/// <summary>
/// https://projecteuler.net/problem=56
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result PowerfulDigitSum(Problem arguments)
{
var limit = arguments.IntNumber;
long max = 100; // include all 100 * 1^b to begin with
for (int a = 2; a < limit; a++)
{
for (int b = 1; b < limit; b++)
{
var ab = BigInteger.Pow(a, b);
var sum = UtilityMath.DigitsSum(ab.ToString());
if (sum > max)
{
max = sum;
}
}
}
var answer = max.ToString();
var message = string.Format("The maximum digital sum of natural numbers of the form, a^b, where a, b < {0}, is {1}.", limit, 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);
}
public static Result PowerDigitSum(Problem arguments)
{
var e = Convert.ToInt16(arguments.LongNumber);
var b = arguments.IntNumber;
var p = UtilityMath.PowOverflow(b, e);
var s = UtilityMath.DigitsSum(p);
var m = string.Format("Sum of digits of {0}^{1} is {2}.", b, e, s);
var r = new Result(arguments.Id, m);
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=80
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result SquareRootDigitalExpansion(Problem arguments)
{
var count = (int)arguments.Numbers[0];
var digits = (int)arguments.Numbers[1];
long sum = 0;
#region Sqrt Test
for (double expected_number = 0.001; expected_number < 100; expected_number += 0.5d)
{
double actual_number = UtilityMath.Sqrt_By_Substraction(expected_number);
if ((expected_number - (actual_number * actual_number)) > .0005)
{
throw new ArithmeticException(string.Format("Sqrt by substraction differed with margin of error for {0}", expected_number));
}
}
#endregion
for (var number = 1; number <= count; number++)
{
if (!UtilityMath.IsPerferctSquare((double)number))
{
var sqrt = UtilityMath.SqrtDigitExpansion(number, digits);
sum += UtilityMath.DigitsSum(sqrt.ToString());
}
}
var answer = sum.ToString();
var message = string.Format("The total of the digital sums of the first {0} decimal digits for all the irrational square roots of the first {1} natural numbers is {2}.", digits, count, 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);
}