Binary Search Tree Lookup in C

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// 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
// 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: 2.
// 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 bst_lookup(const int *keys, size_t keys_length, const int *left_child, size_t left_child_length, const int *right_child, size_t right_child_length, int root, int target) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (keys_length > 1000000 || (keys_length && !keys)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    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; }
    int n = (int)keys_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)keys_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)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 (!(((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; }
    }
    while (1) {
        int alg_condition = (root != alg_sub(0, 1, &alg_error));
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        int alg_condition_1 = (keys[root] == target);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_1) {
            alg_result = root;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            goto alg_cleanup;
        }
        int alg_condition_2 = (target < keys[root]);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_2) {
            root = left_child[root];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        } else {
            root = right_child[root];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
    }
    alg_result = alg_sub(0, 1, &alg_error);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    return alg_result;
}

int main(void) {
    int keys[] = {4, 2, 6};
    int left_child[] = {1, -1, -1};
    int right_child[] = {2, -1, -1};
    int root = 0;
    int target = 6;
    int result = bst_lookup(keys, 3, left_child, 3, right_child, 3, root, target);
    printf("%d\n", result);
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}