最佳得分Boggle板

Question

我对这个(现在已不复存在的)问题的答案很感兴趣，但它从未被纠正/改进过。

给定一组6边的扭动骰子(从这个问题窃取的配置)，在两分钟的处理时间内确定哪个板配置将允许最高的分数。(也就是说，哪个骰子在哪一个位置与哪一边向上允许最大的得分字库？)

目标

• 您的代码应该运行不超过2分(120秒)。在那个时候，它应该自动停止运行并打印结果。
• 最后的挑战得分将是平均Boggle得分5次运行的程序。
  • 如果打成平手，胜利者将是找到更多单词的算法。
  • 如果仍然有一个平分，胜利者将是谁的算法找到更长(8+)字。

RULES/CONSTRAINTS

• 这是一个代码挑战；代码长度与此无关。
• 请参考此链接获得一个单词列表(使用ISPELL "english.0"列表-这个皱眉列表缺少了一些非常常见的单词)。
  • 这个清单可以在代码中以任何方式引用/导入/阅读。
  • 只有与regex ^([a-pr-z]|qu){3,16}$匹配的单词才会被计算在内。(只有小写字母，3-16个字符，曲必须作为一个单位使用.)

• 单词是通过将相邻的字母(水平、垂直和对角线)以正确的顺序拼出而形成的，而不需要在单个单词中使用一次以上的模具。
  • 单词必须是3个字母或更长；较短的单词不会获得分数。
  • 复写的字母是可以接受的，只是不是骰子。
  • 从板的一边到另一边的边/交叉的字是不允许的。

• 最后的Boggle (不挑战)得分是所有找到的单词的积分值的总和。
  • 为每个单词分配的点值基于单词的长度。(见下文)
  • 普通的Boggle规则将扣减/折扣由另一个玩家找到的单词。假设这里没有其他球员参与，所有发现的单词都在总分中起作用。
  • 然而，在同一个网格中发现不止一次的单词应该只计算一次。

• 您的函数/程序必须找到最佳的安排；简单地硬编码一个预定的列表是不行的。
• 您的输出应该是一个4x4网格的理想游戏板，一个列表的所有找到的词为该板，和Boggle分数匹配这些词。

模具配置

A  A  E  E  G  N
E  L  R  T  T  Y
A  O  O  T  T  W
A  B  B  J  O  O
E  H  R  T  V  W
C  I  M  O  T  U
D  I  S  T  T  Y
E  I  O  S  S  T
D  E  L  R  V  Y
A  C  H  O  P  S
H  I  M  N  Qu U
E  E  I  N  S  U
E  E  G  H  N  W
A  F  F  K  P  S
H  L  N  N  R  Z
D  E  I  L  R  X

标准摆动计分表

Word length => Points
<= 2 - 0 pts
   3 - 1  
   4 - 1  
   5 - 2  
   6 - 3  
   7 - 5
>= 8 - 11 pts
*Words using the "Qu" die will count the full 2 letters for their word, not just the 1 die.

示例输出

A  L  O  J  
V  U  T  S  
L  C  H  E  
G  K  R  X

CUT
THE
LUCK
HEX
....

140 points

如果需要进一步澄清，请询问！

Answer 1

VBA (目前平均为80-110分，未完成)

这是我的工作过程，但这还远远不是最好的；我在任何一个板上的绝对最好的分数，在许多测试运行后，大约是120。仍然需要一些更好的总体清理，我相信在很多地方都会有更高的效率。

• 2012.05.09：
  • 原始投寄

• 2012.05.10-2012.05.18：
  • 改进的评分算法
  • 改进寻路逻辑

• 2012.06.07 - 2012.06.12：
  • 将字数限制从8字减少到6字。允许有更多的字数较小的板。似乎在平均分数上有了轻微的提高。(每次运行检查10-15块左右的板，1比2)
  • 按照面包箱的建议，我创建了一个树结构来容纳单词列表。这确实大大加快了板上单词的后端检查速度。
  • 我玩的是改变最大字号(速度和分数)，我还没有决定5还是6对我来说是一个更好的选择。6结果在100-120总板检查，而5个结果在500-1000 (这两个仍然远低于其他例子提供到目前为止)。
  • 问题:在多次连续运行之后，进程开始变慢，因此仍有一些内存需要管理。

