feat(Board): generate random fish distribution on game board

This commit refactors the generateFields() method in the companion object to produce a better distribution of fish on the game board.

Previously, the method randomly generated the fish placement with a maximum of 5 holes per side, and a minimum of 5 1-fish fields per side. The remainingFish variable was used to keep track of the number of fish left to place, and maxholes was used to ensure the maximum number of holes was not exceeded.

The new implementation replaces the previous algorithm with a weighted probability distribution. The method now uses a list of Field objects and their corresponding probabilities to determine the number of fish that should be placed on each field.

To ensure that the sum of the probabilities is 1, an IllegalArgumentException is thrown if the weighted sum does not equal 1. The method then determines the range of possible fish values that can be placed on the field, based on the number of fields remaining to be filled and the sum of fish already placed.

The method then generates a random float between 0 and 1 and selects the corresponding fish value based on the probability distribution. The selected value is then assigned to the current field.

Finally, the method shuffles the board to ensure that the placement of fish is random, and returns the resulting game board.

Overall, this refactor results in a more evenly distributed placement of fish on the board, and eliminates the likelihood of having less than 8 1-fish fields. It also adds a constant distribution of (BoardSize*BoardSize*2) so 128 Fish on the Board.

Author: Max

plugin/src/main/kotlin/sc/plugin2023/Board.kt

@@ -3,6 +3,8 @@ package sc.plugin2023
 import com.thoughtworks.xstream.annotations.XStreamAlias
 import com.thoughtworks.xstream.annotations.XStreamImplicit
 import sc.api.plugins.*
+import kotlin.math.min
+import kotlin.math.roundToInt
 import sc.framework.deepCopy
 import kotlin.random.Random
 import sc.plugin2023.util.PenguinConstants as Constants
@@ -11,7 +13,7 @@ import sc.plugin2023.util.PenguinConstants as Constants
 @XStreamAlias(value = "board")
 class Board(
     @XStreamImplicit(itemFieldName = "row")
-    override val gameField: MutableTwoDBoard<Field> = generateFields()
+    override val gameField: MutableTwoDBoard<Field> = generateFields(),
 ): RectangularBoard<Field>(), IBoard {
 
     constructor(board: Board): this(board.gameField.deepCopy())
@@ -69,9 +71,10 @@ class Board(
     companion object {
         /** Generiert ein neues Spielfeld mit zufällig auf dem Spielbrett verteilten Fischen. */
         private fun generateFields(seed: Int = Random.nextInt()): MutableTwoDBoard<Field> {
-            var remainingFish = Constants.BOARD_SIZE * Constants.BOARD_SIZE
             val random = Random(seed)
-            println("Board Seed: $seed")
+            println("Board seed: $seed")
+            
+            var remainingFish = Constants.BOARD_SIZE * Constants.BOARD_SIZE
             var maxholes = 5
             // Pro Hälfte 32 Felder, mind. 27 Schollen
             // Maximal (64-20)/2 = 22 2-Fisch-Schollen,
@@ -95,5 +98,78 @@ class Board(
             }
         }
 
+        private fun generateFieldsRandom(seed: Int = Random.nextInt()): MutableTwoDBoard<Field> {
+            val random = Random(seed)
+            println("Board seed: $seed")
+            
+            val length = Constants.BOARD_SIZE
+            val width = Constants.BOARD_SIZE
+            val weightedInts =
+                listOf(Field(0) to 0.1f, Field(1) to 0.2f, Field(2) to 0.4f, Field(3) to 0.2f, Field(4) to 0.1f)
+            val totalSum = length * width
+            val halfWidth = width / 2
+            val halfEnforcedOnes = Constants.BOARD_SIZE / 2
+            val fields: TwoDBoard<Field> = Array(length) { Array(width) { Field(0) } }
+            var countOne = 0
+            
+            for(i in 0 until length) {
+                for(j in 0 until halfWidth) {
+                    if(i * halfWidth + j < halfEnforcedOnes) {
+                        fields[i][j] = Field(1)
+                        countOne += 1
+                        continue
+                    }
+                    
+                    val currentSum = fields.sumOf { it -> it.sumOf { it.fish } }
+                    val notFilled = totalSum - (i * halfWidth + j)
+                    
+                    val weightedSum = weightedInts.sumOf { it.second.toDouble() }
+                    if(weightedSum.roundToInt() != 1) {
+                        throw IllegalArgumentException("The sum of the probabilities must be 1. It is $weightedSum")
+                    }
+                    
+                    val lowestPossible = weightedInts.filter { it.first.fish >= (totalSum - currentSum) / notFilled }
+                        .minOf { it.first.fish }
+                    val highestPossible = min(totalSum - currentSum, weightedInts.maxOf { it.first.fish })
+                    
+                    val possibleValues =
+                        weightedInts.filter { it.first.fish in lowestPossible..highestPossible }.map { it.first.fish }
+                    val possibleWeights =
+                        weightedInts.filter { it.first.fish in lowestPossible..highestPossible }.map { it.second }
+                    
+                    val value = random.nextFloat()
+                    var cumulativeWeight = 0f
+                    var index = 0
+                    while(index < possibleValues.size && cumulativeWeight + possibleWeights[index] < value) {
+                        cumulativeWeight += possibleWeights[index]
+                        index++
+                    }
+                    
+                    fields[i][j] = Field(possibleValues[index])
+                    countOne += if(fields[i][j].fish == 1) 1 else 0
+                }
+            }
+            
+            for(i in 0 until length) {
+                for(j in 0 until halfWidth) {
+                    val x = random.nextInt(length)
+                    val y = random.nextInt(halfWidth)
+                    fields[i][j] = fields[x][y].also { fields[x][y] = fields[i][j] }
+                }
+            }
+            
+            for(i in 0 until length) {
+                for(j in 0 until halfWidth) {
+                    // TODO ??
+                    //  fields[i] += fields[length - i - 1][halfWidth - j - 1]
+                }
+            }
+            
+            return fields.let {
+                it + it.reversedArray().map { list ->
+                    Array(Constants.BOARD_SIZE) { index -> list[Constants.BOARD_SIZE - index - 1].deepCopy() }
+                }
+            }
+        }
     }
 }