As I understand, MySQL stores clustered index in its custom tree-like data structure (similar to the B+-tree).
The node of this tree is called "page" and may contain a significant number of keys. Let's say 100. Suppose we are looking for key K1. Using the tree we can find page P1, which contains key K1 or a pointer to the page to look further.
But how then MYSQL finds the key or appropriate pointer to look within the same page? Do keys inside the page stored in array and MYSQL uses binary search or are they stored in some local tree or It's just a linear scan of all keys inside the page?