using System;
using System.Collections.Generic;
using System.Linq;

namespace DataStructures.Probabilistic
{
    public class HyperLogLog<T> where T : notnull
    {
        private const int P = 16;
        private const double Alpha = .673;
        private readonly int[] registers;
        private readonly HashSet<int> setRegisters;

        /// <summary>
        /// Initializes a new instance of the <see cref="HyperLogLog{T}"/> class.
        /// </summary>
        public HyperLogLog()
        {
            var m = 1 << P;
            registers = new int[m];
            setRegisters = new HashSet<int>();
        }

        /// <summary>
        /// Merge's two HyperLogLog's together to form a union HLL.
        /// </summary>
        /// <param name="first">the first HLL.</param>
        /// <param name="second">The second HLL.</param>
        /// <returns>A HyperLogLog with the combined values of the two sets of registers.</returns>
        public static HyperLogLog<T> Merge(HyperLogLog<T> first, HyperLogLog<T> second)
        {
            var output = new HyperLogLog<T>();
            for (var i = 0; i < second.registers.Length; i++)
            {
                output.registers[i] = Math.Max(first.registers[i], second.registers[i]);
            }

            output.setRegisters.UnionWith(first.setRegisters);
            output.setRegisters.UnionWith(second.setRegisters);
            return output;
        }

        /// <summary>
        /// Adds an item to the HyperLogLog.
        /// </summary>
        /// <param name="item">The Item to be added.</param>
        public void Add(T item)
        {
            var x = item.GetHashCode();
            var binString = Convert.ToString(x, 2); // converts hash to binary
            var j = Convert.ToInt32(binString.Substring(0, Math.Min(P, binString.Length)), 2); // convert first b bits to register index
            var w = (int)Math.Log2(x ^ (x & (x - 1))); // find position of the right most 1.
            registers[j] = Math.Max(registers[j], w); // set the appropriate register to the appropriate value.
            setRegisters.Add(j);
        }

        /// <summary>
        /// Determines the approximate cardinality of the HyperLogLog.
        /// </summary>
        /// <returns>the approximate cardinality.</returns>
        public int Cardinality()
        {
            // calculate the bottom part of the harmonic mean of the registers
            double z = setRegisters.Sum(index => Math.Pow(2, -1 * registers[index]));

            // calculate the harmonic mean of the set registers
            return (int)Math.Ceiling(Alpha * setRegisters.Count * (setRegisters.Count / z));
        }
    }
}
