Typing Test

Question

What is the best algorithm to score a typing test?
A user types from a sample. You compare the two samples and determine how accurate the sample is. A missed word, an extra word or a misspelled word are wrong. Having more than 2 spaces between words is also incorrect. Having more than 10 words incorrect in a row is an invalid sample
I have come up with a very complicated algorithm and wonder if there is some genius who came up with an elegent solution to this. Mine, I do not believe, is not elegant.
My Algorithm --
1. Check for extra spaces.
2. Tokenize the sample.
3. Compare the user to the sample word for word until and incorrect word is found.
4. Once an incorrect word is found you must determine if it is incorrectly spelled, extra or there is a missing word. This is done by finding whether the least number of errors exists if it is misspelled, missing or extra out of the next 5 words with the default being misspelled.
5. Follow these procedures to the end.
More abstractly you are comparing two lists and determining the commonality of them
a b c c d e
a b c d e
there is one error here.

Answer 1

I have had a great deal of luck with the Levenshtein. There were still holes in my previous hack algorithm. Levenshtein finds an optimal edit path, but does not find the best path, which is what I really want. I have used the Levenshtein algorithm to make decisions on which direction to take the path and have improved the edit path. Whether or not it is necessarily true (in the proveable sense) I can't tell you.
Heres the basic algorithm now.
compare string a to to string b. b is larger in my case always, so an equal number of b and a tokens are compared.
int distance = 0;
if a[i] != b[i]
error++;
a[i] = b;
distance = Levenshtein(a,b); // computes the distance if you choose this path. I only look ahead 10 (or to then end of the string I am comparing to. )
do the same for an insertion and a removal, finding the best distance between the three possibilities.
You can make better editing decisions this way and come up with a low distance. I'm guessing that if you looked ahead to the end of the string it would be even more accurate, but that would get ugly based depending on the size of the string. Right now there is one iteration of the string and then 3 iterations of 10 for every error.
with a maximum of n + 30n, which is a linear complexity. If you use a length of the entire string its getting closer to N^2.