经典面试问题：12小球问题算法(源码)

(文档请参考：http://blog.youkuaiyun.com/CXXSoft/archive/2006/09/28/1299731.aspx)

3、运行效果

4、 算法源码

... {
作品名称:小球问题通用解决方案
开发作者:成晓旭
开发时间:2003年01月22日
完成时间:2003年01月23日
修改时间1:2003年11月14日
增加用户问题条件设置绘制方法
修改时间2:2003年11月18日
增加比较过程的记录功能
}
unitCommon;

interface

uses
Windows,SysUtils,Classes,Graphics,BallType;

// 清除画面方法
procedureClearCanvas(aCanvas:TCanvas;aRect:TRect);
// 小球问题条件设置方法
procedureDraw_Ball_Config(
AllBall:arrayofTC_Ball;
ACanvas:TCanvas;
aClearRect:TRect;
bShowTrace:Boolean);
// 小球问题解决方法
procedureSerach_Error_Ball(
AllBall:arrayofTC_Ball;
ACanvas:TCanvas;
aClearRect:TRect;
bShowTrace:Boolean);
var
strLog1:AnsiString;
strLog2:AnsiString;
strLog3:AnsiString;


implementation
// 单元内部常量定义
const
Fir_Pivot_X = 200 ;
Fir_Pivot_Y = 80 ;
Hint_X = 10 ;
One_DrawDelta = 140 ;
One_PreDelta = 70 ;
One_FroDelta = 30 ;
strADyB = ' 比较：A端(重)>B端(轻) ' + CHR( 13 ) + CHR( 10 );
strAXDB = ' 比较：A端=B端 ' + CHR( 13 ) + CHR( 10 );
strAXyB = ' 比较：A端(轻)<B端(重) ' + CHR( 13 ) + CHR( 10 );
A_Team = ' A组： ' ;
B_Team = ' B组： ' ;
preTail0 = ' 号球 ' + CHR( 13 ) + CHR( 10 );
preTail1 = ' 号球 ' ;
proHead = ' 结论：异常球在[ ' ;
lastResult = ' 结论：异常球是 ' ;
nextHint = CHR( 13 ) + CHR( 10 ) + ' 启示： ' ;
ErrorHint = ' 命题不严密,请检查设置条件！ ' ;

functionSearchBall_At4(AllBall:arrayofTC_Ball;
A,G:arrayofByte;varvErr_Ball_Order:Byte;
varvIsHeavy:Boolean;ACanvas:TCanvas;bShowTrace:Boolean):Boolean;
var
A2,B2:Word;
A3,B3:Word;
Loop:Word;
bNumber:Byte;
bPartA,bPartB:arrayofTC_Ball;
bCmpPara:TC_CmpPara;
str:AnsiString;
begin
vErr_Ball_Order: = 0 ;
vIsHeavy: = False;
A2: = AllBall[A[ 1 ]].Weight + AllBall[A[ 2 ]].Weight + AllBall[G[ 1 ]].Weight;
B2: = AllBall[A[ 3 ]].Weight + AllBall[G[ 2 ]].Weight + AllBall[G[ 3 ]].Weight;

str: = A_Team + IntToStr(AllBall[A[ 1 ]].Order) + ' , '
+ IntToStr(AllBall[A[ 2 ]].Order) + ' , '
+ IntToStr(AllBall[G[ 1 ]].Order);
str: = str + preTail0;
strLog2: = strLog2 + str;
str: = B_Team + IntToStr(AllBall[A[ 3 ]].Order) + ' , '
+ IntToStr(AllBall[G[ 2 ]].Order) + ' , '
+ IntToStr(AllBall[G[ 3 ]].Order);
str: = str + preTail0;
strLog2: = strLog2 + str;
bNumber: = 3 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
bPartA[ 0 ]: = AllBall[A[ 1 ]];
bPartA[ 1 ]: = AllBall[A[ 2 ]];
bPartA[ 2 ]: = AllBall[G[ 1 ]];

bPartB[ 0 ]: = AllBall[A[ 3 ]];
bPartB[ 1 ]: = AllBall[G[ 2 ]];
bPartB[ 2 ]: = AllBall[G[ 3 ]];

Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y + One_DrawDelta),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);

if A2 = B2then
begin
A3: = AllBall[A[ 4 ]].Weight;
B3: = AllBall[G[ 1 ]].Weight;
strLog2: = strLog2 + strAXDB;
str: = proHead;
str: = str + IntToStr(AllBall[A[ 4 ]].Order);
str: = str + ' ] ' + preTail1 + ' 【排3余1】 ' ;
strLog2: = strLog2 + str;
str: = ' 用任一正常球与之比较,即可知异常球是偏轻偏重！ ' ;
strLog2: = strLog2 + nextHint + str;
withbCmpPara do
begin
Pre_LNumber: = 4 ;
Fro_LNumber: = 1 ;
SetLength(Pre_Latency,Pre_LNumber);
SetLength(Fro_Latency,Fro_LNumber);
for Loop: = 0 toPre_LNumber - 1 do
Pre_Latency[Loop]: = AllBall[Loop + 9 ];
Fro_Latency[ 0 ]: = AllBall[A[ 4 ]];
end;

Balance_One_Latency(Point(Hint_X,Fir_Pivot_Y + One_DrawDelta - One_PreDelta),
Point(Hint_X,Fir_Pivot_Y + One_DrawDelta + One_FroDelta),
bCmpPara,ACanvas,bShowTrace);
bNumber: = 1 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
bPartA[ 0 ]: = AllBall[A[ 4 ]];
bPartB[ 0 ]: = AllBall[G[ 1 ]];

Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y + One_DrawDelta * 2 ),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);

if A3 = B3then
begin
vErr_Ball_Order: = 0 ;
strLog3: = ' 异常球与正常球一样重！ ' + ErrorHint;
end
else
begin
vErr_Ball_Order: = A[ 4 ];
vIsHeavy: = A3 > B3;
end;
end
else
begin
A3: = AllBall[A[ 1 ]].Weight;
B3: = AllBall[A[ 2 ]].Weight;
if A2 > B2then
strLog2: = strLog2 + strADYB
else
strLog2: = strLog2 + strAXYB;
str: = proHead;
str: = str + IntToStr(AllBall[A[ 1 ]].Order) + ' , '
+ IntToStr(AllBall[A[ 2 ]].Order) + ' , '
+ IntToStr(AllBall[A[ 3 ]].Order);
str: = str + ' ] ' + preTail1 + ' 【排1余3】 ' ;
strLog2: = strLog2 + str;
str: = ' 下一轮必须在本轮比较的同一端的两球中进行.即取： '
+ IntToStr(AllBall[A[ 1 ]].Order) + ' , '
+ IntToStr(AllBall[A[ 2 ]].Order)
+ ' 号球,在推算结果时,还必须用到此轮A、B端谁轻谁重！ ' ;
strLog2: = strLog2 + nextHint + str;
bNumber: = 1 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
bPartA[ 0 ]: = AllBall[A[ 1 ]];
bPartB[ 0 ]: = AllBall[A[ 2 ]];

Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y + One_DrawDelta * 2 ),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);

if A3 = B3then
begin
vErr_Ball_Order: = A[ 3 ];
vIsHeavy: = A2 < B2;
end
else
begin
if A2 > B2then
begin
if A3 > B3then
vErr_Ball_Order: = A[ 1 ]
else
vErr_Ball_Order: = A[ 2 ];
// IsHeavy:=True;
end
else
begin
if A3 > B3then
vErr_Ball_Order: = A[ 2 ]
else
vErr_Ball_Order: = A[ 1 ];
// IsHeavy:=NOTTrue;
end;
vIsHeavy: = A2 > B2;
end;
end;
Result: = vErr_Ball_Order <> 0 ;
end;


functionSearchBall_At8(AllBall:arrayofTC_Ball;IsAdyB:Boolean;
A,B,G:arrayofByte;varvErr_Ball_Order:Byte;
varvIsHeavy:Boolean;ACanvas:TCanvas;bShowTrace:Boolean):Boolean;
var
A2,B2:Word;
A3,B3:Word;
bNumber:Byte;
bPartA,bPartB:arrayofTC_Ball;
senPivot,thrPivot:TPoint;
str:AnsiString;
begin
vErr_Ball_Order: = 0 ;
vIsHeavy: = False;
A2: = AllBall[A[ 1 ]].Weight + AllBall[A[ 2 ]].Weight + AllBall[B[ 1 ]].Weight;
B2: = AllBall[A[ 3 ]].Weight + AllBall[B[ 2 ]].Weight + AllBall[G[ 1 ]].Weight;

str: = A_Team + IntToStr(AllBall[A[ 1 ]].Order) + ' , '
+ IntToStr(AllBall[A[ 2 ]].Order) + ' , '
+ IntToStr(AllBall[B[ 1 ]].Order);
str: = str + preTail0;
strLog2: = strLog2 + str;
str: = B_Team + IntToStr(AllBall[A[ 3 ]].Order) + ' , '
+ IntToStr(AllBall[B[ 2 ]].Order) + ' , '
+ IntToStr(AllBall[G[ 1 ]].Order);
str: = str + preTail0;
strLog2: = strLog2 + str;
bNumber: = 3 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
bPartA[ 0 ]: = AllBall[A[ 1 ]];
bPartA[ 1 ]: = AllBall[A[ 2 ]];
bPartA[ 2 ]: = AllBall[B[ 1 ]];

bPartB[ 0 ]: = AllBall[A[ 3 ]];
bPartB[ 1 ]: = AllBall[B[ 2 ]];
bPartB[ 2 ]: = AllBall[G[ 1 ]];

Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y + One_DrawDelta),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);
if A2 = B2then
begin
A3: = AllBall[B[ 3 ]].Weight;
B3: = AllBall[B[ 4 ]].Weight;
strLog2: = strLog2 + strAXDB;
str: = proHead;
str: = str + IntToStr(AllBall[A[ 4 ]].Order) + ' , '
+ IntToStr(AllBall[B[ 3 ]].Order) + ' , '
+ IntToStr(AllBall[B[ 4 ]].Order);
str: = str + ' ] ' + preTail1 + ' 【排5余3】 ' ;
strLog2: = strLog2 + str;
str: = ' 下一轮必须在本轮比较的同一端的两球中进行.即取： '
+ IntToStr(AllBall[B[ 3 ]].Order) + ' , '
+ IntToStr(AllBall[B[ 4 ]].Order)
+ ' 号球,在推算结果时,还必须用到此轮A、B端谁轻谁重！ ' ;
strLog2: = strLog2 + nextHint + str;
bNumber: = 1 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
bPartA[ 0 ]: = AllBall[B[ 3 ]];

bPartB[ 0 ]: = AllBall[B[ 4 ]];

Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y + One_DrawDelta * 2 ),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);

if A3 = B3then
begin
vErr_Ball_Order: = A[ 4 ];
vIsHeavy: = IsAdyB;
end
else
begin
if IsAdyBthen
begin
if A3 > B3then
vErr_Ball_Order: = B[ 4 ]
else
vErr_Ball_Order: = B[ 3 ];
// IsHeavy:=NOTIsAdyB;
end
else
begin
if A3 > B3then
vErr_Ball_Order: = B[ 3 ]
else
vErr_Ball_Order: = B[ 4 ];
// IsHeavy:=NOTIsAdyB;
end;
vIsHeavy: = NOTIsAdyB;
end;
end
else
begin
if A2 > B2then
strLog2: = strLog2 + strADYB
else
strLog2: = strLog2 + strAXYB;
str: = proHead;
str: = str + IntToStr(AllBall[A[ 1 ]].Order) + ' , '
+ IntToStr(AllBall[A[ 2 ]].Order) + ' , '
+ IntToStr(AllBall[A[ 3 ]].Order) + ' , '
+ IntToStr(AllBall[B[ 1 ]].Order) + ' , '
+ IntToStr(AllBall[B[ 2 ]].Order);
str: = str + ' ] ' + preTail1 + ' 【排3余5】 ' ;
strLog2: = strLog2 + str;
str: = ' 此时,必须综合分析近两次的比较结果.当近两次比较的天平倾向相同时, '
+ ' 必须比较共同产生倾向因素的两个球;倾向相反时, '
+ ' 任取一个正常球与A组第3个球( '
+ IntToStr(AllBall[A[ 2 ]].Order)
+ ' )或B组第1个球( '
+ IntToStr(AllBall[B[ 1 ]].Order)
+ ' )比较. ' ;
strLog2: = strLog2 + nextHint + str;
if ((IsAdyB = True)and(A2 > B2))or((IsAdyB = False)and(A2 < B2))then
begin
A3: = AllBall[A[ 1 ]].Weight;
B3: = AllBall[A[ 2 ]].Weight;
bNumber: = 1 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
bPartA[ 0 ]: = AllBall[A[ 1 ]];
bPartB[ 0 ]: = AllBall[A[ 2 ]];
Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y + One_DrawDelta * 2 ),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);
if A3 = B3then
begin
vErr_Ball_Order: = B[ 2 ];
vIsHeavy: = NOTIsAdyB;
end
else if A2 > B2then
begin
if A3 > B3then
vErr_Ball_Order: = A[ 1 ]
else
vErr_Ball_Order: = A[ 2 ];
vIsHeavy: = IsAdyB;
end
else if A2 < B2then
begin
if A3 > B3then
vErr_Ball_Order: = A[ 2 ]
else
vErr_Ball_Order: = A[ 1 ];
vIsHeavy: = IsAdyB;
end;
end
else if ((IsAdyB = True)and(A2 < B2))or((IsAdyB = False)and(A2 > B2))then
begin
A3: = AllBall[A[ 3 ]].Weight;
B3: = AllBall[G[ 1 ]].Weight;
bNumber: = 1 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
bPartA[ 0 ]: = AllBall[A[ 1 ]];
bPartB[ 0 ]: = AllBall[G[ 1 ]];
Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y + One_DrawDelta * 2 ),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);
if A3 = B3then
begin
vErr_Ball_Order: = B[ 1 ];
vIsHeavy: = NOTIsAdyB;
end
else if A3 > B3then
begin
if IsAdyBthen
begin
vErr_Ball_Order: = A[ 3 ];
vIsHeavy: = IsAdyB;
end
else
begin
vErr_Ball_Order: = 0 ;
strLog3: = ' "偏轻"的异常球>正常球！ ' + ErrorHint;
end;
end
else
begin
if IsAdyBthen
begin
vErr_Ball_Order: = 0 ;
strLog3: = ' "偏重"的异常球<正常球！ ' + ErrorHint;
end
else
begin
vErr_Ball_Order: = A[ 3 ];
vIsHeavy: = IsAdyB;
end
end;
end;
end;
Result: = vErr_Ball_Order <> 0 ;
end;

procedureSerach_Error_Ball(
AllBall:arrayofTC_Ball;
ACanvas:TCanvas;aClearRect:TRect;
bShowTrace:Boolean);
var
A,B:Word;
Loop:Word;
BufC:array[ 0 .. 4 ]ofByte;
BufT:array[ 0 .. 8 ]ofByte;
BufA,BufB:array[ 0 .. 4 ]ofByte;
BufG:array[ 0 .. 4 ]ofByte;
bOrder:Byte;
bHeavy:Boolean;
FoundBall:TC_SearchBall;
str:AnsiString;
bNumber:Byte;
bPartA,bPartB:arrayofTC_Ball;
bCmpPara:TC_CmpPara;
begin
A: = 0 ;
strLog1: = '' ;
strLog2: = '' ;
strLog3: = '' ;
ClearCanvas(aCanvas,aClearRect);
str: = A_Team;
for Loop: = 1 to 4 do
begin
A: = A + AllBall[Loop].Weight;
str: = str + IntToStr(AllBall[Loop].Order) + ' , ' ;
// bPartA[Loop]:=AllBall[Loop];
end;
str: = str + preTail0;
strLog1: = strLog1 + str;
B: = 0 ;
str: = B_Team;
for Loop: = 5 to 8 do
begin
B: = B + AllBall[Loop].Weight;
str: = str + IntToStr(AllBall[Loop].Order) + ' , ' ;
// bPartB[Loop]:=AllBall[Loop];
end;
str: = str + preTail0;
strLog1: = strLog1 + str;
bNumber: = 4 ;
SetLength(bPartA,bNumber);
SetLength(bPartB,bNumber);
for Loop: = 0 tobNumber - 1 do
begin
bPartA[Loop]: = AllBall[Loop + 1 ];
bPartB[Loop]: = AllBall[Loop + bNumber + 1 ];
end;
Balance_One_Compare(Point(Fir_Pivot_X,Fir_Pivot_Y),
bNumber,bPartA,bPartB,ACanvas,bShowTrace);