你们中的一些人可能觉得这很可怕，但就像我说的，WIP。我非常愿意接受建设性的批评！抱歉身体太长了..。

骰子类模块：

Option Explicit

Private Sides() As String

Sub NewDie(NewLetters As String)
    Sides = Split(NewLetters, ",")
End Sub

Property Get Side(i As Integer)
    Side = Sides(i)
End Property

树类模块：

Option Explicit

Private zzroot As TreeNode


Sub AddtoTree(ByVal TreeWord As Variant)
Dim i As Integer
Dim TempNode As TreeNode

    Set TempNode = TraverseTree(TreeWord, zzroot)
    SetNode TreeWord, TempNode

End Sub

Private Function SetNode(ByVal Value As Variant, parent As TreeNode) As TreeNode
Dim ValChar As String
    If Len(Value) > 0 Then
        ValChar = Left(Value, 1)
        Select Case Asc(ValChar) - 96
            Case 1:
                Set parent.Node01 = AddNode(ValChar, parent.Node01)
                Set SetNode = parent.Node01
            Case 2:
                Set parent.Node02 = AddNode(ValChar, parent.Node02)
                Set SetNode = parent.Node02
            ' ... - Reduced to limit size of answer.
            Case 26:
                Set parent.Node26 = AddNode(ValChar, parent.Node26)
                Set SetNode = parent.Node26
            Case Else:
                Set SetNode = Nothing
        End Select

        Set SetNode = SetNode(Right(Value, Len(Value) - 1), SetNode)
    Else
        Set parent.Node27 = AddNode(True, parent.Node27)
        Set SetNode = parent.Node27
    End If
End Function

Function AddNode(ByVal Value As Variant, NewNode As TreeNode) As TreeNode
    If NewNode Is Nothing Then
        Set AddNode = New TreeNode
        AddNode.Value = Value
    Else
        Set AddNode = NewNode
    End If
End Function
Function TraverseTree(TreeWord As Variant, parent As TreeNode) As TreeNode
Dim Node As TreeNode
Dim ValChar As String
    If Len(TreeWord) > 0 Then
        ValChar = Left(TreeWord, 1)

        Select Case Asc(ValChar) - 96
            Case 1:
                Set Node = parent.Node01
            Case 2:
                Set Node = parent.Node02
            ' ... - Reduced to limit size of answer.
            Case 26:
                Set Node = parent.Node26
            Case Else:
                Set Node = Nothing
        End Select

        If Not Node Is Nothing Then
            Set TraverseTree = TraverseTree(Right(TreeWord, Len(TreeWord) - 1), Node)
            If Not TraverseTree Is Nothing Then
                Set TraverseTree = parent
            End If
        Else
            Set TraverseTree = parent
        End If
    Else
        If parent.Node27.Value Then
            Set TraverseTree = parent
        Else
            Set TraverseTree = Nothing
        End If
    End If
End Function

Function WordScore(TreeWord As Variant, Step As Integer, Optional parent As TreeNode = Nothing) As Integer
Dim Node As TreeNode
Dim ValChar As String
    If parent Is Nothing Then Set parent = zzroot
    If Len(TreeWord) > 0 Then
        ValChar = Left(TreeWord, 1)

        Select Case Asc(ValChar) - 96
            Case 1:
                Set Node = parent.Node01
            Case 2:
                Set Node = parent.Node02
            ' ... - Reduced to limit size of answer.
            Case 26:
                Set Node = parent.Node26
            Case Else:
                Set Node = Nothing
        End Select

        If Not Node Is Nothing Then
            WordScore = WordScore(Right(TreeWord, Len(TreeWord) - 1), Step + 1, Node)
        End If
    Else
        If parent.Node27 Is Nothing Then
            WordScore = 0
        Else
            WordScore = Step
        End If
    End If
End Function

Function ValidWord(TreeWord As Variant, Optional parent As TreeNode = Nothing) As Integer
Dim Node As TreeNode
Dim ValChar As String
    If parent Is Nothing Then Set parent = zzroot
    If Len(TreeWord) > 0 Then
        ValChar = Left(TreeWord, 1)

        Select Case Asc(ValChar) - 96
            Case 1:
                Set Node = parent.Node01
            Case 2:
                Set Node = parent.Node02
            ' ... - Reduced to limit size of answer.
            Case 26:
                Set Node = parent.Node26
            Case Else:
                Set Node = Nothing
        End Select

        If Not Node Is Nothing Then
            ValidWord = ValidWord(Right(TreeWord, Len(TreeWord) - 1), Node)
        Else
            ValidWord = False
        End If
    Else
        If parent.Node27 Is Nothing Then
            ValidWord = False
        Else
            ValidWord = True
        End If
    End If
End Function

