Binary Search Tree Lookup in C#

using System;
// Binary Search Tree Lookup in C#
//
// PURPOSE
// A binary search tree chooses a branch by comparing the target with the current node key.
//
// METHOD
// At each node return on equality, otherwise follow the left child for a smaller target or
// the right child for a larger target.
//
// COMPLEXITY
// O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
// balanced.
//
// CONTRACT
// keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
// node ID 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 bst_lookup(ReadOnlySpan<int> keys, ReadOnlySpan<int> left_child, ReadOnlySpan<int> right_child, int root, int target) {
        checked {
            int n = keys.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((keys.Length == n));
            alg_require((left_child.Length == n));
            alg_require((right_child.Length == n));
            alg_require(((root >= (-1)) && (root < n)));
            for (int alg_i = 0; alg_i < left_child.Length; alg_i++) {
                int alg_value = left_child[alg_i];
                alg_require(((alg_value >= (-1)) && (alg_value < n)));
            }
            for (int alg_i = 0; alg_i < right_child.Length; alg_i++) {
                int alg_value = right_child[alg_i];
                alg_require(((alg_value >= (-1)) && (alg_value < n)));
            }
            while ((root != (-1))) {
                if ((keys[root] == target)) {
                    return root;
                }
                if ((target < keys[root])) {
                    root = left_child[root];
                } else {
                    root = right_child[root];
                }
            }
            return (-1);
        }
    }

    static void Main() {
        int[] keys = new int[] {4, 2, 6};
        int[] left_child = new int[] {1, -1, -1};
        int[] right_child = new int[] {2, -1, -1};
        int root = 0;
        int target = 6;
        int result = bst_lookup(keys, left_child, right_child, root, target);
        Console.WriteLine(result);
    }
}