If I have a recurrence equation: $$T(n) = 3T\big(\frac{n}{4}\big) + cn^2$$
It says it splits a problem of size n into 3 subproblems of size n/4. Then it keeps splitting it until the problem size at the leaves is 1 or less. The first part that does not make sense to me is how can you split a problem of size n into 3 problems of size n/4. To me it seems that there are now 3 problems of size n/4, but where is the remaining 1/4 of n? Who is solving that?
Also, the number of leaves is $$n^{\big(\frac{loga}{logb}\big)}$$ Assuming n=1000, it can be calculated that there are 235 leaves. So 235 problems of size 1 are solved, how are the rest of 765 solved?
I have a feeling that I have misunderstood some principle, but I do not know what exactly.