if A = Bthen
begin
strLog1: = strLog1 + strAXDB;
str: = proHead;
for Loop: = 1 to 4 do
begin
BufC[Loop]: = AllBall[ 8 + Loop].Order;
str: = str + IntToStr(AllBall[ 8 + Loop].Order) + ' , ' ;
end;
str: = str + ' ] ' + preTail1 + ' 【排8余4】 ' ;
strLog1: = strLog1 + str;
for Loop: = 1 to 8 do
BufT[Loop]: = AllBall[Loop].Order;
withbCmpPara do
begin
Pre_LNumber: = 12 ;
Fro_LNumber: = 4 ;
SetLength(Pre_Latency,Pre_LNumber);
SetLength(Fro_Latency,Fro_LNumber);
for Loop: = 0 toPre_LNumber - 1 do
Pre_Latency[Loop]: = AllBall[Loop + 1 ];
for Loop: = 0 toFro_LNumber - 1 do
Fro_Latency[Loop]: = AllBall[Loop + 9 ];
end;

Balance_One_Latency(Point( 10 ,Fir_Pivot_Y - One_PreDelta),Point( 10 ,Fir_Pivot_Y + One_FroDelta),
bCmpPara,ACanvas,bShowTrace);

if SearchBall_At4(AllBall,BufC,BufT,bOrder,bHeavy,ACanvas,bShowTrace)then
begin
FoundBall.Ball: = AllBall[bOrder];
FoundBall.IsHeavy: = bHeavy;
if FoundBall.IsHeavythen
FoundBall.ErrorMsg: = ' 【偏重】 '
else
FoundBall.ErrorMsg: = ' 【偏轻】 ' ;
str: = ' 【 ' + IntToStr(FoundBall.Ball.Order) + ' 】= '
+ IntToStr(FoundBall.Ball.Weight) + ' ' + FoundBall.ErrorMsg;
strLog3: = lastResult + str;
end;
end
else
begin
if A > Bthen
strLog1: = strLog1 + strADYB
else
strLog1: = strLog1 + strAXYB;
str: = proHead;
for Loop: = 1 to 8 do
str: = str + IntToStr(AllBall[Loop].Order) + ' , ' ;
str: = str + ' ] ' + preTail1 + ' 【排4余8】 ' ;
strLog1: = strLog1 + str;
for Loop: = 1 to 4 do
begin
BufA[Loop]: = AllBall[Loop].Order;
BufB[Loop]: = AllBall[ 4 + Loop].Order;
BufG[Loop]: = AllBall[ 8 + Loop].Order;
end;
withbCmpPara do
begin
Pre_LNumber: = 12 ;
Fro_LNumber: = 4 ;
SetLength(Pre_Latency,Pre_LNumber);
SetLength(Fro_Latency,Fro_LNumber);
for Loop: = 0 toPre_LNumber - 1 do
Pre_Latency[Loop]: = AllBall[Loop + 1 ];
for Loop: = 0 toFro_LNumber - 1 do
Fro_Latency[Loop]: = AllBall[Loop + 9 ];
end;

Balance_One_Latency(Point(Hint_X,Fir_Pivot_Y - One_PreDelta),Point( 10 ,Fir_Pivot_Y + One_FroDelta),
bCmpPara,ACanvas,bShowTrace);

if SearchBall_At8(AllBall,A > B,BufA,BufB,BufG,bOrder,bHeavy,ACanvas,bShowTrace)then
begin
FoundBall.Ball: = AllBall[bOrder];
FoundBall.IsHeavy: = bHeavy;
if FoundBall.IsHeavythen
FoundBall.ErrorMsg: = ' 【偏重】 '
else
FoundBall.ErrorMsg: = ' 【偏轻】 ' ;
str: = ' 【 ' + IntToStr(FoundBall.Ball.Order) + ' 】= '
+ IntToStr(FoundBall.Ball.Weight) + ' ' + FoundBall.ErrorMsg;
strLog3: = lastResult + str;
end;
end;
// MessageBox(0,PChar(Str),'小球问题',MB_OKorMB_IConInformation);

end;

procedureDraw_Ball_Config(
AllBall:arrayofTC_Ball;
ACanvas:TCanvas;
aClearRect:TRect;
bShowTrace:Boolean);
begin
ClearCanvas(aCanvas,aClearRect);
Process_Initial_Ball(
Point( 0 ,Fir_Pivot_Y - One_PreDelta - 10 ),
AllBall,ACanvas,bShowTrace);
end;

procedureClearCanvas(aCanvas:TCanvas;aRect:TRect);
begin
withaCanvas do
begin
Brush.Style: = bsSolid;
Brush.Color: = clWhite;
FillRect(aRect);
end;
end;

end.

