Compare two equations to see if they are ever equal. #congruence #Hackerrank

kangaroos.js

/*
Solution for HackerRank > Algorithms > Implementation > Kangaroo
https://www.hackerrank.com/challenges/kangaroo

In this example, 0 <= x1 <= x2
*/

function kangaroos() {
	var x1 = 43;
	var v1 = 5;
	var x2 = 49;
	var v2 = 3;
	var done = false;

    // Test for simple solutions
    switch (true){
	case (x1 == x2 && v1 == v2) :
			done = true;
			console.log("YES");
			break;
		
		case ((x1 + v1) < v2) || ((x2 + v2) < v1) :
			done = true;
			console.log("NO");
			break;
		
		case ((x1 < x2 && v1 <= v2) || (x2 < x1 && v2 <= v1)) :
			done = true;
			console.log("NO");
			break;
    }

    // If all switch cases are false, test for congruence
    if (!done){
        var sm, lg;
        if (Math.abs(x1 - x2) <= Math.abs(v2 -v1)) {
            lg = v2 - v1;
            sm = x1 - x2;
        } else {
            lg = x1 - x2;
            sm = v2 - v1;
        }
        
        // Is is possible for roo1 to be congruent to roo2?
        (lg % sm == 0) ? console.log("YES") : console.log("NO");
    }
}