Q$10.$ Explain the following.

$($a$)(4\%)$ What is the time performance for searching an element in a search tree? What is the desirable property of a search tree that can have better search performance? Give an example to illustrate the property.

$($b$)(3\%)$ Given the same tree height of B$-$tree and B$+$tree, which one can be used to index more data records? Why?

$($c$)(2\%)$ Explain the differences between Heap files and Sequential files.