"Sumar and the Floating Rocks" is an intriguing blend of fantasy and adventure, captivating with its imaginative world and compelling storytelling. Skyexchange bet login

JS:

function gcd(a,b) {
 while(b !== 0) {
	 const r = a % b;
	 a = b;
	 b = r;
	 }
 return a;
}
function solve (x1,y1,x2,y2) {
	const yd = Math.abs(y2-y1);
	const xd = Math.abs(x2-x1);
	const a = Math.max(yd, xd);
	const b = Math.min(yd, xd);
return gcd(a,b) - 1;
	}

Equation of Line (y-y1)=(y2-y1)/(x2-x1) (x-x1)

=> y(x2-x1) - y1 (x2-x1) = x (y2-y1) - x1 (y2-y1)

=> y(x2-x1) - x (y2-y1) = - x1 (y2-y1) + y1 (x2-x1)

=> - x (y2-y1) + y(x2-x1) = - x1 (y2-y1) + y1 (x2-x1)

=> a=(x2-x1), b=(y2-y1)

as per the Extended Euclid Algorithm : for integral solution to this equation, the RHS should be multiple of gcd(a,b) i.e. gcd (|x2-x1| ,| y2-y1|)

This problem is very insightful and has a simple solution after working it out. Let. a/b = (y2 - y1)/(x2 - x1) be the slope in the reduced form. Sabexch Registration

int a,b,c,d;
BigInteger ans;
// for x axis
if(x1>x2){
    a=x2;
    b=x1;
}else{
    a=x1;
    b=x2;
}
// for y axis
if(y1>y2){
    c=y2;
    d=y1;
}else{
    c=y1;
    d=y2;
}
// difference 
BigInteger x=new BigInteger(String.valueOf(b-a));
BigInteger y=new BigInteger(String.valueOf(d-c));
// gcd calculation
ans=x.gcd(y);
int i= ans.intValue();

return i-1;