Private Sub Class_Initialize()
    Set zzroot = New TreeNode
End Sub

Private Sub Class_Terminate()
    Set zzroot = Nothing
End Sub

TreeNode类模块：

Option Explicit

Public Value As Variant
Public Node01 As TreeNode
Public Node02 As TreeNode
' ... - Reduced to limit size of answer.
Public Node26 As TreeNode
Public Node27 As TreeNode

主要模块：

Option Explicit

Const conAllSides As String = ";a,a,e,e,g,n;e,l,r,t,t,y;a,o,o,t,t,w;a,b,b,j,o,o;e,h,r,t,v,w;c,i,m,o,t,u;d,i,s,t,t,y;e,i,o,s,s,t;d,e,l,r,v,y;a,c,h,o,p,s;h,i,m,n,qu,u;e,e,i,n,s,u;e,e,g,h,n,w;a,f,f,k,p,s;h,l,n,n,r,z;d,e,i,l,r,x;"
Dim strBoard As String, strBoardTemp As String, strWords As String, strWordsTemp As String
Dim CheckWordSub As String
Dim iScore As Integer, iScoreTemp As Integer
Dim Board(1 To 4, 1 To 4) As Integer
Dim AllDice(1 To 16) As Dice
Dim AllWordsTree As Tree
Dim AllWords As Scripting.Dictionary
Dim CurWords As Scripting.Dictionary
Dim FullWords As Scripting.Dictionary
Dim JunkWords As Scripting.Dictionary
Dim WordPrefixes As Scripting.Dictionary
Dim StartTime As Date, StopTime As Date
Const MAX_LENGTH As Integer = 5
Dim Points(3 To 8) As Integer

Sub Boggle()
Dim DiceSetup() As String
Dim i As Integer, j As Integer, k As Integer

    StartTime = Now()

    strBoard = vbNullString
    strWords = vbNullString
    iScore = 0

    ReadWordsFileTree

    DiceSetup = Split(conAllSides, ";")

    For i = 1 To 16
        Set AllDice(i) = New Dice
        AllDice(i).NewDie "," & DiceSetup(i)
    Next i

    Do While WithinTimeLimit

        Shuffle

        strBoardTemp = vbNullString
        strWordsTemp = vbNullString
        iScoreTemp = 0

        FindWords

        If iScoreTemp > iScore Or iScore = 0 Then
            iScore = iScoreTemp
            k = 1
            For i = 1 To 4
                For j = 1 To 4
                    strBoardTemp = strBoardTemp & AllDice(k).Side(Board(j, i)) & "  "
                    k = k + 1
                Next j
                strBoardTemp = strBoardTemp & vbNewLine
            Next i
            strBoard = strBoardTemp
            strWords = strWordsTemp

        End If

    Loop

    Debug.Print strBoard
    Debug.Print strWords
    Debug.Print iScore & " points"

    Set AllWordsTree = Nothing
    Set AllWords = Nothing
    Set CurWords = Nothing
    Set FullWords = Nothing
    Set JunkWords = Nothing
    Set WordPrefixes = Nothing

End Sub

Sub ShuffleBoard()
Dim i As Integer

    For i = 1 To 16
        If Not WithinTimeLimit Then Exit Sub
        Board(Int((i - 1) / 4) + 1, 4 - (i Mod 4)) = Int(6 * Rnd() + 1)
    Next i

End Sub

Sub Shuffle()
Dim n As Long
Dim Temp As Variant
Dim j As Long

    Randomize
    ShuffleBoard
    For n = 1 To 16
        If Not WithinTimeLimit Then Exit Sub
        j = CLng(((16 - n) * Rnd) + n)
        If n <> j Then
            Set Temp = AllDice(n)
            Set AllDice(n) = AllDice(j)
            Set AllDice(j) = Temp
        End If
    Next n

    Set FullWords = New Scripting.Dictionary
    Set CurWords = New Scripting.Dictionary
    Set JunkWords = New Scripting.Dictionary

End Sub

Sub ReadWordsFileTree()
Dim FSO As New FileSystemObject
Dim FS
Dim strTemp As Variant
Dim iLength As Integer
Dim StartTime As Date

    StartTime = Now()
    Set AllWordsTree = New Tree
    Set FS = FSO.OpenTextFile("P:\Personal\english.txt")

    Points(3) = 1
    Points(4) = 1
    Points(5) = 2
    Points(6) = 3
    Points(7) = 5
    Points(8) = 11

