KMP substring search, longest prefix suffix in PHP

KMP.php

<?php

function buildLPS( $string ) {
	$lps = [ 0 ];
	$i   = 0;
	$j   = $i + 1;

	while ( strlen( $string ) > count( $lps ) ) {

		if ( $string[ $i ] === $string[ $j ] ) {
			$lps[ $j ] = $i + 1;
			$i ++;
			$j ++;
		} elseif ( $i === 0 ) {
			$lps[ $j ] = 0;
			$j ++;
		} else {
			$i = $lps[ $i - 1 ];
		}
	}

	return $lps;
}

function kmpIsTherePattern( $string, $pattern ) {
	$lps = buildLPS( $pattern );

	$i = 0;
	$j = 0;

	while ( $j < strlen( $string ) ) {

		if ( $string[ $j ] === $pattern[ $i ] ) {

			if ( $i === strlen( $pattern ) - 1 ) {
				return [ 'start' => $j - strlen( $pattern ) + 1, 'end' => $j ];
			}

			$i ++;
			$j ++;
		} elseif ( $i === 0 ) {
			$j ++;
		} else {
			$i = $lps[ $i - 1 ];
		}
	}

	return false;
}

var_dump( kmpIsTherePattern( 'abcxabcdabxabcdabcdabcy', 'abcdabcy' ) );