Iterative Binary Tree Preorder in C#

using System;
// Iterative Binary Tree Preorder in C#
//
// PURPOSE
// Preorder traversal visits each binary-tree node once without recursion.
//
// METHOD
// Keep a stack of nodes and visit states. State zero descends left, state one descends
// right, and state two exits. Emit the node at the traversal-specific state.
//
// COMPLEXITY
// O(n) time and O(n) allocated stack space; live stack usage is O(tree height).
//
// CONTRACT
// Parallel left_child and right_child arrays contain -1 or node IDs. root=-1 means empty.
// The structure must be a valid tree, not cyclic or shared. output has n entries; writes
// node IDs and returns visited count.
// 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: 3.
// Expected output after call: [0, 1, 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 tree_preorder(ReadOnlySpan<int> left_child, ReadOnlySpan<int> right_child, int root, Span<int> output) {
        checked {
            int n = left_child.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((left_child.Length == n));
            alg_require((right_child.Length == n));
            alg_require((output.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)));
            }
            int[] stack = new int[alg_size((n + 1))];
            int[] state = new int[alg_size((n + 1))];
            int top = 0;
            int u = 0;
            int phase = 0;
            int count = 0;
            if ((root == (-1))) {
                return 0;
            }
            stack[0] = root;
            top = 1;
            while ((top > 0)) {
                u = stack[(top - 1)];
                phase = state[(top - 1)];
                if ((phase == 0)) {
                    output[count] = u;
                    count = (count + 1);
                }
                if ((phase == 0)) {
                    state[(top - 1)] = 1;
                    if ((left_child[u] != (-1))) {
                        stack[top] = left_child[u];
                        state[top] = 0;
                        top = (top + 1);
                    }
                } else {
                    if ((phase == 1)) {
                        state[(top - 1)] = 2;
                        if ((right_child[u] != (-1))) {
                            stack[top] = right_child[u];
                            state[top] = 0;
                            top = (top + 1);
                        }
                    } else {
                        top = (top - 1);
                    }
                }
            }
            return count;
        }
    }

    static void Main() {
        int[] left_child = new int[] {1, -1, -1};
        int[] right_child = new int[] {2, -1, -1};
        int root = 0;
        int[] output = new int[] {0, 0, 0};
        int result = tree_preorder(left_child, right_child, root, output);
        Console.WriteLine(result);
        // Expected output: [0, 1, 2]
        Console.WriteLine("[" + string.Join(", ", output) + "]");
    }
}