Assignment 4 In this assignment, you will implement your own interpreter pattern to check a given sentence complies with the sentence requirements given below. Your implementation make sure to do necessary corrections on the sentence. Sentence Requirements: • Every sentence starts with a capital letter. • No sentence can start with a number. • Every sentence ends with a period “.”. • No consecutive words can be same. An exemplary sentence and its corrected version: “ 1 this is is a a sample sentence” Corrected sentence: “This is a sample sentence.” Deliverable: Your Java source code with appropriate design and classes/interface(s).

1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…

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Course: Algorithm Project: We will use the defintion of of n-Queens Problem from the chapter Backtracking.  In this project you need to describe Problem and Algorithm and Indicate input and output clearly.  Analyze and prove the time complexity of your algorithm. Implement the algorithm using backtracking(including writing testing case).illustrate key functions with comments indicating: What it does, what each parameter is used for, how it handles errors etc. Indicate the testing scenarios and testing the results in a clear way. Make sure source is commented appropriately and structured well.