phase 2

Assets/Engine/Assets/Prefabs/UI/Puzzle Plan Entry.prefab

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Assets/Engine/Assets/Prefabs/UI/Puzzle Plan Entry.prefab.meta

@@ -0,0 +1,7 @@
+fileFormatVersion: 2
+guid: cad05994b2fb37746988912bce5a31f5
+PrefabImporter:
+  externalObjects: {}
+  userData: 
+  assetBundleName: 
+  assetBundleVariant: 

Assets/Engine/Assets/Prefabs/UI/Text.prefab

@@ -79,4 +79,4 @@ MonoBehaviour:
     m_HorizontalOverflow: 0
     m_VerticalOverflow: 0
     m_LineSpacing: 1
-  m_Text: 'Time:'
+  m_Text: Text

Assets/Engine/Runtime/Engine.cs

@@ -22,7 +22,7 @@ namespace EscapeRoomEngine.Engine.Runtime
         [InfoBox("If a space was generated without any puzzles in it, the engine will try generating another new space. To prevent infinite loops, the amount of retries is bound.")]
         public int maxSpaceGenerationTries = 1000;
         [Tooltip("The engine will try to generate a room that takes approximately this many seconds to complete.")]
-        public float initialTargetTime = 5 * 60;
+        public float initialTargetTime = 10 * 60;
         public Vector3 roomOffset = new(0, 1000, 0);
         [Required] public EngineTheme theme;
 
@@ -83,7 +83,11 @@ namespace EscapeRoomEngine.Engine.Runtime
             var tries = 0;
             Space space;
             Passage exit = null;
-            var puzzle = PlanPuzzles();
+            
+            // choose the next puzzle
+            // PlanPuzzles();
+            var puzzle = ChoosePuzzle();
+            GameControl.Instance.CurrentPuzzle = puzzle;
 
             do
             {
@@ -119,21 +123,41 @@ namespace EscapeRoomEngine.Engine.Runtime
             room.AddSpace(space, exit);
         }
 
-        /// <summary>
+        private PuzzleModuleDescription ChoosePuzzle()
-        /// Updates the list of puzzles planned for this run and returns the puzzle to put in the next room.
-        /// </summary>
-        private PuzzleModuleDescription PlanPuzzles()
         {
-
+            // choose a puzzle from the plan and remove it from both the plan and later available puzzles (so it is only chosen once)
-            var nextPuzzle = _plannedPuzzles.PopRandomElement();
+            var puzzle = _plannedPuzzles.PopRandomElement();
-            
+            _availablePuzzles.Remove(puzzle);
-            EstimatedTimeRemaining = Measure.AverageTime(_plannedPuzzles);
+            return puzzle;
-
-            return nextPuzzle;
         }
 
         #endregion
 
+        /// <summary>
+        /// Updates the list of puzzles planned for this run.
+        /// </summary>
+        public void PlanPuzzles()
+        {
+            var n = _availablePuzzles.Count;
+            var estimates = new int[n];
+            var indices = new Range(0, n).ToArray();
+            var target = Mathf.RoundToInt(GameControl.Instance.TargetTime - GameControl.Instance.EstimatedTimeRoom);
+            _plannedPuzzles = new List<PuzzleModuleDescription>();
+
+            for (var i = 0; i < n; i++)
+            {
+                estimates[i] = Mathf.RoundToInt(Measure.EstimateTime(_availablePuzzles[i]));
+            }
+            var chosen = Backtrack.Closest(indices, estimates, target);
+            foreach (var i in chosen)
+            {
+                _plannedPuzzles.Add(_availablePuzzles[i]);
+            }
+            
+            EstimatedTimeRemaining = Measure.EstimateTime(_plannedPuzzles);
+            GameControl.Instance.PlannedPuzzles = _plannedPuzzles;
+        }
+
         public void HidePreviousRoom(bool destroy = true)
         {
             if (NumberOfRooms > 2)

Assets/Engine/Runtime/Measurements/Measure.cs

@@ -18,13 +18,20 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
         private static Dictionary<int, PuzzleMeasurement> _runningMeasurements;
         private static Session _currentSession;
 