5、 显示绘制源码

... {
作品名称:小球问题通用解决方案
开发作者:成晓旭
开发时间:2003年01月22日
完成时间:2003年01月22日
修改时间1:2003年11月15日
增加小于问题初始状态绘制方法
}
unitBallType;

interface

uses
Dialogs,Windows,Classes,SysUtils,Graphics;


type

// 小球问题:小球抽象数据类型
TC_Ball = PackedRecord
Order:Byte;
Weight:Byte;
BgColor:TColor;
TextColor:TColor;
end;

// 小球问题:被寻找的目标小球抽象数据类型
TC_SearchBall = PackedRecord
Ball:TC_Ball;
IsHeavy:Boolean;
ErrorMsg:AnsiString;
end;

// 小球问题:一次比较的参数的抽象数据类型
TC_CmpPara = PackedRecord
Pre_LNumber:Byte;
Pre_Latency:arrayofTC_Ball;
Fro_LNumber:Byte;
Fro_Latency:arrayofTC_Ball;
end;
// 小球问题:小球抽象类
TC_Ball_Class = class

private
bDrawOrder:Boolean;
bAbstractBall:TC_Ball;
bStartPoint:TPoint;
bSize:Integer;
bTextColor:TColor;
bBgColor:TColor;
bColorChanged:Boolean;
bCanvas:TCanvas;
public
procedureSetBgAndTextColor(bgColor:TColor;ttColor:TColor);
procedureDrawSelf();
constructorCreate(bTrance:Boolean);
end;

// 小球问题:天平抽象类
TC_Balance = class
// published
bMainPivot:TPoint;
bPartAPivot:TPoint;
bPartBPivot:TPoint;
bColor:TColor;
bPivotColor:TColor;
bCanvas:TCanvas;
bWeightA:Integer;
bWeightB:Integer;
private
bWidth:Integer;
bHeight:Integer;
bDelta:Integer;
public
procedureDrawSelf();
end;


// 小球问题:天平比较一次抽象类[行为抽象]
TC_Compare = class
cbPivot:TPoint;
cbPreStart,cbFroStart:TPoint;
cbCmpPara:TC_CmpPara;
cbCount:Byte;
cbPre_Latency:arrayofTC_Ball;
cBallPartA:arrayofTC_Ball;
cBallPartB:arrayofTC_Ball;
cbFro_Latency:arrayofTC_Ball;
cBalance:TC_Balance;
cCanvas:TCanvas;
private
cbPPartA,cbPPartB:TPoint;
pPre_Latency:arrayofTC_Ball_Class;
pPartA:arrayofTC_Ball_Class;
pPartB:arrayofTC_Ball_Class;
pFro_Latency:arrayofTC_Ball_Class;
isShowTrace:Boolean;
procedureDraw_Balance();
procedureDraw_Part_A();
procedureDraw_Part_B();
procedureDraw_Latency();
public
procedureDraw_AllBall();
procedureWeigh_Out();
constructorCreate(bTrace:Boolean);
end;

// 小球问题抽象类<2003-11-14至今未被使用,是为方法的通用性而设计>
TC_Ball_Problem = class
bpBall:arrayofTC_Ball;
bpCompareCount:Byte;
bpBallCount:Byte;
bpCanvas:TCanvas;
bpCompare:arrayofTC_Compare;
pBalace:TC_Balance;
public
// procedureWeigh_Out(bCenterX,bCenterY:Integer);
end;
// 天平的一次比较结果处理算法
procedureBalance_One_Latency(
BallStart1,BallStart2:TPoint;
OneCmpPara:TC_CmpPara;
ACanvas:TCanvas;
bTrace:Boolean);
// 天平的一次比较执行算法
procedureBalance_One_Compare(
BalancePivot:TPoint;
BallNum:Byte;
PartA,PartB:arrayofTC_Ball;
ACanvas:TCanvas;
bTrace:Boolean);
// 问题条件设置处理算法(小于的初始状态演示算法)
procedureProcess_Initial_Ball(
StartPoint:TPoint;
AllBall:arrayofTC_Ball;
ACanvas:TCanvas;
bTrace:Boolean
);
implementation

... {TC_Ball_Class}

constructorTC_Ball_Class.Create(bTrance:Boolean);
begin
bDrawOrder: = NOTbTrance;
end;

procedureTC_Ball_Class.DrawSelf();
var
strDrawText:String;
w,h,r:Integer;
begin
// 暂时增加
if bDrawOrderthen
strDrawText: = IntToStr(bAbstractBall.Order)
else
strDrawText: = IntToStr(bAbstractBall.Weight);
if bColorChangedthen
begin
bCanvas.Brush.Color: = bBgColor;
bCanvas.Pen.Color: = bBgColor;
bCanvas.Font.Color: = bTextColor;
end
else
begin
bCanvas.Brush.Color: = bAbstractBall.BgColor;
bCanvas.Pen.Color: = bAbstractBall.BgColor;
bCanvas.Font.Color: = bAbstractBall.TextColor;
end;
bCanvas.Font.Size: = bSize;
bCanvas.Font.Style: = [fsBold];
w: = bCanvas.TextWidth(strDrawText);
h: = bCanvas.TextHeight(strDrawText);
if w > hthen
r: = w
else
r: = h;
// 注意:此处的计算比例,是根据矩形的内接圆、外切圆推算出来的,
// 再加以实现绘制时的位置系数调试、调整而来
bCanvas.Ellipse(bStartPoint.X,bStartPoint.Y,bStartPoint.X + r * 1414 div 1000 ,bStartPoint.Y + r * 1414 div 1000 );
if (Length(strDrawText) = 1 )then
bCanvas.TextOut(bStartPoint.X + r * 414 div 1000 ,bStartPoint.Y + r * 207 div 1000 ,strDrawText)
else if (Length(strDrawText) = 2 )then
bCanvas.TextOut(bStartPoint.X + r * 214 div 1000 ,bStartPoint.Y + r * 228 div 1000 ,strDrawText);
end;

procedureTC_Ball_Class.SetBgAndTextColor(bgColor:TColor;ttColor:TColor);
begin
Self.bBgColor: = bgColor;
Self.bTextColor: = ttColor;
bColorChanged: = true ;
end;

