The book is Discrete Mathematics with Applications by SUSANNA S.

Analysis of Algorithms 2

Finding the middle in Divide and Conquer Algorithms For even-numbered arrays, you must choose what to pick for the middle element. The choice is arbitrary, but in the book, they choose the smaller index, so that's what I'll do as well.

$$ \left\lfloor\frac{i+j}{2}\right\rfloor $$

Types of Problems

Tractability problems are able to be solved in polynomial time are said to be tractable whereas problems that are able to be solved in non-polynomial time are said to be intractable.

Biggest Open Question in Computer Science

Can every NP algorithm (intractable) also a P algorithm (tractable)?

NP-complete

A set of problems that are believed to be intractable and not solvable in polynomial time.