Iterative Binary Tree Inorder in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Iterative Binary Tree Inorder in C++
//
// PURPOSE
// Inorder 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++17: const vector references for inputs, mutable references for outputs, RAII workspace,
// standard lower_bound for LIS. Invalid inputs throw invalid_argument; overflow throws
// overflow_error; allocation failure propagates bad_alloc.
//
// EXAMPLE
// Expected return: 3.
// Expected output after call: [1, 0, 2].
// Run: g++ -std=c++17 -O2 example.cpp -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static void alg_require(bool valid) { if (!valid) throw std::invalid_argument("invalid algorithm input"); }
static int alg_checked(int64_t v) { if (v < INT32_MIN || v > INT32_MAX) throw std::overflow_error("32-bit result overflow"); return (int)v; }
static int alg_add(int a,int b) { return alg_checked((int64_t)a+b); }
static int alg_sub(int a,int b) { return alg_checked((int64_t)a-b); }
static int alg_mul(int a,int b) { return alg_checked((int64_t)a*b); }
static size_t alg_size(int n) { alg_require(n>=0 && n<=4000000); return (size_t)n; }

int tree_inorder(const std::vector<int>& left_child, const std::vector<int>& right_child, int root, std::vector<int>& output) {
    alg_require(left_child.size() <= 1000000);
    alg_require(right_child.size() <= 1000000);
    alg_require(output.size() <= 1000000);
    int n = (int)left_child.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)left_child.size() == n));
    alg_require(((int)right_child.size() == n));
    alg_require(((int)output.size() == n));
    alg_require(((root >= alg_sub(0, 1)) && (root < n)));
    for (int alg_i = 0; alg_i < (int)left_child.size(); alg_i++) {
        int alg_value = left_child[alg_i];
        alg_require(((alg_value >= alg_sub(0, 1)) && (alg_value < n)));
    }
    for (int alg_i = 0; alg_i < (int)right_child.size(); alg_i++) {
        int alg_value = right_child[alg_i];
        alg_require(((alg_value >= alg_sub(0, 1)) && (alg_value < n)));
    }
    std::vector<int> stack(alg_size(alg_add(n, 1)), 0);
    std::vector<int> state(alg_size(alg_add(n, 1)), 0);
    int top = 0;
    int u = 0;
    int phase = 0;
    int count = 0;
    if ((root == alg_sub(0, 1))) {
        return 0;
    }
    stack[0] = root;
    top = 1;
    while ((top > 0)) {
        u = stack[alg_sub(top, 1)];
        phase = state[alg_sub(top, 1)];
        if ((phase == 1)) {
            output[count] = u;
            count = alg_add(count, 1);
        }
        if ((phase == 0)) {
            state[alg_sub(top, 1)] = 1;
            if ((left_child[u] != alg_sub(0, 1))) {
                stack[top] = left_child[u];
                state[top] = 0;
                top = alg_add(top, 1);
            }
        } else {
            if ((phase == 1)) {
                state[alg_sub(top, 1)] = 2;
                if ((right_child[u] != alg_sub(0, 1))) {
                    stack[top] = right_child[u];
                    state[top] = 0;
                    top = alg_add(top, 1);
                }
            } else {
                top = alg_sub(top, 1);
            }
        }
    }
    return count;
}

int main(void) {
    std::vector<int> left_child = {1, -1, -1};
    std::vector<int> right_child = {2, -1, -1};
    int root = 0;
    std::vector<int> output = {0, 0, 0};
    int result = tree_inorder(left_child, right_child, root, output);
    printf("%d\n", result);
    // Expected output: [1, 0, 2]
    for (int alg_print = 0; alg_print < 3; alg_print++) printf("%d ", output[alg_print]);
    printf("\n");
    return 0;
}