Description
1. Use Newton-Raphson iteration to calculate the square root of a float given on the comand line. Try using N as a starting guess. Print out the intermediate values on the way to convergence. You should also check for non-convergence (like if the intermediate values are beginning to diverge, so you don't loop forever or overflow the stack). Implement the function 2 ways: first using iteration (i.e. a loop), then re-implement the function using recursion. Print out both results, and compare to the value determined by the built-in sqrt() function in the <cmath> library. > NewtonRaphsonSqrt 50 iter: 2, est: 50 iter: 4, est: 25.5 iter: 6, est: 13.7304 iter: 8, est: 8.68597 iter: 10, est: 7.22119 iter: 12, est: 7.07263 iter: 14, est: 7.07107 [iterative] sqrt(50)=7.07107 recursive estimate: 50 recursive estimate: 25.5 recursive estimate: 13.7304 recursive estimate: 8.68597 recursive estimate: 7.22119 recursive estimate: 7.07263 recursive estimate: 7.07107 [recursive] sqrt(50)=7.07107 [built-in] sqrt(50)=7.07107 [verifying] 7.07107^2 = 50 (Just for fun: try modifying the code to calculate cube-root of x, or ln(x).) 2. Write a program that generates all subsets of a list of items given on the command line. Make two versions of the program: an iterative version (subsetsI), and a recursive version (subsetsR). Each version should have a function that, given a vector of strings, returns a vector of vectors containing all subsets, which your program should then print out. (The order of lines, and of items within lines, doesn't matter.) (Hint: in this program, you will need to make copies of vectors. This is easily done by assignment: "vector<string> v2=v1;" makes a copy of v1, so modifying v2 doesn't affect v1.) > subsetsR apples bananas grapes pears apples bananas apples bananas grapes apples grapes bananas grapes apples bananas grapes pears apples pears bananas pears apples bananas pears grapes pears apples grapes pears bananas grapes pears apples bananas grapes pears > subsetsI A B C A B A B C A C B C A B C
