推箱子,【算法】从推箱子的解答步骤还原关卡地图

推箱子是一款经典的电子游戏,要求玩家在二维地图上把箱子推到指定地点,当中牵涉到大量的空间逻辑推理。HTML5 Sokoban 是一个非常不错的在线推箱子的网页。推箱子关卡一般用XSB格式来保存和交流,解答步骤则使用LURD格式,请参见:XSB和LURD格式简介。
XSB格式规定使用以下符号:
  • @ ==> 人 man
  • + ==> 人在目标点 man _disibledevent=> 箱子 box
  • * ==> 箱子在目标点 box _disibledevent=> 墙 wall
  • . ==> 目标点 goal
  • - ==> 地板 floor,还可以使用空格或者下划线表示。
LURD格式规定使用以下八个拉丁字母(小写字母表示移动,大写字母表示推动):
  • l 或 L ==> 左 Left
  • r 或 R ==> 右 Right
  • u 或 U ==> 上 Up
  • d 或 D ==> 下 Down
有一天,我突然想到,能不能从推箱子的解答步骤还原出关卡地图来呢?因为LURD数据已经包含了足够的信息,可以据此还原出一个最简的关卡地图出来。下面就是实现这个想法的 Lurd2Xsb.cs 程序:
001: using System; 002: using System.Text; 003: using System.Drawing; 004: 005: namespace Skyiv.Ben.Game 006: { 007: public sealed class Lurd2Xsb 008: { 009: void SetBrick(byte[,] map, int x, int y) { map[x, y] = 8; } 010: void SetFloor(byte[,] map, Point pt) { map[pt.X, pt.Y] |= 1; } 011: void SetGoal(byte[,] map, Point pt) { map[pt.X, pt.Y] |= 2; } 012: void SetBox(byte[,] map, Point pt) { map[pt.X, pt.Y] |= 4; } 013: void UnsetBox(byte[,] map, Point pt) { map[pt.X, pt.Y] &= 0xFB; } 014: bool HasBox(byte[,] map, int x, int y) { return (map[x, y] & 4) != 0; } 015: bool IsGoal(byte[,] map, int x, int y) { return (map[x, y] & 2) != 0; } 016: bool IsFloor(byte[,] map, int x, int y) { return (map[x, y] & 1) != 0; } 017: bool IsBrick(byte[,] map, int x, int y) { return map[x, y] == 8; } 018: bool IsWall(byte[,] map, int x, int y) { return map[x, y] == 0; } 019: bool IsBrickOrWall(byte[,] map, int x, int y) { return IsBrick(map, x, y) || IsWall(map, x, y); } 020: 021: void MarkBrick(byte[,] map, int x, int y) 022: { 023: if (!IsWall(map, x, y)) return; 024: if (!IsBrickOrWall(map, x - 1, y - 1)) return; 025: if (!IsBrickOrWall(map, x - 1, y + 1)) return; 026: if (!IsBrickOrWall(map, x + 1, y - 1)) return; 027: if (!IsBrickOrWall(map, x + 1, y + 1)) return; 028: if (!IsBrickOrWall(map, x - 1, y)) return; 029: if (!IsBrickOrWall(map, x + 1, y)) return; 030: if (!IsBrickOrWall(map, x, y - 1)) return; 031: if (!IsBrickOrWall(map, x, y + 1)) return; 032: SetBrick(map, x, y); 033: } 034: 035: int GetX(byte[,] map, int y0, int y1, int x, int x2) 036: { 037: for (var y = y0; y < y1; y++) 038: if (!IsBrick(map, x, y)) return x; 039: return x2; 040: } 041: 042: int GetY(byte[,] map, int x0, int x1, int y, int y2) 043: { 044: for (var x = x0; x < x1; x++) 045: if (!IsBrick(map, x, y)) return y; 046: return y2; 047: } 048: 049: Rectangle GetRectangle(byte[,] map) 050: { 051: int x0 = 1, y0 = 1, x1 = map.GetLength(0) - 2, y1 = map.GetLength(1) - 2; 052: x0 = GetX(map, y0, y1, x0, x0 + 1); 053: x1 = GetX(map, y0, y1, x1, x1 - 1); 054: y0 = GetY(map, x0, x1, y0, y0 + 1); 055: y1 = GetY(map, x0, x1, y1, y1 - 1); 056: return Rectangle.FromLTRB(x0, y0, x1, y1); 057: } 058: 059: string GetXsb(byte[,] map, Point man) 060: { 061: var rect = GetRectangle(map); 062: for (var y = rect.Top; y <= rect.Bottom; y++) 063: for (var x = rect.Left; x <= rect.Right; x++) 064: MarkBrick(map, x, y); 065: rect = GetRectangle(map); 066: var xsb = new StringBuilder(); 