using System.Collections.Generic;
using System.Numerics;

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Number of halving and tripling steps to reach 1 in the '3n+1' problem.
    ///     </para>
    ///     <para>
    ///         Wikipedia: https://en.wikipedia.org/wiki/Collatz_conjecture.
    ///     </para>
    ///     <para>
    ///         OEIS: https://oeis.org/A006577.
    ///     </para>
    /// </summary>
    public class ThreeNPlusOneStepsSequence : ISequence
    {
        /// <summary>
        /// Gets sequence of number of halving and tripling steps to reach 1 in the '3n+1' problem.
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                BigInteger startingValue = 1;

                while (true)
                {
                    BigInteger counter = 0;
                    BigInteger currentValue = startingValue;

                    while (currentValue != 1)
                    {
                        if (currentValue.IsEven)
                        {
                            currentValue /= 2;
                        }
                        else
                        {
                            currentValue = 3 * currentValue + 1;
                        }

                        counter++;
                    }

                    yield return counter;
                    startingValue++;
                }
            }
        }
    }
}