Sudoku Backtracking Solver in PHP

<?php
declare(strict_types=1);
// Sudoku Backtracking Solver in PHP
//
// PURPOSE
// A Sudoku solver fills a 9 by 9 grid while respecting row, column, and box uniqueness.
//
// METHOD
// Validate givens into three occupancy tables, collect empty cells, then try candidate
// digits with iterative backtracking. On exhaustion restore each original empty cell to
// zero.
//
// COMPLEXITY
// Exponential worst-case search in the number of empty cells; O(81) bounded workspace.
//
// CONTRACT
// board has 81 values in [0,9], where 0 means empty. Returns 1 after solving, 0 if
// unsatisfiable, -1 for conflicting givens. On failure leaves board unchanged.
// 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: 1.
// Expected board after call: [5, 3, 4, 6, 7, 8, 9, 1, 2, 6, 7, 2, 1, 9, 5, 3, 4, 8, 1, 9, 8,
// 3, 4, 2, 5, 6, 7, 8, 5, 9, 7, 6, 1, 4, 2, 3, 4, 2, 6, 8, 5, 3, 7, 9, 1, 7, 1, 3, 9, 2, 4,
// 8, 5, 6, 9, 6, 1, 5, 3, 7, 2, 8, 4, 2, 8, 7, 4, 1, 9, 6, 3, 5, 3, 4, 5, 2, 8, 6, 1, 7, 9].
// 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 sudoku_solve(array &$board): int {
    alg_require(array_is_list($board));
    alg_require((count($board) == 81));
    for ($alg_i = 0; $alg_i < count($board); $alg_i++) {
        $alg_value = $board[$alg_i];
        alg_require((($alg_value >= 0) && ($alg_value <= 9)));
    }
    $rows = array_fill(0, alg_size(90), 0);
    $cols = array_fill(0, alg_size(90), 0);
    $boxes = array_fill(0, alg_size(90), 0);
    $empty = array_fill(0, alg_size(81), 0);
    $count = 0;
    $position = 0;
    $cell = 0;
    $r = 0;
    $c = 0;
    $box = 0;
    $digit = 0;
    while (($cell < 81)) {
        $r = intdiv($cell, 9);
        $c = ($cell % 9);
        $box = alg_add(alg_mul(intdiv($r, 3), 3), intdiv($c, 3));
        $digit = $board[$cell];
        if (($digit == 0)) {
            $empty[$count] = $cell;
            $count = alg_add($count, 1);
        } else {
            if ((($rows[alg_add(alg_mul($r, 10), $digit)] != 0) || ($cols[alg_add(alg_mul($c, 10), $digit)] != 0) || ($boxes[alg_add(alg_mul($box, 10), $digit)] != 0))) {
                return alg_sub(0, 1);
            }
            $rows[alg_add(alg_mul($r, 10), $digit)] = 1;
            $cols[alg_add(alg_mul($c, 10), $digit)] = 1;
            $boxes[alg_add(alg_mul($box, 10), $digit)] = 1;
        }
        $cell = alg_add($cell, 1);
    }
    while ((($position >= 0) && ($position < $count))) {
        $cell = $empty[$position];
        $r = intdiv($cell, 9);
        $c = ($cell % 9);
        $box = alg_add(alg_mul(intdiv($r, 3), 3), intdiv($c, 3));
        $digit = $board[$cell];
        if (($digit != 0)) {
            $rows[alg_add(alg_mul($r, 10), $digit)] = 0;
            $cols[alg_add(alg_mul($c, 10), $digit)] = 0;
            $boxes[alg_add(alg_mul($box, 10), $digit)] = 0;
        }
        $digit = alg_add($digit, 1);
        while ((($digit <= 9) && (($rows[alg_add(alg_mul($r, 10), $digit)] != 0) || ($cols[alg_add(alg_mul($c, 10), $digit)] != 0) || ($boxes[alg_add(alg_mul($box, 10), $digit)] != 0)))) {
            $digit = alg_add($digit, 1);
        }
        if (($digit == 10)) {
            $board[$cell] = 0;
            $position = alg_sub($position, 1);
        } else {
            $board[$cell] = $digit;
            $rows[alg_add(alg_mul($r, 10), $digit)] = 1;
            $cols[alg_add(alg_mul($c, 10), $digit)] = 1;
            $boxes[alg_add(alg_mul($box, 10), $digit)] = 1;
            $position = alg_add($position, 1);
        }
    }
    if (($position == $count)) {
        return 1;
    }
    return 0;
}

$board = [5, 3, 4, 6, 7, 8, 9, 1, 2, 6, 7, 2, 1, 9, 5, 3, 4, 8, 1, 9, 8, 3, 4, 2, 5, 6, 7, 8, 5, 9, 7, 6, 1, 4, 2, 3, 4, 2, 6, 8, 5, 3, 7, 9, 1, 7, 1, 3, 9, 2, 4, 8, 5, 6, 9, 6, 1, 5, 3, 7, 2, 8, 4, 2, 8, 7, 4, 1, 9, 6, 3, 5, 3, 4, 5, 2, 8, 6, 1, 7, 0];
$result = sudoku_solve($board);
echo $result, PHP_EOL;
// Expected board: [5, 3, 4, 6, 7, 8, 9, 1, 2, 6, 7, 2, 1, 9, 5, 3, 4, 8, 1, 9, 8, 3, 4, 2, 5, 6, 7, 8, 5, 9, 7, 6, 1, 4, 2, 3, 4, 2, 6, 8, 5, 3, 7, 9, 1, 7, 1, 3, 9, 2, 4, 8, 5, 6, 9, 6, 1, 5, 3, 7, 2, 8, 4, 2, 8, 7, 4, 1, 9, 6, 3, 5, 3, 4, 5, 2, 8, 6, 1, 7, 9]
echo json_encode($board), PHP_EOL;