# How can recursion tree split a problem into smaller pieces that do not add up?

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.

We are looking for an element $$x$$ inside a sorted array $$A$$. We compare $$x$$ to the element at the middle $$m$$ of $$A$$. If $$m = x$$, we're done. If $$m > x$$, we recurse on the left half, and if $$m > x$$, we recurse on the right half. The recurrence for the worst-case running time is $$T(n) = T(n/2) + O(1),$$ whose solution is $$T(n) = O(\log n)$$.