-        public static float AverageTime(IEnumerable<PuzzleModuleDescription> puzzles) =>
-            puzzles.Sum(puzzle => PuzzleStorage.Instance.Load(puzzle).AverageTimeToSolve);
         public static float AverageTime(PuzzleModuleDescription puzzle) =>
             PuzzleStorage.Instance.Load(puzzle).AverageTimeToSolve;
+        public static float AverageTime(IEnumerable<PuzzleModuleDescription> puzzles) => puzzles.Sum(AverageTime);
         public static float AverageTime(Room room) =>
             room.puzzles.Sum(puzzle => AverageTime((PuzzleModuleDescription)puzzle.description));
 
+        public static float EstimateTime(PuzzleModuleDescription puzzle) =>
+            PuzzleStorage.Instance.Load(puzzle).EstimateTimeToSolve(SessionPercentile());
+        public static float EstimateTime(IEnumerable<PuzzleModuleDescription> puzzles) => puzzles.Sum(EstimateTime);
+        public static float EstimateTime(Room room) =>
+            room.puzzles.Sum(puzzle => EstimateTime((PuzzleModuleDescription)puzzle.description));
+
+        public static float SessionPercentile() => _currentSession?.MeanPercentile ?? 0.5f;
+
         public static void StartMeasuring(PuzzleModuleDescription puzzle)
         {
             _runningMeasurements[puzzle.Id] = new PuzzleMeasurement

Assets/Engine/Runtime/Measurements/Puzzle.cs

@@ -17,6 +17,7 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
 
         public float TotalTimeSpentOnPuzzle => Measurements.Sum(measurement => measurement.Time);
         public float AverageTimeToSolve => Measurements.Count > 0 ? TotalTimeSpentOnPuzzle / Measurements.Count : 0f;
+        public NormalDistribution Distribution => new(TimesAsSamples());
 
         [UsedImplicitly]
         public Puzzle() {}
@@ -25,6 +26,23 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
             ID = puzzle.Id;
         }
 
+        /// <summary>
+        /// Estimate how long a player in the given percentile will take to solve this puzzle.
+        /// </summary>
+        public float EstimateTimeToSolve(float percentile) => Distribution.InverseCumulative(percentile);
+
+        private float[] TimesAsSamples()
+        {
+            var samples = new float[Measurements.Count];
+            
+            for (var i = 0; i < Measurements.Count; i++)
+            {
+                samples[i] = Measurements[i].Time;
+            }
+
+            return samples;
+        }
+
         public override string ToString()
         {
             return $"{Engine.Theme.GetPuzzle(ID)}: avg. {AverageTimeToSolve.ToTimeSpan():m':'ss} ({string.Join(", ", Measurements)})";

Assets/Engine/Runtime/Measurements/PuzzleStorage.cs

@@ -8,6 +8,8 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
 {
     public class PuzzleStorage : MonoBehaviour
     {
+        private const int SchemaVersion = 1;
+        
         public static PuzzleStorage Instance { get; private set; }
 
         [SerializeField]
@@ -17,7 +19,20 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
 
         private void OnEnable()
         {
-            _realm = Realm.GetInstance(databasePath);
+            var config = new RealmConfiguration
+            {
+                SchemaVersion = SchemaVersion,
+                MigrationCallback = (migration, oldSchemaVersion) =>
+                {
+                    if (oldSchemaVersion < 1)
+                    {
+                        // migration from version 0 to 1
+                    }
+                    
+                    Logger.Log($"Migrated database to version {SchemaVersion}", LogType.Measuring);
+                }
+            };
+            _realm = Realm.GetInstance(config.ConfigWithPath(databasePath));
         }
 
         private void Awake()
@@ -41,10 +56,7 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
         {
             session.Time = time;
             
-            _realm.Write(() =>
+            _realm.Write(() => _realm.Add(session));
-            {
-                _realm.Add(session);
-            });
         }
 
         #endregion
@@ -84,6 +96,9 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
                 
                 // add solved puzzle to session
                 session.PuzzlesSolved.Add(found);
+                
+                // add time percentile to session
+                session.Percentiles.Add(found.Distribution.Cumulative(measurement.Time));
             });
         }
 

Assets/Engine/Runtime/Measurements/Session.cs

@@ -1,5 +1,6 @@
 using System.Collections.Generic;
 using System.Diagnostics.CodeAnalysis;
+using System.Linq;
 using EscapeRoomEngine.Engine.Runtime.Utilities;
 using JetBrains.Annotations;
 using MongoDB.Bson;
@@ -13,8 +14,11 @@ namespace EscapeRoomEngine.Engine.Runtime.Measurements
         [PrimaryKey]
         public ObjectId ID { get; set; }
         public float Time { get; set; }
+        public IList<float> Percentiles { get; }
         public IList<Puzzle> PuzzlesSolved { get; }
 
