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using System;

namespace IStation.Numerics
{
    /// <summary>
    /// Class to represent a permutation for a subset of the natural numbers.
    /// </summary>
    [Serializable]
    public class Permutation
    {
        #region fields

        /// <summary>
        /// Entry _indices[i] represents the location to which i is permuted to.
        /// </summary>
        private readonly int[] _indices;

        #endregion fields

        #region Constructor

        /// <summary>
        /// Initializes a new instance of the Permutation class.
        /// </summary>
        /// <param name="indices">An array which represents where each integer is permuted too: indices[i] represents that integer i
        /// is permuted to location indices[i].</param>
        public Permutation(int[] indices)
        {
            if (!CheckForProperPermutation(indices))
            {
                throw new ArgumentException("The integer array does not represent a valid permutation.", nameof(indices));
            }

            _indices = (int[])indices.Clone();
        }

        #endregion

        /// <summary>
        /// Gets the number of elements this permutation is over.
        /// </summary>
        public int Dimension => _indices.Length;

        /// <summary>
        /// Computes where <paramref name="idx"/> permutes too.
        /// </summary>
        /// <param name="idx">The index to permute from.</param>
        /// <returns>The index which is permuted to.</returns>
        public int this[int idx] => _indices[idx];

        /// <summary>
        /// Computes the inverse of the permutation.
        /// </summary>
        /// <returns>The inverse of the permutation.</returns>
        public Permutation Inverse()
        {
            var invIdx = new int[Dimension];
            for (int i = 0; i < invIdx.Length; i++)
            {
                invIdx[_indices[i]] = i;
            }

            return new Permutation(invIdx);
        }

        /// <summary>
        /// Construct an array from a sequence of inversions.
        /// </summary>
        /// <example>
        /// From wikipedia: the permutation 12043 has the inversions (0,2), (1,2) and (3,4). This would be
        /// encoded using the array [22244].
        /// </example>
        /// <param name="inv">The set of inversions to construct the permutation from.</param>
        /// <returns>A permutation generated from a sequence of inversions.</returns>
        public static Permutation FromInversions(int[] inv)
        {
            var idx = new int[inv.Length];
            for (int i = 0; i < inv.Length; i++)
            {
                idx[i] = i;
            }

            for (int i = inv.Length - 1; i >= 0; i--)
            {
                if (idx[i] != inv[i])
                {
                    int t = idx[i];
                    idx[i] = idx[inv[i]];
                    idx[inv[i]] = t;
                }
            }

            return new Permutation(idx);
        }

        /// <summary>
        /// Construct a sequence of inversions from the permutation.
        /// </summary>
        /// <example>
        /// From wikipedia: the permutation 12043 has the inversions (0,2), (1,2) and (3,4). This would be
        /// encoded using the array [22244].
        /// </example>
        /// <returns>A sequence of inversions.</returns>
        public int[] ToInversions()
        {
            var idx = (int[])_indices.Clone();

            for (int i = 0; i < idx.Length; i++)
            {
                if (idx[i] != i)
                {
                    int q = Array.FindIndex(idx, i + 1, x => x == i);
                    var t = idx[i];
                    idx[i] = q;
                    idx[q] = t;
                }
            }

            return idx;
        }

        /// <summary>
        /// Checks whether the <paramref name="indices"/> array represents a proper permutation.
        /// </summary>
        /// <param name="indices">An array which represents where each integer is permuted too: indices[i] represents that integer i
        /// is permuted to location indices[i].</param>
        /// <returns>True if <paramref name="indices"/> represents a proper permutation, <c>false</c> otherwise.</returns>
        static bool CheckForProperPermutation(int[] indices)
        {
            var idxCheck = new bool[indices.Length];

            for (int i = 0; i < indices.Length; i++)
            {
                if (indices[i] >= indices.Length || indices[i] < 0)
                {
                    return false;
                }

                idxCheck[indices[i]] = true;
            }

            for (int i = 0; i < indices.Length; i++)
            {
                if (idxCheck[i] == false)
                {
                    return false;
                }
            }

            return true;
        }
    }
}