Editing String-searching algorithm (section)

=== Naive string search ===
A simple and inefficient way to see where one string occurs inside another is to check at each index, one by one. First, we see if there is a copy of the needle starting at the first character of the haystack; if not, we look to see if there's a copy of the needle starting at the second character of the haystack, and so forth. In the normal case, we only have to look at one or two characters for each wrong position to see that it is a wrong position, so in the average case, this takes [[Big O notation|O]](''n'' + ''m'') steps, where ''n'' is the length of the haystack and ''m'' is the length of the needle; but in the worst case, searching for a string like "aaaab" in a string like "aaaaaaaaab", it takes [[Big O notation|O]](''nm'')