... {TC_Balance}

procedureTC_Balance.DrawSelf;
procedureDrawTray(ACanvas:TCanvas;aX,aY,Awidth,AHeight:Integer;aDeltaY:Integer);
begin
withACanvas do
begin
MoveTo(aX,aY);
LineTo(aX - AWidth,aY + aDeltaY);
LineTo(aX - AWidth - AHeight,aY - AHeight + aDeltaY);
MoveTo(aX,aY);
LineTo(aX + AWidth,aY - aDeltaY);
LineTo(aX + AWidth + AHeight,aY - aHeight - aDeltaY);
end;
end;

var
X0,Y0,X1,Y1,X2,Y2,D,H:Integer;
begin
bDelta: = 6 ;
if bWeightA > bWeightBthen // [A>B]
bDelta: = bDelta
else if bWeightA = bWeightBthen // [A=B]
bDelta: = 0
else // [A<B]
bDelta: = - bDelta;
X0: = bMainPivot.X;
Y0: = bMainPivot.Y;
D: = bWidth;
H: = bHeight;
bCanvas.Pen.Color: = bPivotColor;
bCanvas.Brush.Color: = bPivotColor;
bCanvas.Polygon([Point(X0,Y0),Point(X0 - H,Y0 + H),Point(X0 + H,Y0 + H),Point(X0,Y0)]);
bCanvas.Pen.Color: = bColor;
DrawTray(bCanvas,X0,Y0,D,H,bDelta);
X1: = X0 - D - H;
Y1: = Y0 - H + bDelta;
DrawTray(bCanvas,X1,Y1,Ddiv 2 ,H, 0 );
X2: = X0 + D + H;
Y2: = Y0 - H - bDelta;
DrawTray(bCanvas,X2,Y2,Ddiv 2 ,H, 0 );
bPartAPivot.X: = X1;
bPartAPivot.Y: = Y1;
bPartBPivot.X: = X2;
bPartBPivot.Y: = Y2;
end;

... {TC_Compare}
constructorTC_Compare.Create(bTrace:Boolean);
begin
isShowTrace: = bTrace;
end;

procedureTC_Compare.Draw_AllBall;
const
strHint = ' 比较前： ' ;
var
Loop:Integer;
begin
SetLength(pPre_Latency,cbCmpPara.Pre_LNumber);
SetLength(cbCmpPara.Pre_Latency,cbCmpPara.Pre_LNumber);
for Loop: = 0 tocbCmpPara.Pre_LNumber - 1 do
begin
pPre_Latency[Loop]: = TC_Ball_Class.Create(isShowTrace);
pPre_Latency[Loop].bAbstractBall: = cbCmpPara.Pre_Latency[Loop];
pPre_Latency[Loop].bSize: = 10 ;
pPre_Latency[Loop].bStartPoint: = Point( 80 + cbPreStart.X + Loop * 25 ,cbPreStart.Y);
pPre_Latency[Loop].SetBgAndTextColor(clBlue,clYellow);
pPre_Latency[Loop].bCanvas: = cCanvas;
pPre_Latency[Loop].bCanvas.Font.Size: = 11 ;
pPre_Latency[Loop].bCanvas.Font.Style: = [fsBold];
pPre_Latency[Loop].bCanvas.Font.Color: = clBlack;
pPre_Latency[Loop].bCanvas.Brush.Color: = clWhite;
pPre_Latency[Loop].bCanvas.TextOut(cbPreStart.X,cbPreStart.Y,strHint);
pPre_Latency[Loop].DrawSelf();
pPre_Latency[Loop].Free();
end;
end;

procedureTC_Compare.Draw_Balance;
var
Loop:Integer;
begin
cBalance: = TC_Balance.Create();
cBalance.bWeightA: = 0 ;
cBalance.bWeightB: = 0 ;
for Loop: = 0 tocbCount - 1 do
begin
cBalance.bWeightA: = cBalance.bWeightA + cBallPartA[Loop].Weight;
cBalance.bWeightB: = cBalance.bWeightB + cBallPartB[Loop].Weight;
end;
cBalance.bMainPivot: = cbPivot;
cBalance.bPivotColor: = clFuchsia;
cBalance.bColor: = clBlue;
cBalance.bWidth: = 100 ;
cBalance.bHeight: = 18 ;
cBalance.bCanvas: = cCanvas;
cBalance.DrawSelf();
cbPPartA: = cBalance.bPartAPivot;
cbPPartB: = cBalance.bPartBPivot;
cBalance.Free();
end;

procedureTC_Compare.Draw_Latency;
const
strHint = ' 比较后： ' ;
var
Loop:Integer;
begin
SetLength(pFro_Latency,cbCmpPara.Fro_LNumber);
// SetLength(cbCmpPara.Fro_Latency,cbCmpPara.Fro_LNumber);
// 注意:下面Pre_Latency不能用Fro_Latency来代替,不知道为什么2003-11-20
SetLength(cbCmpPara.Pre_Latency,cbCmpPara.Fro_LNumber);
for Loop: = 0 tocbCmpPara.Fro_LNumber - 1 do
begin
pFro_Latency[Loop]: = TC_Ball_Class.Create(isShowTrace);
pFro_Latency[Loop].bAbstractBall: = cbCmpPara.Fro_Latency[Loop];
pFro_Latency[Loop].bSize: = 10 ;
pFro_Latency[Loop].bStartPoint: = Point( 80 + cbFroStart.X + Loop * 25 ,cbFroStart.Y);
pFro_Latency[Loop].SetBgAndTextColor(clGreen,clYellow);
pFro_Latency[Loop].bCanvas: = cCanvas;
pFro_Latency[Loop].bCanvas.Font.Size: = 11 ;
pFro_Latency[Loop].bCanvas.Font.Style: = [fsBold];
pFro_Latency[Loop].bCanvas.Font.Color: = clBlack;
pFro_Latency[Loop].bCanvas.Brush.Color: = clWhite;
pFro_Latency[Loop].bCanvas.TextOut(cbFroStart.X,cbFroStart.Y,strHint);
pFro_Latency[Loop].DrawSelf();
pFro_Latency[Loop].Free();
end;
end;

