public static void Solve()
{
var T = Scanner.Scan <int>();
const long inf = long.MaxValue;
while (T-- > 0)
{
var(X, Y, P, Q) = Scanner.Scan <long, long, long, long>();
var a = X * 2 + Y * 2;
var b = P + Q;
var answer = inf;
for (var t1 = X; t1 < X + Y; t1++)
{
for (var t2 = P; t2 < P + Q; t2++)
{
var(t, lcm) = Mathematics.ChineseRemainderTheorem(new[] { t1, t2 }, new[] { a, b });
if (lcm == 0)
{
continue;
}
answer = Math.Min(answer, t);
}
}
Console.WriteLine(answer == inf ? "infinity" : $"{answer}");
}
}
public void ChineseRemainderTheoremInvalidArgumentsTest()
{
Assert.Throws <ArgumentException>(() =>
Mathematics.ChineseRemainderTheorem(new long[] { 1, 2 }, new long[] { 3 }));
Assert.Throws <ArgumentException>(() =>
Mathematics.ChineseRemainderTheorem(new long[] { 1, 2 }, new long[] { -1, -2 }));
}
public void ChineseRemainderTheorem2ItemsTest()
{
for (var a = 1; a <= 20; a++)
{
for (var b = 1; b <= 20; b++)
{
for (var c = -10; c <= 10; c++)
{
for (var d = -10; d <= 10; d++)
{
var(rem, mod) = Mathematics.ChineseRemainderTheorem(new long[] { c, d }, new long[] { a, b });
var lcm = a * b / GreatestCommonDivisor(a, b);
if (mod == 0)
{
for (var x = 0; x < lcm; x++)
{
Assert.That(x % a != c || x % b != d, Is.True);
}
continue;
}
Assert.That(mod, Is.EqualTo(lcm));
Assert.That(rem % a, Is.EqualTo(Mathematics.SafeModulo(c, a)));
Assert.That(rem % b, Is.EqualTo(Mathematics.SafeModulo(d, b)));
}
}
}
}
}
public override long Part2Long()
{
long i = 0;
Dictionary <long, long> bus = new Dictionary <long, long>();
foreach (var id in parser.Lines[1].Split(','))
{
if (id.Equals("x") == false)
{
try
{
bus.Add(i, long.Parse(id));
}
catch
{
// nope
}
}
i++;
}
long result = Mathematics.ChineseRemainderTheorem(bus.Values.ToArray(), bus.Keys.ToArray());
return(result);
}
public void ChineseRemainderTheorem3ItemsTest()
{
for (var a = 1; a <= 5; a++)
{
for (var b = 1; b <= 5; b++)
{
for (var c = 1; c <= 5; c++)
{
for (var d = -5; d <= 5; d++)
{
for (var e = -5; e <= 5; e++)
{
for (var f = -5; f <= 5; f++)
{
var(rem, mod) = Mathematics.ChineseRemainderTheorem(new long[] { d, e, f }, new long[] { a, b, c });
var lcm = a * b / GreatestCommonDivisor(a, b);
lcm *= c / GreatestCommonDivisor(lcm, c);
if (mod == 0)
{
for (var x = 0; x < lcm; x++)
{
Assert.That(x % a != d || x % b != e || x % c != f, Is.True);
}
continue;
}
Assert.That(mod, Is.EqualTo(lcm));
Assert.That(rem % a, Is.EqualTo(Mathematics.SafeModulo(d, a)));
Assert.That(rem % b, Is.EqualTo(Mathematics.SafeModulo(e, b)));
Assert.That(rem % c, Is.EqualTo(Mathematics.SafeModulo(f, c)));
}
}
}
}
}
}
}
public void ChineseRemainderTheoremHandmadeTest()
{
var(rem, mod) = Mathematics.ChineseRemainderTheorem(new long[] { 1, 2, 1 }, new long[] { 2, 3, 2 });
Assert.That(rem, Is.EqualTo(5));
Assert.That(mod, Is.EqualTo(6));
}