I had a quiz question on my school
"Boyer Moore algorithm has the worst-case time complexity O(MN) where M is the length of the string and N is the length of the pattern."
it is True False question and i answered False for the statement above because i always read that N is the lenght of text and M is the lenght of pattern but my instructor says it doesn't matter how you define M and N so because of it claims statement is True is it correct ? if not how can i prove him that statement is false scientifically ?
Your instructor is right. Changing the names doesn't matter at all, the time complexity is M * N. It's everything simplified to the expression that: 'the order of factors doesn't change the product'.
If M and N are inverted, complexity is still N * M or M * N.
It would be completely different if the time complexity were, for example O (M^2 log N), then yeah, if you invert what M means and N means, the complexity is completely different.