067: for (var y = rect.Top; y <= rect.Bottom; y++) 068: { 069: for (var x = rect.Left; x <= rect.Right; x++) 070: { 071: if (IsGoal(map, x, y)) 072: { 073: if (man.X == x && man.Y == y) xsb.Append('+'); 074: else if (HasBox(map, x, y)) xsb.Append('*'); 075: else xsb.Append('.'); 076: } 077: else if (IsFloor(map, x, y)) 078: { 079: if (man.X == x && man.Y == y) xsb.Append('@'); 080: else if (HasBox(map, x, y)) xsb.Append('$'); 081: else xsb.Append('-'); 082: } 083: else if (IsBrick(map, x, y)) xsb.Append('_'); 084: else xsb.Append('#'); 085: } 086: xsb.AppendLine(); 087: } 088: return xsb.ToString(); 089: } 090: 091: void LeftOrRight(byte[,] map, ref Point man, int step) 092: { 093: man.X += step; 094: if (HasBox(map, man.X, man.Y)) UnsetBox(map, man); 095: else SetGoal(map, man); 096: man.X -= step; 097: SetBox(map, man); 098: man.X -= step; 099: SetFloor(map, man); 100: } 101: 102: void UpOrDown(byte[,] map, ref Point man, int step) 103: { 104: man.Y += step; 105: if (HasBox(map, man.X, man.Y)) UnsetBox(map, man); 106: else SetGoal(map, man); 107: man.Y -= step; 108: SetBox(map, man); 109: man.Y -= step; 110: SetFloor(map, man); 111: } 112: 113: byte[,] GetMap(string lurd, Size size, ref Point man) 114: { 115: var map = new byte[size.Width, size.Height]; 116: SetFloor(map, man); 117: for (var i = lurd.Length - 1; i >= 0; i--) 118: { 119: switch (lurd[i]) 120: { 121: case 'l': man.X++; SetFloor(map, man); break; 122: case 'r': man.X--; SetFloor(map, man); break; 123: case 'u': man.Y++; SetFloor(map, man); break; 124: case 'd': man.Y--; SetFloor(map, man); break; 125: case 'L': LeftOrRight(map, ref man, -1); break; 126: case 'R': LeftOrRight(map, ref man, 1); break; 127: case 'U': UpOrDown(map, ref man, -1); break; 128: case 'D': UpOrDown(map, ref man, 1); break; 129: } 130: } 131: return map; 132: } 133: 134: Rectangle GetBoundary(string lurd) 135: { 136: var boundary = new Rectangle(0, 0, 1, 1); 137: var man = new Point(); 138: for (var i = lurd.Length - 1; i >= 0; i--) 139: { 140: switch (lurd[i]) 141: { 142: case 'l': case 'L': man.X++; if (boundary.Right <= man.X) boundary.Width++; break; 143: case 'r': case 'R': man.X--; if (boundary.Left > man.X) { boundary.Width++; boundary.X--; } break; 144: case 'u': case 'U': man.Y++; if (boundary.Bottom <= man.Y) boundary.Height++; break; 145: case 'd': case 'D': man.Y--; if (boundary.Top > man.Y) { boundary.Height++; boundary.Y--; } break; 146: } 147: } 148: return boundary; 149: } 150: 151: public string GetXsbFromLurd(string lurd) 152: { 153: var boundary = GetBoundary(lurd); 154: var size = new Size(boundary.Width + 6, boundary.Height + 6); 155: var man = new Point(3 - boundary.X, 3 - boundary.Y); 156: var map = GetMap(lurd, size, ref man); 157: return GetXsb(map, man); 158: } 159: 160: static void Main() 161: { 162: Console.Write(new Lurd2Xsb().GetXsbFromLurd(Console.In.ReadToEnd())); 163: } 164: } 165: }
简要说明:
  • GetXsbFromLurd 方法根据输入的LURD数据还原出XSB格式的最简关卡地图。
  • GetBoundary 方法根据输入的LURD数据计算出地图的边界。
  • GetMap 方法根据输入的LURD数据生成关卡地图的二维字节数组表示。
