/// <summary>
/// https://projecteuler.net/problem=51 --skip=12,15,20,26,60
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result PrimeDigitReplacements(Problem arguments)
{
/// <summary>
/// Return true if all digits in a numbers are the same, except those that repeat the
/// same digit and it just increases/decreases from one to the other. For example
/// CompareNumbers(124353,124757)=true, CompareNumbers(124353,124151)=true,
/// CompareNumbers(121313,121757)=false. Also if numbers are the same return false.
/// </summary>
/// <param name="left"></param>
/// <param name="right"></param>
/// <returns></returns>
bool NumbersBelongToSameDigitFamily(int left, int right, int repeating_sequences = 1)
{
var repeating = new Dictionary <char, List <int> >();
var sleft = left.ToString();
var sright = right.ToString();
if (left == right)
{
return(false);
}
if (sleft.Length != sright.Length)
{
return(false);
}
for (var i = 0; i < sleft.Length; i++)
{
var rdigit = sright[i];
var ldigit = sleft[i];
if ((repeating.Count < repeating_sequences) && !repeating.ContainsKey(ldigit) && (sleft.Count(c => c == ldigit) >= 2))
{
if (repeating.ContainsKey(ldigit) && repeating[ldigit].Contains(i))
{
continue;
}
else
{
repeating.Add(ldigit, new List <int>());
foreach (var(digit, j) in sleft.Enumerate())
{
if (digit == ldigit)
{
repeating[ldigit].Add(j);
}
}
bool match = true;
foreach (var k in repeating[ldigit])
{
match = match && sright[k] == rdigit;
if (!match)
{
break;
}
}
if (!match)
{
return(false);
}
}
}
else if (repeating.ContainsKey(ldigit) && repeating[ldigit].Contains(i))
{
continue;
}
else if (rdigit == ldigit)
{
continue;
}
else if (ldigit != rdigit)
{
return(false);
}
}
return(true);
}
// get all six digit primes
var primes = UtilityMath.GeneratePrimes(100000, 1000000).ToArray();
var repeats = new List <int>();
// get primes with repeated digits (not necessarily adjacent digits)
for (int i = 0; i < primes.Length; i++)
{
var counts = UtilityMath.GetRepeatedDigitCounts(primes[i]);
if (counts.Count(c => c > 1) >= 1) // choose only primes with at least one repeatig digit
{
repeats.Add(primes[i]);
}
}
// get first eight number prime-family
HashSet <int> family = null;
foreach (var prime in repeats)
{
family = new HashSet <int>
{
prime
};
foreach (var n in repeats)
{
if (NumbersBelongToSameDigitFamily(prime, n))
{
family.Add(n);
}
if (family.Count == 8)
{
break;
}
}
if (family.Count == 8)
{
break;
}
}
primes = null;
repeats = null;
var answer = family?.First().ToString();
var message = string.Format("The smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family is {0}.", answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}