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Given (n) , what is the Count of (x,y) pairs that satisfy the equation x^2+y^2 = n^2. Is there any way I can re-write this code just without using nested loop?
int counter=0;
int x=0;
for (int i =(int) n-1; i>=0 ; i--){
if(i == x)
break;
for (int j = 1; j< (int)n ; j++){
if (Math.pow(i,2)+Math.pow(j,2) == Math.pow(n,2)){
counter++;
x = j;
}
}
}
System.out.print(counter);
Your approach is to try every possible $x$ and $y$ and see if $x^2+y^2=n^2$. However, $n$ is fixed and, for any $x$, either $n^2-x^2$ is a perfect square or it isn't. You can calculate what $y$ is, instead of looping and trying every possible value.
Actual code is off-topic but it's confusing that you're trying to solve a problem about $x$ and $y$, but you've represented those quantities in variables called i and j. And even worse that you have a variable called x that represents something else entirely. (In fact, I'm not sure it's even correct. You seem to be using x to avoid reporting, e.g., $x=3$, $y=4$ and $x=4$, $y=3$ as separate solutions for $n=5$. But they are separate solutions and the question, at least as you've summarized it, doesn't say that they should be counted as the same.)
