Add difficulty calculation

Adds base classes for difficulty calculations, hooks them up with
carousel container, and adds a port of the osu difficulty calculator.

osu.Game.Modes.Osu/OsuDifficultyCalculator.cs

@@ -0,0 +1,193 @@
+// Copyright (c) 2007-2017 ppy Pty Ltd <contact@ppy.sh>.
+// Licensed under the MIT Licence - https://raw.githubusercontent.com/ppy/osu/master/LICENCE
+
+using osu.Game.Beatmaps;
+using osu.Game.Modes.Osu.Objects;
+using System;
+using System.Collections.Generic;
+using osu.Game.Modes.Objects;
+
+namespace osu.Game.Modes.Osu
+{
+    public class OsuDifficultyCalculator : DifficultyCalculator<OsuHitObject>
+    {
+        private const double STAR_SCALING_FACTOR = 0.0675;
+        private const double EXTREME_SCALING_FACTOR = 0.5;
+
+        protected override PlayMode PlayMode => PlayMode.Osu;
+
+        /// <summary>
+        /// HitObjects are stored as a member variable.
+        /// </summary>
+        internal List<OsuHitObjectDifficulty> DifficultyHitObjects = new List<OsuHitObjectDifficulty>();
+
+        public OsuDifficultyCalculator(Beatmap beatmap) : base(beatmap)
+        {
+        }
+
+        protected override HitObjectConverter<OsuHitObject> Converter => new OsuHitObjectConverter();
+
+        protected override void PreprocessHitObjects()
+        {
+            foreach (var h in Objects)
+                if (h.Type == HitObjectType.Slider)
+                    ((Slider)h).Curve.Calculate();
+        }
+
+        protected override double ComputeDifficulty(Dictionary<String, String> categoryDifficulty)
+        {
+            // Fill our custom DifficultyHitObject class, that carries additional information
+            DifficultyHitObjects.Clear();
+
+            foreach (var hitObject in Objects)
+                DifficultyHitObjects.Add(new OsuHitObjectDifficulty(hitObject));
+
+            // Sort DifficultyHitObjects by StartTime of the HitObjects - just to make sure.
+            DifficultyHitObjects.Sort((a, b) => a.BaseHitObject.StartTime.CompareTo(b.BaseHitObject.StartTime));
+
+            if (!CalculateStrainValues()) return 0;
+
+            double speedDifficulty = CalculateDifficulty(DifficultyType.Speed);
+            double aimDifficulty = CalculateDifficulty(DifficultyType.Aim);
+
+            // OverallDifficulty is not considered in this algorithm and neither is HpDrainRate. That means, that in this form the algorithm determines how hard it physically is
+            // to play the map, assuming, that too much of an error will not lead to a death.
+            // It might be desirable to include OverallDifficulty into map difficulty, but in my personal opinion it belongs more to the weighting of the actual peformance
+            // and is superfluous in the beatmap difficulty rating.
+            // If it were to be considered, then I would look at the hit window of normal HitCircles only, since Sliders and Spinners are (almost) "free" 300s and take map length
+            // into account as well.
+
+            // The difficulty can be scaled by any desired metric.
+            // In osu!tp it gets squared to account for the rapid increase in difficulty as the limit of a human is approached. (Of course it also gets scaled afterwards.)
+            // It would not be suitable for a star rating, therefore:
+
+            // The following is a proposal to forge a star rating from 0 to 5. It consists of taking the square root of the difficulty, since by simply scaling the easier
+            // 5-star maps would end up with one star.
+            double speedStars = Math.Sqrt(speedDifficulty) * STAR_SCALING_FACTOR;
+            double aimStars = Math.Sqrt(aimDifficulty) * STAR_SCALING_FACTOR;
+
+            if (categoryDifficulty != null)
+            {
+                categoryDifficulty.Add("Aim", aimStars.ToString("0.00"));
+                categoryDifficulty.Add("Speed", speedStars.ToString("0.00"));
+
+                double hitWindow300 = 30/*HitObjectManager.HitWindow300*/ / TimeRate;
+                double preEmpt = 450/*HitObjectManager.PreEmpt*/ / TimeRate;
+
+                categoryDifficulty.Add("OD", (-(hitWindow300 - 80.0) / 6.0).ToString("0.00"));
+                categoryDifficulty.Add("AR", (preEmpt > 1200.0 ? -(preEmpt - 1800.0) / 120.0 : -(preEmpt - 1200.0) / 150.0 + 5.0).ToString("0.00"));
+
+                int maxCombo = 0;
+                foreach (OsuHitObjectDifficulty hitObject in DifficultyHitObjects)
+                    maxCombo += hitObject.MaxCombo;
+
+                categoryDifficulty.Add("Max combo", maxCombo.ToString());
+            }
+
+            // Again, from own observations and from the general opinion of the community a map with high speed and low aim (or vice versa) difficulty is harder,
+            // than a map with mediocre difficulty in both. Therefore we can not just add both difficulties together, but will introduce a scaling that favors extremes.
