Algorithms: Tree Algorithms

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Iterative Binary Tree Postorder in C
//
// PURPOSE
// Postorder 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
// C99: checked calloc/free workspace, const input pointers, explicit size_t lengths. Errors
// return INT_MIN with errno=EINVAL, ERANGE, or ENOMEM. Check errno before using a result.
// Input/output arrays must not alias. No variable-length stack arrays.
//
// EXAMPLE
// Expected return: 3.
// Expected output after call: [1, 2, 0].
// Run: gcc -std=c99 -O2 example.c -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 int alg_checked(int64_t v, int *error) {
    if (v < INT_MIN || v > INT_MAX) { *error = 1; return 0; }
    return (int)v;
}
static int alg_add(int a, int b, int *e) { return alg_checked((int64_t)a+b,e); }
static int alg_sub(int a, int b, int *e) { return alg_checked((int64_t)a-b,e); }
static int alg_mul(int a, int b, int *e) { return alg_checked((int64_t)a*b,e); }

int tree_postorder(const int *left_child, size_t left_child_length, const int *right_child, size_t right_child_length, int root, int *output, size_t output_length) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    int *stack = NULL;
    int *state = NULL;
    if (left_child_length > 1000000 || (left_child_length && !left_child)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (right_child_length > 1000000 || (right_child_length && !right_child)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (output_length > 1000000 || (output_length && !output)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    int n = (int)left_child_length;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((n >= 0) && (n <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)left_child_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)right_child_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)output_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((root >= alg_sub(0, 1, &alg_error)) && (root < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    for (int alg_i = 0; alg_i < (int)left_child_length; alg_i++) {
        int alg_value = left_child[alg_i];
        if (!(((alg_value >= alg_sub(0, 1, &alg_error)) && (alg_value < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    for (int alg_i = 0; alg_i < (int)right_child_length; alg_i++) {
        int alg_value = right_child[alg_i];
        if (!(((alg_value >= alg_sub(0, 1, &alg_error)) && (alg_value < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    {
        int alg_length = alg_add(n, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        stack = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*stack));
        if (!stack) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    {
        int alg_length = alg_add(n, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        state = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*state));
        if (!state) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int top = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int u = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int phase = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int count = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int alg_condition_1 = (root == alg_sub(0, 1, &alg_error));
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_condition_1) {
        alg_result = 0;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        goto alg_cleanup;
    }
    stack[0] = root;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    top = 1;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (top > 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        u = stack[alg_sub(top, 1, &alg_error)];
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        phase = state[alg_sub(top, 1, &alg_error)];
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        int alg_condition_2 = (phase == 2);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_2) {
            output[count] = u;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            count = alg_add(count, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
        int alg_condition_3 = (phase == 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_3) {
            state[alg_sub(top, 1, &alg_error)] = 1;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            int alg_condition_4 = (left_child[u] != alg_sub(0, 1, &alg_error));
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (alg_condition_4) {
                stack[top] = left_child[u];
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                state[top] = 0;
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                top = alg_add(top, 1, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
        } else {
            int alg_condition_5 = (phase == 1);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (alg_condition_5) {
                state[alg_sub(top, 1, &alg_error)] = 2;
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                int alg_condition_6 = (right_child[u] != alg_sub(0, 1, &alg_error));
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                if (alg_condition_6) {
                    stack[top] = right_child[u];
                    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                    state[top] = 0;
                    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                    top = alg_add(top, 1, &alg_error);
                    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                }
            } else {
                top = alg_sub(top, 1, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
        }
    }
    alg_result = count;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    free(stack);
    free(state);
    return alg_result;
}

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

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Iterative Binary Tree Postorder in C++
//
// PURPOSE
// Postorder 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, 2, 0].
// 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_postorder(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 == 2)) {
            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_postorder(left_child, right_child, root, output);
    printf("%d\n", result);
    // Expected output: [1, 2, 0]
    for (int alg_print = 0; alg_print < 3; alg_print++) printf("%d ", output[alg_print]);
    printf("\n");
    return 0;
}

using System;
// Iterative Binary Tree Postorder in C#
//
// PURPOSE
// Postorder 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: [1, 2, 0].
// 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_postorder(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 == 2)) {
                    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_postorder(left_child, right_child, root, output);
        Console.WriteLine(result);
        // Expected output: [1, 2, 0]
        Console.WriteLine("[" + string.Join(", ", output) + "]");
    }
}