  • LeftOrRight 和 UpOrDown 方法处理LURD数据中推动箱子的步骤。
  • GetXsb 方法根据关卡地图的二维字节数组表示生成XSB格式数据。
  • GetRectangle 方法判断二维字节数组中实际表示数据的边界范围。
  • MarkBrick 方法标记砖块(相当于人不可到达的空地,作用和墙是一样的)。
  • 第 9 到 19 行的一系列 SetXXX 和 IsXXX 等方法都是简单地对二维字节数组操作。
比如说 HTML5 Sokoban 网页上 m1 关卡集第 12 关如下所示:
image【算法】从推箱子的解答步骤还原关卡地图推箱子
经过49步后通关,其LURD数据如下所示(m1-12.lurd):
uululldRdRluurDrDDrddlluRuuulldRurDDrrrddllUdlluR
那么,我们执行以下命令:
Lurd2Xsb.exe < m1-12.lurd > m1-12.xsb
得到的XSB数据如下所示:
#####____ #---##___ #-$--#___ ##-$-#### _###@.--# __#--.#-# __#-----# __#######
将以上XSB数据在 HTML5 Sokoban 网页上载入关卡,如下图所示:
imageimage【算法】从推箱子的解答步骤还原关卡地图推箱子
可见该程序较好地还原了关卡地图。
2007年10月我还写了系列随笔:使用 C# 开发智能手机软件:推箱子。当时使用的数据格式有所不同,但是可以写一个简单的 Xsb2Bxa 程序来进行软件。下图就是经转换到载入到 PushBox 软件中的其中一个关卡:
imageimageimage【算法】从推箱子的解答步骤还原关卡地图推箱子
下面就是 Xsb2Bxa.cs 程序:
01: using System; 02: using System.IO; 03: using System.Text; 04: 05: namespace Skyiv.Ben.Game 06: { 07: sealed class Xsb2Bxa 08: { 09: void TransformXsb(string name, StringBuilder sb) 10: { 11: foreach (var line in File.ReadLines(name + ".xsb")) 12: { 13: if (line.Length == 0) continue; 14: foreach (var c in line) 15: { 16: switch (c) 17: { 18: case '#': sb.Append('#'); break; 19: case '@': sb.Append('('); break; 20: case '+': sb.Append(')'); break; 21: case '$': sb.Append('x'); break; 22: case '*': sb.Append('X'); break; 23: case '.': sb.Append('+'); break; 24: case '-': sb.Append('-'); break; 25: case ' ': sb.Append('-'); break; 26: case '_': sb.Append('%'); break; 27: } 28: } 29: sb.AppendLine(); 30: } 31: } 32: 33: void TransformLurd(string name, StringBuilder sb) 34: { 35: var file = name + ".lurd"; 36: if (!File.Exists(file)) return; 37: sb.Append(':'); 38: foreach (var c in File.ReadAllText(file)) 39: { 40: switch (c) 41: { 42: case 'l': sb.Append('N'); break; 43: case 'u': sb.Append('O'); break; 44: case 'r': sb.Append('L'); break; 45: case 'd': sb.Append('M'); break; 46: case 'L': sb.Append('S'); break; 47: case 'U': sb.Append('T'); break; 48: case 'R': sb.Append('Q'); break; 49: case 'D': sb.Append('R'); break; 50: } 51: } 52: sb.AppendLine(); 53: } 54: 55: string GetBxaFromXsbAndLurd(string name) 56: { 57: var sb = new StringBuilder(); 58: TransformXsb(name, sb); 59: TransformLurd(name, sb); 60: return sb.ToString(); 61: } 62: 63: void Run() 64: { 65: using (var sw = new StreamWriter("ben.bxa", false, Encoding.GetEncoding("GB2312"))) 66: { 67: sw.WriteLine("!银河"); 68: var count = 0; 69: foreach (var file in Directory.GetFiles(".", "*.xsb")) 70: { 71: var name = Path.GetFileNameWithoutExtension(file); 72: sw.WriteLine("'[{0}] {1}", ++count, name); 73: sw.WriteLine(GetBxaFromXsbAndLurd(name)); 74: } 75: } 76: } 77: 78: static void Main() 79: { 80: try 81: { 82: new Xsb2Bxa().Run(); 83: } 84: catch (Exception ex) 85: { 86: Console.WriteLine(ex.Message); 87: } 88: } 89: } 90: }
本文中的所有源代码可以到 http://bitbucket.org/ben.skyiv/lurd2xsb/downloads 页面下载。
也可以使用 hg clone http://bitbucket.org/ben.skyiv/lurd2xsb 命令下载。
关于 hg ,请参阅 Mercurial 备忘录。
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