public bool isRotationOf(FiveGonRing ring)
{
// I'm sure there's a much better way of doing this...
// (and no longer technically needed.)
int[] t1 = new int[] { 0, 1, 2, 3, 4 };
// 0,1,2,3,4 -> 1,2,3,4,0
if (this.checkSeqEq(t1, new int[] { 1, 2, 3, 4, 0 }, ring))
{
return(true);
}
// 0,1,2,3,4 -> 2,3,4,0,1
if (this.checkSeqEq(t1, new int[] { 2, 3, 4, 0, 1 }, ring))
{
return(true);
}
// 0,1,2,3,4 -> 3,4,0,1,2
if (this.checkSeqEq(t1, new int[] { 3, 4, 0, 1, 2 }, ring))
{
return(true);
}
// 0,1,2,3,4 -> 4,0,1,2,3
if (this.checkSeqEq(t1, new int[] { 4, 0, 1, 2, 3 }, ring))
{
return(true);
}
// otherwise:
return(false);
}
private bool checkSeqEq(int[] t1, int[] t2, FiveGonRing ring)
{
Debug.Assert(t1.Length == t2.Length);
for (int i = 0; i < t1.Length; i++)
{
if (!this.getTuple(t1[i]).SequenceEqual(ring.getTuple(t2[i])))
{
return(false);
}
}
return(true);
}
public long soln1()
{
var sw = Stopwatch.StartNew();
List <int> p1 = new List <int>();
int nPerms = 0;
int nMagic = 0;
List <FiveGonRing> magicRings = new List <FiveGonRing>();
//Console.WriteLine("There are {0:n0} permutations to consider.", getAllPerms(p1).Count());
foreach (var p in getAllPerms(p1))
{
//Console.WriteLine(string.Join<int>(", ", p));
var ring = new FiveGonRing(p.ToArray());
Debug.Assert(ring.isValidRing(), string.Format("{0} is not a valid ring.", ring.ToString()));
int s = ring.getMagicRingSum();
if (s > 0)
{
if (!magicRings.Any(r => ring.isRotationOf(r)))
{
//Console.WriteLine("{0} is a magic ring, with sum {1}.", ring.ToString(), s);
nMagic++;
magicRings.Add(ring);
}
}
nPerms++;
}
// get rid of any rings where the length of the digit string isn't 16.
magicRings.RemoveAll(x => x.getDigitString().Length != 16);
foreach (var ring in magicRings.OrderBy(x => x.getMagicRingSum()))
{
Console.WriteLine("{0} is a magic ring, with sum {1}.", ring.ToString(), ring.getMagicRingSum());
}
Console.WriteLine("{0} permutations generated.", nPerms);
Console.WriteLine("{0} magic rings generated.", nMagic);
Console.WriteLine("The max digit string is {0}.", magicRings.Max(x => x.getDigitString()));
sw.Stop();
Console.WriteLine("elapsed: {0} ms", sw.Elapsed.TotalMilliseconds);
return(0);
}