Knuth Morris Pratt Pattern Matching in PHP

<?php
declare(strict_types=1);
// Knuth Morris Pratt Pattern Matching in PHP
//
// PURPOSE
// KMP avoids rechecking text tokens by remembering which matched pattern suffix is also a
// prefix. The prefix table tells where to resume after a mismatch.
//
// METHOD
// Build the longest proper prefix/suffix table for the pattern. During matching, fall back
// through that table without moving the text position backward. A full matched prefix gives
// the first occurrence.
//
// COMPLEXITY
// O(n+m) time and O(m) auxiliary space.
//
// CONTRACT
// Inputs are integer token sequences. Empty pattern matches at 0. Returns first matching
// index or -1. KMP does not define Unicode tokenization.
// 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: 2.
// 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 kmp_match(array $text, array $pattern): int {
    alg_require(array_is_list($text));
    alg_require(array_is_list($pattern));
    $n = count($text);
    $m = count($pattern);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((($m >= 0) && ($m <= 1000000)));
    alg_require((count($pattern) == $m));
    alg_require((count($text) == $n));
    if (($m == 0)) {
        return 0;
    }
    $prefix = array_fill(0, alg_size(alg_add($m, 1)), 0);
    $i = 1;
    $j = 0;
    while (($i < $m)) {
        while ((($j > 0) && ($pattern[$i] != $pattern[$j]))) {
            $j = $prefix[alg_sub($j, 1)];
        }
        if (($pattern[$i] == $pattern[$j])) {
            $j = alg_add($j, 1);
        }
        $prefix[$i] = $j;
        $i = alg_add($i, 1);
    }
    $i = 0;
    $j = 0;
    while (($i < $n)) {
        while ((($j > 0) && ($text[$i] != $pattern[$j]))) {
            $j = $prefix[alg_sub($j, 1)];
        }
        if (($text[$i] == $pattern[$j])) {
            $j = alg_add($j, 1);
        }
        if (($j == $m)) {
            return alg_add(alg_sub($i, $m), 1);
        }
        $i = alg_add($i, 1);
    }
    return alg_sub(0, 1);
}

$text = [1, 2, 1, 2, 3];
$pattern = [1, 2, 3];
$result = kmp_match($text, $pattern);
echo $result, PHP_EOL;