public static void Main(string[] args)
{
bool isFirstRun = true;
while (true)
{
if (isFirstRun)
{
System.Console.WriteLine("UWW CS215 Fano Plane Automorphism Finder" + Environment.NewLine + "Authored by Connor Grady, Grant Jones, and Collin Stolpa");
}
else
{
System.Console.WriteLine();
}
string input = CollectInput();
string[] items = new string[7] {
"1", "2", "3", "4", "5", "6", "7"
};
Permutations permutations = new Permutations();
List <List <string> > results = permutations.GeneratePermutations(items.ToList());
//WritePermutations(results);
switch (input)
{
case "OutputPerms":
WritePermutations(results);
break;
case "OutputAutos":
// Now that we have the Permutations, let's check for the automorphisms
List <List <string> > automorphisms = results.Where(IsAutomorphism).ToList();
// Convert to Cycle Notation
List <string> automorphicCycles = automorphisms.Select(perm => permutations.ToCycleNotation(results.FirstOrDefault(), perm)).ToList();
// Write cycles to the Console
WriteCycles(automorphicCycles, automorphisms.Select(auto => string.Join("", auto)).ToList());
break;
default:
System.Console.WriteLine("ERROR: No valid selection detected. Please try again...");
break;
}
isFirstRun = false;
}
}
/// <summary>
/// Specifies whether the provided permutation is an automorphism of the Fano Plane Permutations.
/// </summary>
/// <param name="permutation">The permutation derived to check.</param>
/// <returns>Boolean specifying whether the permutation is an automorphism.</returns>
private static bool IsAutomorphism(List <string> permutation)
{
Permutations permutations = new Permutations();
// Get the permutation as a set of 7 sets of 3 characters
List <List <string> > permGroups = permutations.PermTo7SetsOf3(permutation);
// Get the Fano Plane collection
List <List <string> > fanoGroups = FanoPlane.GenerateCollection();
// This will contain the result of all the "true" method comparisons
// If there are 7 "true" bools at the end, then it is an automorphism
List <bool> groupBools = new List <bool>(7);
// For each 3-member group of the permutation
foreach (List <string> permGroup in permGroups)
{
// True if there's at least one 3-member group in the fano plane collection that matches
// this 3-member group of the permutation
bool atLeastOneGroupMatches = false;
// For each 3-member group in the fano collection, for the first group that matches all 3 members (regardless of order),
// set atLeastOneGroupMatches = true, remove that 3-member group from the fano collection, and break from the loop
foreach (List <string> fanoGroup in from fanoGroup in fanoGroups let charsMatch = permGroup.All(fanoGroup.Contains) where charsMatch select fanoGroup)
{
atLeastOneGroupMatches = true;
fanoGroups.Remove(fanoGroup);
break;
}
// Add whatever the value of atLeastOneGroupMatches to the bool collection
groupBools.Add(atLeastOneGroupMatches);
}
// Return a boolean whose value is true if the count of all "true" booleans in the bool collection is 7
return(groupBools.Count(x => x) == 7);
}
