Ternary Search in Sorted Arrays in Java

// Ternary Search in Sorted Arrays in Java
//
// PURPOSE
// Ternary search compares two interior positions to discard two thirds of a sorted interval.
//
// METHOD
// Compute two partition positions. Return a matching position, otherwise retain the left,
// middle, or right third containing the target.
//
// COMPLEXITY
// O(log n) time, O(1) space. Binary search generally uses fewer comparisons; this is
// distinct from optimization on unimodal functions.
//
// CONTRACT
// Ascending input; returns any matching index or -1.
// 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: 2.
// 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 ternary_search(int[] a, int target) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int low = 0;
        int high = Math.subtractExact(n, 1);
        int third = 0;
        int first = 0;
        int second = 0;
        while ((low <= high)) {
            third = (Math.subtractExact(high, low) / 3);
            first = Math.addExact(low, third);
            second = Math.subtractExact(high, third);
            if ((a[first] == target)) {
                return first;
            }
            if ((a[second] == target)) {
                return second;
            }
            if ((target < a[first])) {
                high = Math.subtractExact(first, 1);
            } else {
                if ((target > a[second])) {
                    low = Math.addExact(second, 1);
                } else {
                    low = Math.addExact(first, 1);
                    high = Math.subtractExact(second, 1);
                }
            }
        }
        return Math.negateExact(1);
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 3, 5, 7};
        int target = 5;
        int result = ternary_search(a, target);
        System.out.println(result);
    }
}