+            double starRating = speedStars + aimStars + Math.Abs(speedStars - aimStars) * EXTREME_SCALING_FACTOR;
+            // Another approach to this would be taking Speed and Aim separately to a chosen power, which again would be equivalent. This would be more convenient if
+            // the hit window size is to be considered as well.
+
+            // Note: The star rating is tuned extremely tight! Airman (/b/104229) and Freedom Dive (/b/126645), two of the hardest ranked maps, both score ~4.66 stars.
+            // Expect the easier kind of maps that officially get 5 stars to obtain around 2 by this metric. The tutorial still scores about half a star.
+            // Tune by yourself as you please. ;)
+
+            return starRating;
+        }
+
+        protected bool CalculateStrainValues()
+        {
+            // Traverse hitObjects in pairs to calculate the strain value of NextHitObject from the strain value of CurrentHitObject and environment.
+            List<OsuHitObjectDifficulty>.Enumerator hitObjectsEnumerator = DifficultyHitObjects.GetEnumerator();
+
+            if (!hitObjectsEnumerator.MoveNext()) return false;
+
+            OsuHitObjectDifficulty currentHitObject = hitObjectsEnumerator.Current;
+            OsuHitObjectDifficulty nextHitObject;
+
+            // First hitObject starts at strain 1. 1 is the default for strain values, so we don't need to set it here. See DifficultyHitObject.
+            while (hitObjectsEnumerator.MoveNext())
+            {
+                nextHitObject = hitObjectsEnumerator.Current;
+                nextHitObject.CalculateStrains(currentHitObject, TimeRate);
+                currentHitObject = nextHitObject;
+            }
+
+            return true;
+        }
+
+        /// <summary>
+        /// In milliseconds. For difficulty calculation we will only look at the highest strain value in each time interval of size STRAIN_STEP.
+        /// This is to eliminate higher influence of stream over aim by simply having more HitObjects with high strain.
+        /// The higher this value, the less strains there will be, indirectly giving long beatmaps an advantage.
+        /// </summary>
+        protected const double STRAIN_STEP = 400;
+
+        /// <summary>
+        /// The weighting of each strain value decays to this number * it's previous value
+        /// </summary>
+        protected const double DECAY_WEIGHT = 0.9;
+
+        protected double CalculateDifficulty(DifficultyType type)
+        {
+            double actualStrainStep = STRAIN_STEP * TimeRate;
+
+            // Find the highest strain value within each strain step
+            List<double> highestStrains = new List<double>();
+            double intervalEndTime = actualStrainStep;
+            double maximumStrain = 0; // We need to keep track of the maximum strain in the current interval
+
+            OsuHitObjectDifficulty previousHitObject = null;
+            foreach (OsuHitObjectDifficulty hitObject in DifficultyHitObjects)
+            {
+                // While we are beyond the current interval push the currently available maximum to our strain list
+                while (hitObject.BaseHitObject.StartTime > intervalEndTime)
+                {
+                    highestStrains.Add(maximumStrain);
+
+                    // The maximum strain of the next interval is not zero by default! We need to take the last hitObject we encountered, take its strain and apply the decay
+                    // until the beginning of the next interval.
+                    if (previousHitObject == null)
+                    {
+                        maximumStrain = 0;
+                    }
+                    else
+                    {
+                        double decay = Math.Pow(OsuHitObjectDifficulty.DECAY_BASE[(int)type], (intervalEndTime - previousHitObject.BaseHitObject.StartTime) / 1000);
+                        maximumStrain = previousHitObject.Strains[(int)type] * decay;
+                    }
+
+                    // Go to the next time interval
+                    intervalEndTime += actualStrainStep;
+                }
+
+                // Obtain maximum strain
+                maximumStrain = Math.Max(hitObject.Strains[(int)type], maximumStrain);
+
+                previousHitObject = hitObject;
+            }
+
+            // Build the weighted sum over the highest strains for each interval
+            double difficulty = 0;
+            double weight = 1;
+            highestStrains.Sort((a, b) => b.CompareTo(a)); // Sort from highest to lowest strain.
+
+            foreach (double strain in highestStrains)
+            {
+                difficulty += weight * strain;
+                weight *= DECAY_WEIGHT;
+            }
+
+            return difficulty;
+        }
+
+        // Those values are used as array indices. Be careful when changing them!
+        public enum DifficultyType : int
+        {
+            Speed = 0,
+            Aim,
+        };
+    }
+}