Pattern matching algorithms

Pattern matching is one of the most common tasks we perform on a day-to-day basis. PHP has built-in support for regular expression, and mostly, we rely on the regular expression and built-in string functions to solve our regular needs for such problems. PHP has a readymade function named strops, which returns the position of the first occurrence of the string in a text. Since it only returns the position of the first occurrence, we can try to write a function that will return all possible positions. We will explore the brute-force approach first, where we will check each of the character for the actual string with each one of the pattern string. Here is the function that will do the job for us:

function strFindAll(string $pattern, string $txt): array { 
    $M = strlen($pattern); 
    $N = strlen($txt); 
    $positions = []; 

    for ($i = 0; $i <= ...