+        public float MeanPercentile => Percentiles.Count == 0 ? .5f : Probability.Mean(Percentiles.ToArray());
+
         [UsedImplicitly]
         public Session()
         {

Assets/Engine/Runtime/UI/GameControl.cs

@@ -1,4 +1,6 @@
-using EscapeRoomEngine.Engine.Runtime.Measurements;
+using System.Collections.Generic;
+using EscapeRoomEngine.Engine.Runtime.Measurements;
+using EscapeRoomEngine.Engine.Runtime.Modules;
 using EscapeRoomEngine.Engine.Runtime.Utilities;
 using NaughtyAttributes;
 using UnityEngine;
@@ -15,20 +17,31 @@ namespace EscapeRoomEngine.Engine.Runtime.UI
     {
         public static GameControl Instance { get; private set; }
 
+        [SerializeField]
+        private float uiUpdateInterval = 1, planUpdateInterval = 1;
         [BoxGroup("Internal")] [SerializeField]
         private Button startButton, stopButton, pauseButton, addTimeButton, removeTimeButton;
         [BoxGroup("Internal")] [SerializeField]
-        private Text timeText, roomTimeText, estimateTimeText, targetTimeText;
+        private Text timeText, roomTimeText, estimateTimeText, targetTimeText, percentileText;
         [BoxGroup("Internal")] [SerializeField]
-        private float uiUpdateInterval = 1;
+        private PuzzlePlan puzzlePlan;
 
         [HideInInspector] public GameState gameState = GameState.Stopped;
+        public PuzzleModuleDescription CurrentPuzzle
+        {
+            set => puzzlePlan.CurrentPuzzle = value;
+        }
+        public List<PuzzleModuleDescription> PlannedPuzzles
+        {
+            set => puzzlePlan.Puzzles = value;
+        }
 
         public float TimeElapsed { get; private set; }
         public float TimeInRoom { get; set; }
         public float TargetTime { get; private set; }
+        public float EstimatedTimeRoom { get; private set; }
 
-        private float _previousUIUpdate;
+        private float _previousUIUpdate, _previousPlanUpdate;
 
         private void Awake()
         {
@@ -57,6 +70,15 @@ namespace EscapeRoomEngine.Engine.Runtime.UI
                 _previousUIUpdate = Time.time;
                 
                 SetTimeText();
+                UpdateStats();
+            }
+            
+            // update plan
+            if (Time.time > _previousPlanUpdate + planUpdateInterval)
+            {
+                _previousPlanUpdate = Time.time;
+                
+                Engine.Instance.PlanPuzzles();
             }
             
             // enable or disable buttons
@@ -129,15 +151,21 @@ namespace EscapeRoomEngine.Engine.Runtime.UI
 
             Engine.Instance.CurrentRoom.Match(some: room =>
             {
-                estimateTimeText.text = TimeToText(
+                EstimatedTimeRoom =
-                    TimeElapsed - TimeInRoom
+                    TimeElapsed - TimeInRoom + Mathf.Max(TimeInRoom, Measure.EstimateTime(room));
-                    + Mathf.Max(TimeInRoom, Measure.AverageTime(room))
+                estimateTimeText.text = TimeToText(EstimatedTimeRoom + Engine.Instance.EstimatedTimeRemaining);
-                    + Engine.Instance.EstimatedTimeRemaining);
             });
         }
 
+        private void UpdateStats()
+        {
+            percentileText.text = PercentageToText(Measure.SessionPercentile());
+        }
+
         private static string TimeToText(float time) => $"{time.ToTimeSpan():mm':'ss}";
 
+        private static string PercentageToText(float percentage) => $"{percentage:P1}";
+
         #endregion
 
