Ternary Search in Sorted Arrays in C#

using System;
// Ternary Search in Sorted Arrays in C#
//
// 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
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 2.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int ternary_search(ReadOnlySpan<int> a, int target) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int low = 0;
            int high = (n - 1);
            int third = 0;
            int first = 0;
            int second = 0;
            while ((low <= high)) {
                third = ((high - low) / 3);
                first = (low + third);
                second = (high - third);
                if ((a[first] == target)) {
                    return first;
                }
                if ((a[second] == target)) {
                    return second;
                }
                if ((target < a[first])) {
                    high = (first - 1);
                } else {
                    if ((target > a[second])) {
                        low = (second + 1);
                    } else {
                        low = (first + 1);
                        high = (second - 1);
                    }
                }
            }
            return (-1);
        }
    }

    static void Main() {
        int[] a = new int[] {1, 3, 5, 7};
        int target = 5;
        int result = ternary_search(a, target);
        Console.WriteLine(result);
    }
}