# Capital N vs small n in time complexity

I came accross the following question and it made me confused:

A quadratic algorithm with processing time T(n) = cn2 spends T(N) seconds for processing N data items. How much time will be spent for processing n = 5000 data items, assuming that N = 100 and T(N) = 1ms?

What is the difference between N and n in time complexity?

There is no special meaning for capital `N` vs lowercase letter `n` in time complexity. In this context `n` and `N` are just used as different values for the same variable, it would make no difference if instead of `N` they gave you `x`.
Now, having in mind the original quadratic function `T(n) = c*n^2`
1. If `N = 100` and `T(N) = 1ms` then they are telling you that ```T(100) = 1ms``` => `1ms = c * 100^2`.
2. What you deduce from the previous statement is `1ms = c * 100^2` => `c = 1ms / 100^2`.
3. Now just replace `c` and `n` in the original formula that is ```T(n) = cn2``` (being `n = 5000`):
`T(5000) = (1/100^2) * 5000^2` => `T(n) = 2.500‬ms` => `T(n) = 2,5s`