         #region Measurements

Assets/Engine/Runtime/UI/PuzzlePlan.cs

@@ -0,0 +1,56 @@
+using System.Collections.Generic;
+using EscapeRoomEngine.Engine.Runtime.Modules;
+using NaughtyAttributes;
+using UnityEngine;
+using UnityEngine.UI;
+
+namespace EscapeRoomEngine.Engine.Runtime.UI
+{
+    public class PuzzlePlan : MonoBehaviour
+    {
+        [SerializeField]
+        private Vector2 entryOffset;
+        [BoxGroup("Internal")] [SerializeField]
+        private RectTransform plan;
+        [BoxGroup("Internal")] [SerializeField]
+        private PuzzlePlanEntry currentPuzzle, entryPrefab;
+        [BoxGroup("Internal")] [SerializeField]
+        private GameObject currentPuzzleTitle, planTitle;
+
+        public PuzzleModuleDescription CurrentPuzzle
+        {
+            set
+            {
+                currentPuzzleTitle.SetActive(true);
+                currentPuzzle.gameObject.SetActive(true);
+                
+                // set the current puzzle
+                currentPuzzle.Puzzle = value;
+            }
+        }
+        public List<PuzzleModuleDescription> Puzzles
+        {
+            set
+            {
+                planTitle.SetActive(true);
+                plan.gameObject.SetActive(true);
+                
+                // remove the old children
+                foreach (RectTransform child in plan)
+                {
+                    Destroy(child.gameObject);
+                }
+                
+                // add the new children
+                var offset = Vector2.zero;
+                value.ForEach(puzzle =>
+                {
+                    var entry = Instantiate(entryPrefab, plan, false);
+                    entry.Position = offset;
+                    entry.Puzzle = puzzle;
+                    offset += entryOffset;
+                });
+            }
+        }
+    }
+}

Assets/Engine/Runtime/UI/PuzzlePlan.cs.meta

@@ -0,0 +1,3 @@
+fileFormatVersion: 2
+guid: ad95894771b8478591e5f5abbe1d0244
+timeCreated: 1671133031

Assets/Engine/Runtime/UI/PuzzlePlanEntry.cs

@@ -0,0 +1,32 @@
+using System;
+using EscapeRoomEngine.Engine.Runtime.Measurements;
+using EscapeRoomEngine.Engine.Runtime.Modules;
+using EscapeRoomEngine.Engine.Runtime.Utilities;
+using NaughtyAttributes;
+using UnityEngine;
+using UnityEngine.UI;
+
+namespace EscapeRoomEngine.Engine.Runtime.UI
+{
+    public class PuzzlePlanEntry : MonoBehaviour
+    {
+        [BoxGroup("Internal")] [Required] [SerializeField]
+        private Text puzzleName, estimatedTime;
+
+        public Vector2 Position
+        {
+            set
+            {
+                puzzleName.rectTransform.anchoredPosition = value;
+            }
+        }
+        public PuzzleModuleDescription Puzzle
+        {
+            set
+            {
+                puzzleName.text = value.puzzleName;
+                estimatedTime.text = $"Time Estimate: {Measure.EstimateTime(value).ToTimeSpan():mm':'ss}";
+            }
+        }
+    }
+}

Assets/Engine/Runtime/UI/PuzzlePlanEntry.cs.meta

@@ -0,0 +1,3 @@
+fileFormatVersion: 2
+guid: 8ef80fc9016c4a46a190769f3b771bfa
+timeCreated: 1671136597

