write code and execute the code turning in test cases and source code) for the following two algorithms to raise an integer to an integer power assume in both cases that n, the exponent, is a power of 2:         Again, in case you don’t have any programming language at hand you can use pseudocode to solve the problem.   Algorithm 1   X**N = X* X**(N-1) X**0 = 1   Algorithm 2

Using recursion, write a function sum that takes a single argument n and computes the sum of all integers between 0 and n inclusive. Do not write this function using a while or for loop. Assume n is non-negative. def sum(n): """Using recursion, computes the sum of all integers between 1 and n, inclusive. Assume n is positive. >>> sum(1) 1 >>> sum(5) # 1 + 2 + 3+ 4+ 5 15 "*** YOUR CODE HERE ***"

Write pseudocode to solve the following problem. Must use iterative dynamic programming (tabulation) and run in O(n) time. Input: positive integer n Output: two non-negative integer x and y where n = x185 + y120 Example: if n=1230 then x=6 and y=1 (1314 = 6(185) + 1(120))

More sophisticated computer-assisted instruction systems monitor the student’s perfor- mance over a period of time. The decision to begin a new topic is often based on the student’s success with previous topics. Write a program that will help an elementary-school student learn multiplication. Use Math.random to produce two positive one-digit integers. To count the number of correct and incorrect responses typed by the student. After the student answers 10 questions, your program should calculate the percentage of correct responses. If the percentage is lower than 75 percent, display Please ask your instructor for extra help, and reset the quiz so another student can try it.