Designs and Analysis of Algorithms Problems

The problems are kind of mathematical way of computer science algorithm such as Turing Machine, Heapify, recursive...etc There are totally 5 problems. In order to be accepted, you only need to know how to finish at least of 3 problems. I will give $30 for each problem, in other words, $150 for maxium. However, please state that which problems you can handle if you can't handle them all. They are easy and can be done in few hours if one knows how to do them. You can see all the problems in detail in the attached zip file. And here's 2 of the 5 problems: **P3)** Given theorem 3: **"**If both E and Ē are r.e then E is recursive" (r.e. = recursively enumerable) ** a) ** Prove that if E is recursive, so is Ē. ** b) ** We can classify a language E as any of three: Recursive **C** r.e. but not recursive **C**not r.e. **(C means subset of).**Given E and Ē identify all possible ways of classifying them regardless of being “legal?? or not. **c)** Identify the only possible classifications of E and Ē that do not violate theorem 3 nor the theorem that will be proved in **a)**. **P4)** Show what is the effect of calling HEAPIFY (A,i) **a)** for i > heap-size[A]/2. Give an example. **b)** when the element A[i] is larger than its children. Explain in detail using the algorithm for HEAPIFY(A,i). ## Deliverables ## Platform no platform.