Assets/Engine/Runtime/Utilities/Backtrack.cs

@@ -0,0 +1,127 @@
+using System;
+
+// ReSharper disable ReturnTypeCanBeEnumerable.Global
+// ReSharper disable ParameterTypeCanBeEnumerable.Local
+
+namespace EscapeRoomEngine.Engine.Runtime.Utilities
+{
+    public struct Backtrack
+    {
+        private int[] indices;
+        private int[] values;
+        private int target;
+
+        public Backtrack(int[] indices, int[] values, int target)
+        {
+            this.indices = indices;
+            this.values = values;
+            this.target = target;
+        }
+
+        /// <summary>
+        /// Find any number of elements from the given set of indices and values with the maximum sum that doesn't exceed the target sum.
+        /// </summary>
+        /// <remarks>This function uses a backtracking approach to find the sum.</remarks>
+        public int[] BruteForceLower(int[] chosen = null, int pos = 0)
+        {
+            chosen ??= Array.Empty<int>();
+            
+            if (Sum(chosen) > target)
+            {
+                // if the sum of the chosen values exceeds the target, return nothing
+                return Array.Empty<int>();
+            }
+            if (pos >= indices.Length)
+            {
+                // if we cannot add any more elements, return all chosen
+                return chosen;
+            }
+
+            // find the best indices when skipping the one at the current position
+            var leave = BruteForceLower(chosen, pos + 1);
+            // find the best indices when including the one at the current position
+            var next = new int[chosen.Length + 1];
+            for (var i = 0; i < chosen.Length; i++)
+            {
+                next[i] = chosen[i];
+            }
+            next[^1] = indices[pos];
+            var pick = BruteForceLower(next, pos + 1);
+            
+            // return the best result
+            return Sum(leave) > Sum(pick) ? leave : pick;
+        }
+
+        /// <summary>
+        /// Find any number of elements from the given set of indices and values with the minimum sum that is higher than the target sum.
+        /// </summary>
+        /// <remarks>This function uses a backtracking approach to find the sum.</remarks>
+        public int[] BruteForceHigher(int[] chosen = null, int pos = int.MaxValue)
+        {
+            chosen ??= indices;
+            if (pos == int.MaxValue)
+            {
+                pos = indices.Length - 1;
+            }
+            
+            if (Sum(chosen) < target)
+            {
+                // if the sum of the chosen values is lower than the target, return all indices (the maximum choice)
+                return indices;
+            }
+            if (pos < 0)
+            {
+                // if we cannot remove any more elements, return all chosen
+                return chosen;
+            }
+
+            // find the best indices when not removing the one at the current position
+            var leave = BruteForceHigher(chosen, pos - 1);
+            // find the best indices when removing the one at the current position
+            var next = new int[chosen.Length - 1];
+            for (var i = 0; i < chosen.Length; i++)
+            {
+                if (i < pos)
+                {
+                    next[i] = chosen[i];
+                } else if (i > pos)
+                {
+                    next[i - 1] = chosen[i];
+                }
+            }
+            var pick = BruteForceHigher(next, pos - 1);
+            
+            // return the best result
+            return Sum(leave) < Sum(pick) ? leave : pick;
+        }
+
+        public int[] BruteForce()
+        {
+            var lower = BruteForceLower();
+            var higher = BruteForceHigher();
+            var errLower = Math.Abs(target - Sum(lower));
+            var errHigher = Math.Abs(target - Sum(higher));
+
+            return errLower < errHigher ? lower : higher;
+        }
+
+        /// <summary>
+        /// Get a subset of indices where the sum of their corresponding values is closest to a target sum.
+        /// </summary>
+        public static int[] Closest(int[] indices, int[] values, int target) =>
+            new Backtrack(indices, values, target).BruteForce();
+
+        private int Sum(int[] chosen)
+        {
+            var sum = 0;
+            
+            // ReSharper disable once LoopCanBeConvertedToQuery
+            foreach (var i in chosen)
+            {
+                sum += values[i];
+            }
+
+            return sum;
+        }
+    }
+}

Assets/Engine/Runtime/Utilities/Backtrack.cs.meta

@@ -0,0 +1,3 @@
+fileFormatVersion: 2
+guid: 313a79a04104480f931206ff7f57d0c5
+timeCreated: 1671126182

Assets/Engine/Runtime/Utilities/Probability.cs

@@ -1,6 +1,7 @@
 using System;
 using System.Linq;
 using MathNet.Numerics.Distributions;
+using UnityEngine;
 using Random = System.Random;
 
 namespace EscapeRoomEngine.Engine.Runtime.Utilities
@@ -8,19 +9,21 @@ namespace EscapeRoomEngine.Engine.Runtime.Utilities
     [Serializable]
     public struct NormalDistribution
     {
-        public double mean, σ;
+        public float μ, σ;
 
-        public static NormalDistribution Standard => new NormalDistribution { mean = 0, σ = 1 };
+        public static NormalDistribution Standard => new NormalDistribution { μ = 0, σ = 1 };
 
-        public NormalDistribution(double[] samples) : this()
+        public NormalDistribution(float[] samples) : this()
         {
-            mean = Probability.Mean(samples);
+            μ = Probability.Mean(samples);
-            σ = Probability.StandardDeviation(samples, mean);
+            σ = Probability.StandardDeviation(samples, μ);
         }
 
-        public double Sample() => σ * Probability.Normal() + mean;
+        public float Sample() => σ * Probability.Normal() + μ;
 
-        public double Cumulative(double x) => new Normal(mean, σ).CumulativeDistribution(x);
+        public float Cumulative(float x) => (float)new Normal(μ, σ).CumulativeDistribution(x);
+
+        public float InverseCumulative(float x) => (float)new Normal(μ, σ).InverseCumulativeDistribution(x);
     }
     
     public static class Probability
@@ -32,22 +35,22 @@ namespace EscapeRoomEngine.Engine.Runtime.Utilities
         /// 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()
+        public static float Normal()
         {
-            double u1, u2, square;
+            float u1, u2, square;
             