procedureTC_Compare.Draw_Part_A;
var
Loop,r:Integer;
begin
SetLength(pPartA,cbCount);
for Loop: = 0 tocbCount - 1 do
begin
pPartA[Loop]: = TC_Ball_Class.Create(isShowTrace);
pPartA[Loop].bAbstractBall.Order: = cBallPartA[Loop].Order;
pPartA[Loop].bAbstractBall.Weight: = cBallPartA[Loop].Weight;
pPartA[Loop].bSize: = 10 ;
pPartA[Loop].SetBgAndTextColor(clYellow,clRed);
pPartA[Loop].bCanvas: = cCanvas;
// 注意:此句一定要有,设置字体的大小属性
pPartA[Loop].bCanvas.Font.Size: = pPartA[Loop].bSize;
if pPartA[Loop].bCanvas.TextWidth(IntToStr(pPartA[Loop].bAbstractBall.Order)) >
pPartA[Loop].bCanvas.TextHeight(IntToStr(pPartA[Loop].bAbstractBall.Order))then
r: = pPartA[Loop].bCanvas.TextWidth(IntToStr(pPartA[Loop].bAbstractBall.Order))
else
r: = pPartA[Loop].bCanvas.TextHeight(IntToStr(pPartA[Loop].bAbstractBall.Order));
r: = r * 1414 div 1000 ;
// 下面的计算公式有点难
pPartA[Loop].bStartPoint.X: = cbPPartA.X - (cbCountdiv 2 ) * r - r * 5 * (cbCountmod 2 )div 10 + Loop * r;
pPartA[Loop].bStartPoint.Y: = cbPPartA.Y - r;
pPartA[Loop].DrawSelf();
pPartA[Loop].Free();
end;

end;

procedureTC_Compare.Draw_Part_B;
var
Loop,r:Integer;
begin
SetLength(pPartb,cbCount);
for Loop: = 0 tocbCount - 1 do
begin
pPartB[Loop]: = TC_Ball_Class.Create(isShowTrace);
pPartB[Loop].bAbstractBall.Order: = cBallPartB[Loop].Order;
pPartB[Loop].bAbstractBall.Weight: = cBallPartB[Loop].Weight;

pPartB[Loop].bSize: = 10 ;
pPartB[Loop].SetBgAndTextColor(clYellow,clRed);
pPartB[Loop].bCanvas: = cCanvas;
pPartB[Loop].bCanvas.Font.Size: = pPartB[Loop].bSize;
if pPartB[Loop].bCanvas.TextWidth(IntToStr(pPartB[Loop].bAbstractBall.Order)) >
pPartB[Loop].bCanvas.TextHeight(IntToStr(pPartB[Loop].bAbstractBall.Order))then
r: = pPartB[Loop].bCanvas.TextWidth(IntToStr(pPartB[Loop].bAbstractBall.Order))
else
r: = pPartB[Loop].bCanvas.TextHeight(IntToStr(pPartB[Loop].bAbstractBall.Order));
r: = r * 1414 div 1000 ;
pPartB[Loop].bStartPoint.X: = cbPPartB.X - (cbCountdiv 2 ) * r - r * 5 * (cbCountmod 2 )div 10 + Loop * r;
pPartB[Loop].bStartPoint.Y: = cbPPartB.Y - r;
pPartB[Loop].DrawSelf();
pPartB[Loop].Free();
end;
end;

procedureTC_Compare.Weigh_Out();
begin
Draw_Balance();
Draw_Part_A();
Draw_Part_B();
end;



procedureBalance_One_Compare(
BalancePivot:TPoint;
BallNum:Byte;
PartA,PartB:arrayofTC_Ball;
ACanvas:TCanvas;
bTrace:Boolean);
var
OneCmp:TC_Compare;
Loop:Integer;
begin
OneCmp: = TC_Compare.Create(bTrace);
OneCmp.cbPivot: = BalancePivot;
OneCmp.cbCount: = BallNum;
OneCmp.cCanvas: = ACanvas;
SetLength(OneCmp.cBallPartA,OneCmp.cbCount);
SetLength(OneCmp.cBallPartB,OneCmp.cbCount);
for Loop: = 0 toOneCmp.cbCount - 1 do
begin
OneCmp.cBallPartA[Loop]: = PartA[Loop];
OneCmp.cBallPartB[Loop]: = PartB[Loop];
end;
OneCmp.Weigh_Out();
OneCmp.Free();
end;

procedureBalance_One_Latency(
BallStart1,BallStart2:TPoint;
OneCmpPara:TC_CmpPara;
ACanvas:TCanvas;
bTrace:Boolean);
var
OneCmp:TC_Compare;
begin
OneCmp: = TC_Compare.Create(bTrace);
OneCmp.cCanvas: = ACanvas;
OneCmp.cbCmpPara: = OneCmpPara;
OneCmp.cbPreStart: = BallStart1;
OneCmp.cbFroStart: = BallStart2;
OneCmp.Draw_AllBall();
OneCmp.Draw_Latency();
OneCmp.Free();
end;

