect in Java

// Quickselect in Java
//
// PURPOSE
// Quickselect finds a zero-based order statistic without fully sorting the input.
//
// METHOD
// Partition around the middle-position pivot using a three-way partition. Retain only the
// side containing rank k, or return the pivot when k lies in the equal region.
//
// COMPLEXITY
// O(n) expected time for random input; O(n squared) worst case for this deterministic pivot.
// O(1) auxiliary space.
//
// CONTRACT
// 0 <= k < n. Mutates input. Returns the kth smallest value, counting duplicates.
// 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: 5.
// Expected a after call: [2, 2, 5, 7, 9].
// 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 quickselect(int[] a, int k) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require(((k >= 0) && (k < n)));
        int low = 0;
        int high = Math.subtractExact(n, 1);
        int left = 0;
        int mid = 0;
        int right = 0;
        int pivot = 0;
        int temp = 0;
        while ((low <= high)) {
            pivot = a[Math.addExact(low, (Math.subtractExact(high, low) / 2))];
            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 ((k < left)) {
                high = Math.subtractExact(left, 1);
            } else {
                if ((k > right)) {
                    low = Math.addExact(right, 1);
                } else {
                    return pivot;
                }
            }
        }
        return Math.negateExact(1);
    }

    public static void main(String[] args) {
        int[] a = new int[] {7, 2, 9, 2, 5};
        int k = 2;
        int result = quickselect(a, k);
        System.out.println(result);
        // Expected a: [2, 2, 5, 7, 9]
        System.out.println(java.util.Arrays.toString(a));
    }
}