             // get two random points inside the unit circle
             do
             {
-                u1 = 2 * _random.NextDouble() - 1;
+                u1 = 2 * (float)_random.NextDouble() - 1;
-                u2 = 2 * _random.NextDouble() - 1;
+                u2 = 2 * (float)_random.NextDouble() - 1;
                 square = u1 * u1 + u2 * u2;
             } while (square >= 1f);
 
-            return u1 * Math.Sqrt(-2 * Math.Log(square) / square);
+            return u1 * Mathf.Sqrt(-2 * Mathf.Log(square) / square);
         }
 
-        public static double Mean(double[] samples)
+        public static float Mean(float[] samples)
         {
             if (samples.Length == 0)
             {
@@ -57,10 +60,10 @@ namespace EscapeRoomEngine.Engine.Runtime.Utilities
             return samples.Sum() / samples.Length;
         }
 
-        public static double StandardDeviation(double[] samples) => StandardDeviation(samples, Mean(samples));
+        public static float StandardDeviation(float[] samples) => StandardDeviation(samples, Mean(samples));
-        public static double StandardDeviation(double[] samples, double mean)
+        public static float StandardDeviation(float[] samples, float mean)
         {
-            var deviations = new double[samples.Length];
+            var deviations = new float[samples.Length];
 
             for (var i = 0; i < samples.Length; i++)
             {
@@ -68,7 +71,7 @@ namespace EscapeRoomEngine.Engine.Runtime.Utilities
                 deviations[i] = d * d;
             }
 
-            return Math.Sqrt(Mean(deviations));
+            return Mathf.Sqrt(Mean(deviations));
         }
     }
 }

Assets/Engine/Runtime/Utilities/Range.cs

@@ -12,6 +12,19 @@
             this.max = max;
         }
 
+        public int[] ToArray(bool includeMax = false)
+        {
+            var count = includeMax ? Length + 1 : Length;
+            var array = new int[count];
+            
+            for (var i = 0; i < count; i++)
+            {
+                array[i] = min + i;
+            }
+
+            return array;
+        }
+
         public override string ToString() => $"{{{min}, ..., {max}}}";
     }
 }

Assets/Engine/Runtime/Utilities/Utilities.cs

@@ -25,8 +25,14 @@ namespace EscapeRoomEngine.Engine.Runtime.Utilities
         
         public static int RandomInclusive(int from, int to) => Random.Range(from, to + 1);
 
-        public static T RandomElement<T>(this List<T> list) => list[Random.Range(0, list.Count)];
+        #endregion
+    }
 
+    public static class ListExtensions
+    {
+        /// <summary>
+        /// remove a random element from a list and return it.
+        /// </summary>
         public static T PopRandomElement<T>(this List<T> list)
         {
             var index = Random.Range(0, list.Count);
@@ -35,7 +41,20 @@ namespace EscapeRoomEngine.Engine.Runtime.Utilities
             return element;
         }
 
-        #endregion
+        public static T RandomElement<T>(this List<T> list) => list[Random.Range(0, list.Count)];
+
+        /// <summary>
+        /// Perform a Fisher-Yates shuffle on a given list, leaving it in a random order.
+        /// </summary>
+        public static void Shuffle<T>(this List<T> list)
+        {
+            for (var n = list.Count - 1; n > 0; n--)
+            {
+                var i = Utilities.RandomInclusive(0, n);
+                var j = Utilities.RandomInclusive(0, n);
+                (list[i], list[j]) = (list[j], list[i]);
+            }
+        }
     }
 
     public static class Vector2IntExtensions

Assets/NuGet.config.meta

@@ -25,7 +25,7 @@ PluginImporter:
   - first:
       Windows Store Apps: WindowsStoreApps
     second:
-      enabled: 1
+      enabled: 0
       settings: {}
   userData: 
   assetBundleName: 

