using System;
using System.Linq;
using MathNet.Numerics.Distributions;
using Random = System.Random;

namespace EscapeRoomEngine.Engine.Runtime.Utilities
{
    [Serializable]
    public struct NormalDistribution
    {
        public double mean, σ;

        public static NormalDistribution Standard => new NormalDistribution { mean = 0, σ = 1 };

        public NormalDistribution(double[] samples) : this()
        {
            mean = Probability.Mean(samples);
            σ = Probability.StandardDeviation(samples, mean);
        }

        public double Sample() => σ * Probability.Normal() + mean;

        public double Cumulative(double x) => new Normal(mean, σ).CumulativeDistribution(x);
    }
    
    public static class Probability
    {
        private static readonly Random _random = new();

        /// <summary>
        /// Sample a random variable from the standard normal distribution.
        /// For simplicity, the result is clamped between -3 and 3. This is accurate for 99.7% of all samples, by the three-σ rule.
        /// </summary>
        /// <remarks>The calculation of the random variable is done by a Box-Muller transform.</remarks>
        public static double Normal()
        {
            double u1, u2, square;
            
            // get two random points inside the unit circle
            do
            {
                u1 = 2 * _random.NextDouble() - 1;
                u2 = 2 * _random.NextDouble() - 1;
                square = u1 * u1 + u2 * u2;
            } while (square >= 1f);

            return u1 * Math.Sqrt(-2 * Math.Log(square) / square);
        }

        public static double Mean(double[] samples)
        {
            if (samples.Length == 0)
            {
                return 0;
            }
            
            return samples.Sum() / samples.Length;
        }

        public static double StandardDeviation(double[] samples) => StandardDeviation(samples, Mean(samples));
        public static double StandardDeviation(double[] samples, double mean)
        {
            var deviations = new double[samples.Length];

            for (var i = 0; i < samples.Length; i++)
            {
                var d = samples[i] - mean;
                deviations[i] = d * d;
            }

            return Math.Sqrt(Mean(deviations));
        }
    }
}