Exponential Base Solver

Question

Alright, with much fretting I decided to sign up on here to ask some questions. I thought I could do this project on my own, but it seems that I cannot.
Okay, this is the assignment (it is confusing, but then again my professor is not the best at english - as he continues to mention):
Write a program that computes the nth root of a number. Given a real number X greater than 1 and less than -1 and given an integer Y, computer the nth root Z such that Z*Z*Z*Z*Z*Z*Z..(Y times)..Z*Z = X, or Z^Y = X (Remember if X is negative Y must be odd.) The user enters values for X and Y and the porgram calculates Z. Compute Z so that when Z is multiplied Y times it will produce an X which is + or - 0.0000001 of the original value of X. You may only use simple arithmetic to do these computations. That is you may only use multiplication, division, addition, and subtraction.
We are using a class called SavitchIn (which I'm sure some of you are familiar with) for input/output. We are not allowed to use any of the classes in Java that allow for higher math functions. Somehow the prof. wants us to basically create a binary search algorithm, yet we haven't even went over them in the book yet. This project was given out at the point where were learning loops - so that's about as complex as the program can get I suppose (although I've noticed some of the more experienced programmers in our class are using arrays - which isn't what the professor described, yet he's marking them off as finished :-/ ). This is a beginner's programming class mind you, but I think the professor expects us to have had experience with programming. :-/ I've made 7 programs up to this point and have had little trouble.
I ask for tips and maybe some example code, but that is all. I'd like to be able to figure it out on my own (I'm a newbie mind you). :-) And remember, only simple math and SavitchIn may be used.
So here's my base code. It isn't the greatest code in the world, or close to being finished - let alone correct, lol. And some of the variable types I put in the code I haven't actually used yet (most of the stuff in this code will probably have to go). I hope the code isn't too confusing:
public class BinarySearchTest2
     public static void main(String[] args)
          System.out.println("This program will calculate the base when the user gives the input of an answer and an exponent for the base");
          System.out.println( );
          double base, exp, ans = 0, testAns = 0, lBase = 1, mid, uBase, count;
          char answer;
          System.out.print("Please enter a number to be used as an exponent.\nExponent: ");
          exp = SavitchIn.readLineDouble( );
          System.out.println( );
          System.out.print("Please enter a number to be used as an answer.\nAnswer: ");
          ans = SavitchIn.readLineDouble( );
          System.out.println( );
          if ((ans > 1) || (ans < -1) && (exp > 0))
               if (exp == 1)
                    System.out.println("The base is: " + ans);
               base = ans/2;
               for (count = 0; count <= exp - 2; count++)
                    if (exp > 1)
                         testAns = base * base;
               if (testAns == ans)
                    System.out.println ("The base is: " + base);
}

Answer 1

I think you may possibly be deficient in Math rather than programming. Do you know what the Nth root of a number is?
What you need to do is make an algo that will multiply itself N times and give you a target number, or I believe you said to devide a target number by another N times and success is measured by an acceptable error value (small difference between the result and the number being used as a divisor)
The problem can be worked very well by using looping stuctures, that is why it has been assigned as such. The people that are using array are probably making lookup tables where say for a value of 2 you would have....
2 4 8 16 32 64 128 256
so when you want say the 5th root of 32, you go to the 5th colum and search down until you find 32. Once you find it, then you know you have the 5th root in column 1 of the row you are searching. If you have to find roots numbers that are not perfect powers raised to N, then you have to find a bound (and I suspect that is what the arrays are about if you have to find roots of any numbers). Using the lookup method described you can get a boundary for you upper and lower values (my number is between say 16 and 81 and I need the 4th root of it. You will be bounded by 2 and 3 so then you make you estimations say 2.5, and lets say 50 is my number. You try 2.5^4 and get 39.0625 too low so you increast at half the distance between 2.5 and your upper bound of 3, and come up with 2.75 and so on.
If this doesn't get you started, then you need to find a different line of work, or read the book, or talk with your prof, or ...