Assets/Scenes/TestScene.unity

@@ -547,6 +547,7 @@ GameObject:
   - component: {fileID: 1568048334}
   - component: {fileID: 1568048339}
   - component: {fileID: 1568048336}
+  - component: {fileID: 1568048340}
   m_Layer: 0
   m_Name: Engine
   m_TagString: Untagged
@@ -567,7 +568,7 @@ MonoBehaviour:
   m_Name: 
   m_EditorClassIdentifier: 
   maxSpaceGenerationTries: 1000
-  initialTargetTime: 300
+  initialTargetTime: 600
   roomOffset: {x: 0, y: 1000, z: 0}
   theme: {fileID: 11400000, guid: 568d9a7d70f3edb4cb6db66a0010f105, type: 2}
 --- !u!4 &1568048335
@@ -598,7 +599,7 @@ MonoBehaviour:
   m_Name: 
   m_EditorClassIdentifier: 
   loggingEnabled: 1
-  typeFilter: 00000000
+  typeFilter: 0000000009000000
 --- !u!114 &1568048339
 MonoBehaviour:
   m_ObjectHideFlags: 0
@@ -612,3 +613,17 @@ MonoBehaviour:
   m_Name: 
   m_EditorClassIdentifier: 
   databasePath: measurements.realm
+--- !u!114 &1568048340
+MonoBehaviour:
+  m_ObjectHideFlags: 0
+  m_CorrespondingSourceObject: {fileID: 0}
+  m_PrefabInstance: {fileID: 0}
+  m_PrefabAsset: {fileID: 0}
+  m_GameObject: {fileID: 1568048333}
+  m_Enabled: 1
+  m_EditorHideFlags: 0
+  m_Script: {fileID: 11500000, guid: 599a288d4210437698dc391e5cc84a8a, type: 3}
+  m_Name: 
+  m_EditorClassIdentifier: 
+  values: a3000000110100007c0000002801000029000000
+  target: 600

Assets/Test Assets/BacktrackingTest.cs

@@ -0,0 +1,47 @@
+using EscapeRoomEngine.Engine.Runtime.Utilities;
+using JetBrains.Annotations;
+using NaughtyAttributes;
+using UnityEngine;
+
+namespace Test_Assets
+{
+    public class BacktrackingTest : MonoBehaviour
+    {
+        public int[] values;
+        public int target;
+
+        [Button]
+        [UsedImplicitly]
+        public void Closest()
+        {
+            PrintResult(Backtrack.Closest(new Range(0, values.Length).ToArray(), values, target));
+        }
+
+        [Button]
+        [UsedImplicitly]
+        public void ClosestLower()
+        {
+            var backtrack = new Backtrack(new Range(0, values.Length).ToArray(), values, target);
+            PrintResult(backtrack.BruteForceLower());
+        }
+
+        [Button]
+        [UsedImplicitly]
+        public void ClosestHigher()
+        {
+            var backtrack = new Backtrack(new Range(0, values.Length).ToArray(), values, target);
+            PrintResult(backtrack.BruteForceHigher());
+        }
+
+        private void PrintResult(int[] indices)
+        {
+            var sum = 0;
+            foreach (var i in indices)
+            {
+                Debug.Log(values[i]);
+                sum += values[i];
+            }
+            Debug.Log($"sum: {sum}");
+        }
+    }
+}

Assets/Test Assets/BacktrackingTest.cs.meta

@@ -0,0 +1,3 @@
+fileFormatVersion: 2
+guid: 599a288d4210437698dc391e5cc84a8a
+timeCreated: 1671127266

Assets/Test Assets/ProbabilityTest.cs

@@ -1,6 +1,5 @@
 using EscapeRoomEngine.Engine.Runtime.Utilities;
 using JetBrains.Annotations;
-using MathNet.Numerics.Distributions;
 using NaughtyAttributes;
 using UnityEngine;
 
@@ -11,7 +10,8 @@ namespace Test_Assets
         public NormalDistribution distribution = NormalDistribution.Standard;
         public int steps = 24;
         public int n = 1000000;
-        public double sample;
+        public float sample;
+        public float percentile = 0.5f;
 
         [Button]
         [UsedImplicitly]
@@ -62,9 +62,16 @@ namespace Test_Assets
             Debug.Log(distribution.Cumulative(sample));
         }
 
-        private double[] Samples()
+        [Button]
+        [UsedImplicitly]
+        public void InversePercentile()
         {
-            var samples = new double[n];
+            Debug.Log(distribution.InverseCumulative(percentile));
+        }
+
+        private float[] Samples()
+        {
+            var samples = new float[n];
             for (var i = 0; i < n; i++)
             {
                 samples[i] = distribution.Sample();