Solving a difficult equation with two variables in Java

Question

My assignment says to do the following:
Search2: Search for a solution to x*x + y*y - 12x -10y + 36 = 0. Search from 0 to 10 in both x and y, searching every y value before moving to the next x. Print the first three solutions found. (Note - a labelled break is handy here!)

I can't figure out the logic for this. I think I have to use more than 2 loops but not sure.
This is what I have so far (It just repeats (6,0)):

for (int j = 0; j <= 10; j++) {
    for (int i = 0; i <= 10; i++) {
        while (((i * i) + (j * j) - (12 * i) - (10 * j) + 36) == 0) {
            System.out.println("(" + i + ", " + j + ")");  
        }  
    }  
}  

UPDATE
Here is the solution:

    int t = 0;

    for (int i = 0; i <= 10; i++) {
        if (t == 3) {
            break;
        }
        for (int j = 0; j <= 10; j++) {
            if (((i * i) + (j * j) - (12 * i) - (10 * j) + 36) == 0) {
                System.out.println("(" + i + ", " + j + ")");
                t++;
            }
        }
    }

Answer 1

Not a bad attempt. Because you're so close, I'll show you a working solution. Basically, you need to do three things:

1. Change while to if
2. Use a variable to count the number of times you find the solution, so you can stop at three
3. Add a label so you can break out of the outer loop from within the inner loop

I also recommend you use variable names the same as the problem - ie x and y - for clarity.

int count = 0;
outerLoop:
for (int y = 0; y <= 10; y++) {
    for (int x = 0; x <= 10; x++) {
        if (x * x + y * y - 12 * x - 10 * y + 36 == 0) {
            System.out.println("(" + x + ", " + y + ")");  
            if (++count == 3)
                break outerLoop;
        }
    }
}

When executed, this code produces:

(6, 0)
(3, 1)
(9, 1)

Sorry for spoon-feeding you, but part of the lesson here is good coding style and practice.

Answer 2

You're using an extra while loop that runs indefinetly.

while (((i * i) + (j * j) - (12 * i) - (10 * j) + 36) == 0) {
    System.out.println("(" + i + ", " + j + ")");  
}

The first time this evaluates to true - i.e. when it reaches (6,0) - it will keep running because i and j are not modified inside.

You need to replace it with an if.

Answer 3

Take a good look at the inner while loop you have. Once the solution to the equation is found, i and j never change, and the formula always evaluates to 0, resulting in an infinite loop.

It might also be wise to rename i and j to x and y, for clarity. You're mostly on the right track though. Don't forget you only have to print the first three solutions.

Answer 4

I wont help you much since this is a pretty simple concept, but think about what you need to loop through, it might make it easier to instead use x and y instad of i or j. Also your printing only (6,0) because thats exactly what you told it to do with the while loop.

One hint, your while loop should have a statement that stops its function, lets say if x < 4, if it ever is greater or = to than it will continue outside the loop.

Answer 5

public class EquationSolver {

    public static void main(String[] args) {

        int found = 0;
        searchSolutions:
        for (int y = 0; y <= 10; y++) {
            for (int x = 0; x <= 10; x++) {
                if (((x * x) + (y * y) - (12 * x) - (10 * y) + 36) == 0) {
                    System.out.println("(" + x + ", " + y + ")");
                    found ++;
                    if (found == 3) {
                        break searchSolutions;
                    }
                }
            }

        }

    }

}

Answer 6

Long time I last wrote some homework of that sort...just for the fun of it :)

public class Main {

    public static void main(String[] args) {
        int[] range = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
        boolean isSolutionFound = Boolean.FALSE;
        int solCounter = 0;

        searchSolutions:
        for (Integer y : range) {
            for (Integer x : range) {
                isSolutionFound = checkForSolution(x, y);
                if (isSolutionFound) {
                    printSolution(x, y);
                    solCounter++;
                }

                if (solCounter == 3) 
                    break searchSolutions;
            }
        }
    }

    private static void printSolution(Integer x, Integer y) {
        System.out.println(x + "," + y); // use some fancy formatting instead
    }

    private static boolean checkForSolution(int x, int y) {
        if (x * x + y * y - 12 * x - 10 * y + 36 == 0)
            return true;
        else
            return false;
    }

}

Answer 7

for (int j = 0; j <= 10; j++)
{
   for (int i = 0; i <= 10; i++)
   {
      if (((i * i) + (j * j) - (12 * i) - (10 * j) + 36) == 0)
      {
         System.out.println("(" + i + ", " + j + ")");
         return;
      }  
   }  
} 

It is import to remember the return; part as you would otherwise still search for solutions although you already found one. If you wan't more solutions, then you should should omit the ´return´ statement.