Requir Algorithms in pseudo code ** MUST** be placed in ode blocks/fences, and use `cpp` as the syntax ighlighter. Algorithms should follow the pseudo code standard escribed in *Pseudocode Handout*. Do NOT change the template except the answer ortion. Formulas and equations should be in math mode sing Latex math symbols. - Markdown math tutorial: ttp://tug.ctan.org/info/undergradmath/undergradmat • pdf Two ways to enter math mode: Insert a pair of dollar signs: \$your quations go here\$. This is the inline math mode. Notice that there is no space between the \$ and he letter*. Insert a pair of double-dollar signs: \$ \ $ our equations go here \$\$, which produces a tandalone equation/formula set.

Format Requirement Algorithms in pseudo code MUST be placed in code blocks/fences, and use either the cpp or java syntax highlighter. Algorithms should follow the pseudo code standard described in handout 1.  Your pseudo code should be placed in a code block, for example Algorithm alg_name(a, b) { // A description of the algorithm // input: a - a positive decimal integer; b - an integer // ouput: the sum of a and b c = a + b // or, c <- a + b return c } Do NOT change the template except the answer portion.  Formulas and equations should be in math mode using Latex math symbols.  Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmath.pdf Ways enter into the math mode in Notion: https://www.notion.so/help/math-equations

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…

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.