grep nth string from a very large file in constant time(file size independent)?

Question

Is there a grep (sed/awk) like tool in linux to find the nth occurrence of a string(regex) from a very large file? Also, I would like to find the number of occurrences of the search string within the file. Remember, the file is really large (> 2 gb).

Answer 1

Grep solution:

grep -on regexp < file.txt

file.txt:

one two one

two

one

two two

two one

Lines with regexp one

grep -on one < test.txt

1:one

1:one

3:one

5:one

How many occurrences:

grep -on one < test.txt | wc -l

4

Line with the Nth occurrence:

grep -m1 one < test.txt | tail -n1

one two one

Update: Now, the solutions don't use cat. Thanks to @tripleee for the hint.