<?php
declare(strict_types=1);
// Iterative Binary Tree Postorder in PHP
//
// PURPOSE
// Postorder 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
// PHP 8.1+ on a 64-bit runtime: packed arrays, strict scalar types, read-only inputs by
// value using copy-on-write, references only for outputs, and checked 32-bit arithmetic.
// Invalid input and overflow throw exceptions. PHP arrays have higher overhead than native
// packed buffers in C/Java.
//
// EXAMPLE
// Expected return: 3.
// Expected output after call: [1, 2, 0].
// Run: php example.php
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(bool $valid): void { if (!$valid) throw new InvalidArgumentException("invalid algorithm input"); }
function alg_checked(int|float $v): int { if ($v < -2147483648 || $v > 2147483647 || floor($v) != $v) throw new OverflowException("32-bit result overflow"); return (int)$v; }
function alg_add(int $a,int $b): int { return alg_checked($a+$b); }
function alg_sub(int $a,int $b): int { return alg_checked($a-$b); }
function alg_mul(int $a,int $b): int { return alg_checked($a*$b); }
function alg_size(int $n): int { alg_require($n>=0 && $n<=4000000); return $n; }

function tree_postorder(array $left_child, array $right_child, int $root, array &$output): int {
    alg_require(array_is_list($left_child));
    alg_require(array_is_list($right_child));
    alg_require(array_is_list($output));
    $n = count($left_child);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($left_child) == $n));
    alg_require((count($right_child) == $n));
    alg_require((count($output) == $n));
    alg_require((($root >= alg_sub(0, 1)) && ($root < $n)));
    for ($alg_i = 0; $alg_i < count($left_child); $alg_i++) {
        $alg_value = $left_child[$alg_i];
        alg_require((($alg_value >= alg_sub(0, 1)) && ($alg_value < $n)));
    }
    for ($alg_i = 0; $alg_i < count($right_child); $alg_i++) {
        $alg_value = $right_child[$alg_i];
        alg_require((($alg_value >= alg_sub(0, 1)) && ($alg_value < $n)));
    }
    $stack = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $state = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $top = 0;
    $u = 0;
    $phase = 0;
    $count = 0;
    if (($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 == 2)) {
            $output[$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;
}

$left_child = [1, -1, -1];
$right_child = [2, -1, -1];
$root = 0;
$output = [0, 0, 0];
$result = tree_postorder($left_child, $right_child, $root, $output);
echo $result, PHP_EOL;
// Expected output: [1, 2, 0]
echo json_encode($output), PHP_EOL;

// Iterative Binary Tree Inorder in Java
//
// 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 3.
// Expected output after call: [1, 0, 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 tree_inorder(int[] left_child, int[] right_child, int root, int[] output) {
        java.util.Objects.requireNonNull(left_child, "left_child");
        java.util.Objects.requireNonNull(right_child, "right_child");
        java.util.Objects.requireNonNull(output, "output");
        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 >= Math.negateExact(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 >= Math.negateExact(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 >= Math.negateExact(1)) && (alg_value < n)));
        }
        int[] stack = new int[alg_size(Math.addExact(n, 1))];
        int[] state = new int[alg_size(Math.addExact(n, 1))];
        int top = 0;
        int u = 0;
        int phase = 0;
        int count = 0;
        if ((root == Math.negateExact(1))) {
            return 0;
        }
        stack[0] = root;
        top = 1;
        while ((top > 0)) {
            u = stack[Math.subtractExact(top, 1)];
            phase = state[Math.subtractExact(top, 1)];
            if ((phase == 1)) {
                output[count] = u;
                count = Math.addExact(count, 1);
            }
            if ((phase == 0)) {
                state[Math.subtractExact(top, 1)] = 1;
                if ((left_child[u] != Math.negateExact(1))) {
                    stack[top] = left_child[u];
                    state[top] = 0;
                    top = Math.addExact(top, 1);
                }
            } else {
                if ((phase == 1)) {
                    state[Math.subtractExact(top, 1)] = 2;
                    if ((right_child[u] != Math.negateExact(1))) {
                        stack[top] = right_child[u];
                        state[top] = 0;
                        top = Math.addExact(top, 1);
                    }
                } else {
                    top = Math.subtractExact(top, 1);
                }
            }
        }
        return count;
    }

    public static void main(String[] args) {
        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_inorder(left_child, right_child, root, output);
        System.out.println(result);
        // Expected output: [1, 0, 2]
        System.out.println(java.util.Arrays.toString(output));
    }
}