    Do Until FS.AtEndOfStream
        strTemp = FS.ReadLine
        If strTemp = LCase(strTemp) Then
            iLength = Len(strTemp)
            iLength = IIf(iLength > 8, 8, iLength)
            If InStr(strTemp, "'") < 1 And iLength > 2 Then
                AllWordsTree.AddtoTree strTemp
            End If
        End If
    Loop
    FS.Close

End Sub

Function GetScoreTree() As Integer
Dim TempScore As Integer

    If Not WithinTimeLimit Then Exit Function

    GetScoreTree = 0

    TempScore = AllWordsTree.WordScore(CheckWordSub, 0)
    Select Case TempScore
        Case Is < 3:
            GetScoreTree = 0
        Case Is > 8:
            GetScoreTree = 11
        Case Else:
            GetScoreTree = Points(TempScore)
    End Select

End Function

Sub SubWords(CheckWord As String)
Dim CheckWordScore As Integer
Dim k As Integer, l As Integer

    For l = 0 To Len(CheckWord) - 3
        For k = 1 To Len(CheckWord) - l
            If Not WithinTimeLimit Then Exit Sub

            CheckWordSub = Mid(CheckWord, k, Len(CheckWord) - ((k + l) - 1))

            If Len(CheckWordSub) >= 3 And Not CurWords.Exists(CheckWordSub) Then
                CheckWordScore = GetScoreTree

                If CheckWordScore > 0 Then
                    CurWords.Add CheckWordSub, CheckWordSub
                    iScoreTemp = iScoreTemp + CheckWordScore
                    strWordsTemp = strWordsTemp & CheckWordSub & vbNewLine
                End If

                If Left(CheckWordSub, 1) = "q" Then
                    k = k + 1
                End If
            End If

        Next k
    Next l

End Sub

Sub FindWords()
Dim CheckWord As String
Dim strBoardLine(1 To 16) As String
Dim Used(1 To 16) As Boolean
Dim i As Integer, j As Integer, k As Integer, l As Integer, m As Integer, n As Integer
Dim StartSquare As Integer
Dim FullCheck As Variant

    n = 1
    For l = 1 To 4
        For m = 1 To 4
            If Not WithinTimeLimit Then Exit Sub
            strBoardLine(n) = AllDice(n).Side(Board(m, l))
            n = n + 1
        Next m
    Next l

    For i = 1 To 16
        For k = 1 To 16

            If Not WithinTimeLimit Then Exit Sub
            If k Mod 2 = 0 Then
                For j = 1 To 16
                    Used(j) = False
                Next j

                Used(i) = True
                MakeWords strBoardLine, Used, i, k / 2, strBoardLine(i)
            End If

        Next k
    Next i

    For Each FullCheck In FullWords.Items
        SubWords CStr(FullCheck)
    Next FullCheck

End Sub

Function MakeWords(BoardLine() As String, Used() As Boolean, _
    Start As Integer, _
    Direction As Integer, CurString As String) As String
Dim i As Integer, j As Integer, k As Integer, l As Integer

    j = 0

    Select Case Direction
        Case 1:
            k = Start - 5
        Case 2:
            k = Start - 4
        Case 3:
            k = Start - 3
        Case 4:
            k = Start - 1
        Case 5:
            k = Start + 1
        Case 6:
            k = Start + 3
        Case 7:
            k = Start + 4
        Case 8:
            k = Start + 5
    End Select

    If k >= 1 And k <= 16 Then
        If Not WithinTimeLimit Then Exit Function

        If Not Used(k) Then
            If ValidSquare(Start, k) Then
                If Not (JunkWords.Exists(CurString & BoardLine(k))) And Not FullWords.Exists(CurString & BoardLine(k)) Then
                    Used(k) = True
                    For l = 1 To MAX_LENGTH
                        If Not WithinTimeLimit Then Exit Function
                        MakeWords = CurString & BoardLine(k)
                        If Not (JunkWords.Exists(MakeWords)) Then
                            JunkWords.Add MakeWords, MakeWords
                        End If
                        If Len(MakeWords) = MAX_LENGTH And Not FullWords.Exists(MakeWords) Then
                            FullWords.Add MakeWords, MakeWords
                        ElseIf Len(MakeWords) < MAX_LENGTH Then
                            MakeWords BoardLine, Used, k, l, MakeWords
                        End If
                    Next l
                    Used(k) = False
                End If
            End If
        End If
    End If

