working with recursion

main.nim

@@ -1,4 +1,4 @@
-import algorithm, options, sequtils, sugar
+import algorithm, math, options, tables, sequtils, sugar
 
 
 type
@@ -15,13 +15,16 @@ type
 
   Die = tuple[color: Color, value: range[1..3]]
 
+  ScoreSet = array[Color, int]
+
   Board = object
     squares: array[1..16, Square]
     camels: array[Color, range[1..16]]
     leader: Color
+    gameOver: bool
 
 
-proc `[]`(b: var Board, idx: range[1..16]): var Square =
+proc `[]`[T](b: var Board, idx: T): var Square =
   b.squares[idx]
 
 
@@ -33,17 +36,18 @@ proc display(b: Board, start, stop: int) =
       echo lead, sq.tile.get
     else:
       echo lead, sq.camels
-  echo "\n"
+  echo ""
 
 
-proc preRoll(b: var Board) =
+proc setLeader(b: var Board) =
-  let colors = [cGreen, cYellow, cPurple, cBlue, cRed]
+  b.leader = b[b.camels.max].camels[^1] # top camel in the last currently-occupied space
-  var rolls = [range[1..16]3, 2, 3, 2, 1]
 
-  for (color, roll) in zip(colors, rolls):
+
-    let dest = roll + 1
+proc setState[T](b: var Board, state: T) =
+  for (color, dest) in state: # note that `state` is ordered, as this determines stacking
     b[dest].camels.add(color)
     b.camels[color] = dest
+  b.setLeader
 
 
 proc advance(b: var Board, die: Die) =
@@ -52,6 +56,11 @@ proc advance(b: var Board, die: Die) =
     startPos = b.camels[color]
   var prepend = false
   var endPos = startPos + roll
+  
+  if endPos > 16: # camel has passed the finish line
+    b.leader = color
+    b.gameOver = true
+    return
   if b[endPos].tile.isSome:
     endPos += int(b[endPos].tile.get)
     if b[endPos].tile.get == tBackward: prepend = true # if moving backward, we will prepend camel to the seq
@@ -67,13 +76,12 @@ proc advance(b: var Board, die: Die) =
       b[startPos].camels[i .. ^1] = @[]
       for moved in subStack:
         b.camels[moved] = endPos
-      b.leader = b[b.camels.max][^1] # top camel in the last currently-occupied space
+      b.setLeader
-
+      break # breaking the outer loop here, not the inner - but only conditionally! gah!
-    break # breaking the outer loop here, not the inner
 
 
 iterator allPermutations[T](x: seq[T]): seq[T] =
-  # returns all permutations of a given array. Order is wonky but we don't care.
+  # returns all permutations of a given seq. Order is wonky but we don't care.
   var workingCopy = x
   yield workingCopy
   while workingCopy.nextPermutation: # this mutates workingCopy
@@ -83,9 +91,53 @@ iterator allPermutations[T](x: seq[T]): seq[T] =
     yield workingCopy
 
 
+proc update(scores: var ScoreSet, toAdd: ScoreSet) =
+  for i, s in toAdd:
+    scores[i] += s
+
+
+proc simOrdering(b: Board, ordering: seq[Color]): ScoreSet =
+  for color in ordering:
+    for roll in 1..3:
+      let d = (color, range[1..3](roll))
+      let nextBoardState = b.dup(advance(d)) # make a copy instead of mutating
+      # only continue recursing if this is not the last die AND the game is not over
+      if ordering.len > 1 and not nextBoardState.gameOver:
+        let nextResult = simOrdering(nextBoardState, ordering[1 .. ^1])
+        result.update(nextResult)
+      else:
+        inc result[nextBoardState.leader]
+
+
+iterator possibleFutures(dice: seq[Color]): seq[Die]
+  # iterate over all possible sequences of die rolls. Each outcome
+  # is returned as a 5-sequence of (color, number) tuples.
+  yield (cRed, range[1..3]3)
+
+
+proc sumLegResults(b: Board, diceRemaining: seq[Color]): ScoreSet =
+  var count = 0
+  for perm in diceRemaining.allPermutations:
+    let permResult = simOrdering(b, perm)
+    result.update(permResult)
+    let total = result.sum
+    stdout.write("simulated: " & $total & "\r")
+    stdout.flushFile
+    count += 1
+  echo ""
+  echo count
+
+
 var b: Board
 b.display(1, 5)
-b.preRoll
+
-let c = b.dup(advance((cRed, range[1..3]3)))
+b.setState({cGreen: 4, cYellow: 3, cPurple: 4, cBlue: 3, cRed: 2})
 b.display(1, 5)
-c.display(1, 5)
+
+b.advance((cRed, range[1..3](2)))
+b.display(1, 5)
+
+let r = b.sumLegResults(@[cRed, cGreen, cBlue, cYellow, cPurple])
+let total = r.sum
+for i, c in r:
+  echo Color(i), ": ", (c / total).round(4) * 100, "% (", c, " / ", total, ")"