public void TestMagicSquares()
{
for (int size = 1; size <= 100; size++)
{
if (size == 2)
{
continue;
}
int[,] a = MathStuff.MagicSquare(size);
bool[] used = new bool[size * size];
int d1sum = 0, d2sum = 0, expSum = 0;
for (int y = 0; y < size; y++)
{
d1sum += a[y, y];
d2sum += a[y, size - y - 1];
int rowSum = 0, colSum = 0;
for (int x = 0; x < size; x++)
{
Assert.IsFalse(used[a[y, x] - 1]);
used[a[y, x] - 1] = true;
rowSum += a[y, x];
colSum += a[x, y];
}
if (y == 0)
{
expSum = rowSum;
}
Assert.AreEqual(expSum, rowSum);
Assert.AreEqual(expSum, colSum);
}
Assert.AreEqual(expSum, d1sum);
Assert.AreEqual(expSum, d2sum);
}
}
public void TestChoose()
{
var lib = new MathStuff();
int p = 13, max = 40;
lib.PrecalcChoose(max, p);
for (int i = 1; i <= max; i++)
{
for (int j = 0; j <= i; j++)
{
int expected = lib.Choose(i, j) % p;
int actual = lib.ChooseMod(i, j, p);
Assert.AreEqual(expected, actual);
}
}
}
public void TestChineseRemainderTheorem()
{
MathStuff lib = new MathStuff();
for (int m = 2; m < 100; m++)
{
for (int n = 2; n < 100; n++)
{
int limit = Math.Min(1000, lib.LCM(m, n));
for (int x = 0; x < limit; x++)
{
int a = x % m, b = x % n;
int y = lib.GCD(m, n) == 1 ? lib.Chinese(a, m, b, n) : lib.ChineseCommon(a, m, b, n);
Assert.AreEqual(x, y);
}
}
}
}
public void TestModInverse()
{
var ml = new MathStuff();
int prime = 100000007;
for (int x = 2; x *x <= prime; x++)
{
if (prime % x == 0)
{
throw new Exception();
}
}
for (long i = 1; i <= 1000000; i++)
{
long j = ml.ModInverse((int)i, prime);
Assert.AreEqual(1, (i * j) % prime);
}
}
public void TestJosephus()
{
Random r = new Random(0);
for (int i = 0; i < 100; i++)
{
int N = r.Next(100, 500);
int K = r.Next(1, 2000);
// Naive solution
bool[] gone = new bool[N];
int cur = 0;
for (int j = 0; j < N - 1; j++)
{
int d = K - 1;
while (d > 0)
{
cur = (cur + 1) % N;
if (!gone[cur])
{
d--;
}
}
// Console.WriteLine("Kicked out " + cur);
gone[cur] = true;
while (gone[cur])
{
cur = (cur + 1) % N;
}
}
int expLeft = Array.IndexOf(gone, false);
// Console.WriteLine(expLeft);
int actLeft = MathStuff.Josephus(N, K);
// Console.WriteLine(actLeft - 1);
Assert.AreEqual(expLeft, actLeft - 1);
}
}