    If Len(MakeWords) = MAX_LENGTH And Not FullWords.Exists(MakeWords) Then
        FullWords.Add MakeWords, MakeWords
        Debug.Print "FULL - " & MakeWords
    End If

End Function

Function ValidSquare(StartSquare As Integer, EndSquare As Integer) As Boolean
Dim sx As Integer, sy As Integer, ex As Integer, ey As Integer

    If Not WithinTimeLimit Then Exit Function

    sx = (StartSquare - 1) Mod 4 + 1
    ex = (EndSquare - 1) Mod 4 + 1

    sy = Int((StartSquare - 1) / 4 + 1)
    ey = Int((EndSquare - 1) / 4 + 1)

    ValidSquare = (sx - 1 <= ex And sx + 1 >= ex) And (sy - 1 <= ey And sy + 1 >= ey) And StartSquare <> EndSquare

End Function

Function WithinTimeLimit() As Boolean
    StopTime = Now()
    WithinTimeLimit = (Round(CDbl(((StopTime - StartTime) - Int(StopTime - StartTime)) * 86400), 0) < 120)
End Function

Answer 2

快速查看搜索空间的大小。

   16! => 20922789888000 Dice Permutations
(6^16) =>  2821109907456 Face Permutations
 59025489844657012604928000 Boggle Grids 

减少，以排除重复的每一个模具。

              16! => 20922789888000 Dice Permutations
(4^4)*(5^6)*(6^5) => 31104000000 Unique Face Permutations
   650782456676352000000000 Boggle Grids 

@面包盒将字典存储为哈希表O(1)检查。

编辑

最佳董事会(到目前为止我已经见证了)

L  E  A  N
S  E  T  M
T  S  B  D
I  E  G  O

Score: 830
Words: 229
SLEETIEST  MANTELETS
MANTEELS  MANTELET  MATELESS
MANTEEL  MANTELS  TESTEES  BETISES  OBTESTS  OBESEST
SLEETS  SLEEST  TESTIS  TESTES  TSETSE  MANTES  MANTEL  TESTAE  TESTEE
STEELS  STELES  BETELS  BESETS  BESITS  BETISE  BODGES  BESEES  EISELS
GESTES  GEISTS  OBTEST
LEANT  LEATS  LEETS  LEESE  LESES  LESTS  LESBO  ANTES  NATES  SLEET  SETAE
SEATS  STIES  STEEL  STETS  STEAN  STEAM  STELE  SELES  TAELS  TEELS  TESTS
TESTE  TELES  TETES  MATES  TESTA  TEATS  SEELS  SITES  BEETS  BETEL  BETES
BESET  BESTS  BESIT  BEATS  BODGE  BESEE  DOGES  EISEL  GESTS  GESTE  GESSE
GEITS  GEIST  OBESE
LEAN  LEAT  LEAM  LEET  LEES  LETS  LEST  LESS  EATS  EELS  ELSE  ETNA  ESES
ESTS  ESSE  ANTE  ANTS  ATES  AMBO  NATS  SLEE  SEEL  SETA  SETS  SESE  SEAN
SEAT  SEAM  SELE  STIE  STET  SEES  TAEL  TAES  TEEL  TEES  TEST  TEAM  TELE
TELS  TETS  TETE  MATE  MATS  MAES  TIES  TEAT  TEGS  SELS  SEGO  SITS  SITE
BEET  BEES  BETA  BETE  BETS  BEST  BEAN  BEAT  BEAM  BELS  BOGS  BEGO  BEGS
DOGE  DOGS  DOBS  GOBS  GEST  GEIT  GETS  OBES
LEA  LEE  LET  LES  EAN  EAT  EEL  ELS  ETA  EST  ESS  ANT  ATE  NAT  NAE  NAM
SEE  SET  SEA  SEL  TAN  TAE  TAM  TEE  TES  TEA  TEL  TET  MNA  MAN  MAT  MAE
TIE  TIS  TEG  SEG  SEI  SIT  BEE  BET  BEL  BOD  BOG  BEG  DOG  DOB  ITS  EGO
GOD  GOB  GET  OBS  OBE
EA  EE  EL  ET  ES  AN  AT  AE  AM  NA  ST  TA  TE  MA
TI  SI  BE  BO  DO  IT  IS  GO  OD  OB

Answer 3

我的条目是超过这里的Dream.In.Code ~30 is每板搜索(在一个2核心机器，应该更快，更多的核心)