// 问题条件设置处理算法(小于的初始状态演示算法)
procedureProcess_Initial_Ball(
StartPoint:TPoint;
AllBall:arrayofTC_Ball;
ACanvas:TCanvas;
bTrace:Boolean);
const
// strHint='初始状态：';
strHint = '' ;
var
Loop:Integer;
aBall:TC_Ball_Class;
begin
for Loop: = Low(AllBall)toHigh(AllBall) - 1 do
begin
aBall: = TC_Ball_Class.Create(bTrace);
aBall.bAbstractBall: = AllBall[Loop + 1 ];
aBall.bSize: = 10 ;
aBall.bStartPoint: = Point( 2 + StartPoint.X + Loop * 25 ,StartPoint.Y);
aBall.bCanvas: = ACanvas;
aBall.bCanvas.Font.Size: = 11 ;
aBall.bCanvas.Font.Style: = [fsBold];
aBall.bCanvas.Font.Color: = clBlack;
aBall.bCanvas.Brush.Color: = clWhite;
aBall.bCanvas.TextOut(StartPoint.X,StartPoint.Y,strHint);
aBall.DrawSelf();
aBall.Free();
end;
end;

end.

6、 界面源码

... {
作品名称:小球问题通用解决方案
开发作者:成晓旭
开发时间:2003年01月21日
完成时间:2003年01月22日
修改时间1:2003年02月10日新增Delphi绘图功能
修改时间2:2003年11月14日新增对问题模拟条件的用户设置功能
修改时间2:2003年11月20日新增ClearCanvas()方法,解决不能清除画面问题
}
unitBMain;

interface

uses
Windows,Messages,SysUtils,Variants,Classes,Graphics,Controls,Forms,
Dialogs,StdCtrls,BallType,Common,Buttons,ExtCtrls;
type
TExceptStyle = (esLight,esHeavy); // 偏轻偏重
const
strHint = ' 中国 ' ;
BallNumber = 12 ; // 小球数量
BallValue = 10 ; // 正常小球的质量
HeavyValue = 15 ; // 偏重小球的质量
LightValue = 5 ; // 偏轻小球的质量

type
TfrmMain = class (TForm)
btnDemo:TButton;
imgMain:TImage;
gbConfig:TGroupBox;
RadioButton1:TRadioButton;
RadioButton2:TRadioButton;
RadioButton3:TRadioButton;
RadioButton4:TRadioButton;
RadioButton5:TRadioButton;
RadioButton6:TRadioButton;
RadioButton7:TRadioButton;
RadioButton8:TRadioButton;
RadioButton9:TRadioButton;
RadioButton10:TRadioButton;
RadioButton11:TRadioButton;
RadioButton12:TRadioButton;
ImgConfig:TImage;
cbEStyle:TCheckBox;
Label1:TLabel;
Memo0:TMemo;
Label2:TLabel;
Label3:TLabel;
Memo1:TMemo;
Label4:TLabel;
Memo2:TMemo;
Label5:TLabel;
Memo3:TMemo;
btnSetNumber:TButton;
btnAuto:TButton;
btnAbout:TButton;
Label6:TLabel;
cbTrance:TCheckBox;
procedureFormShow(Sender:TObject);
procedureRadioButton1Click(Sender:TObject);
procedurebtnDemoClick(Sender:TObject);
procedureFormCreate(Sender:TObject);
procedurebtnSetNumberClick(Sender:TObject);
procedurebtnAutoClick(Sender:TObject);
procedurebtnAboutClick(Sender:TObject);
private
... {Privatedeclarations}
isTrance:Boolean; // 是否跟踪(cbTrance的状态记录)
SmallBall:array[ 0 ..BallNumber]ofTC_Ball; // 小球的抽象数据
ExceptBall:TC_Ball; // 异常小球
ExceptStyle:TExceptStyle; // 异常小球的特性
ExceptBallValue:Integer; // 异常小球的质量
ExceptColor:TColor; // 异常小球的表示颜色
// 处理小球问题条件设置RadioGroup
functionProcessRadioButton(isSort:Boolean):Integer;
// 选择异常小球方法
procedureChooseExceptBall();
// 绘制所有小球方法
// withExceptBall=true<有异常小球的绘制>
// withExceptBall=false<无异常小球的绘制>
procedureDrawSmallBall(withExceptBall:Boolean;isTrance:Boolean);
procedureClearCanvas
(aCanvas:TCanvas);
public
... {Publicdeclarations}
end;

var
frmMain:TfrmMain;

implementation


... {$R*.dfm}
// 单元内部常量定义
const
Soft_Name = ' 小球问题解答过程演示程序0.2版 ' ;
strWaitHint = ' 本功能正在加紧完善中...... ' + CHR( 13 ) + CHR( 10 ) +
' 请拭目以待！ ' ;
strSetNumber = ' 设置[3-12]的小球数目，程序将自动演示问题的解答过程！ '
+ CHR( 13 ) + CHR( 10 ) + strWaitHint;
strAutoAnswer = ' 设置任意数目的小球，程序将根据本题的问题模式， '
+ ' 推算最少的比较次数，并自动演示推算过程！ '
+ CHR( 13 ) + CHR( 10 ) + strWaitHint;
About_Soft_Info = Soft_Name + CHR( 13 ) + CHR( 10 ) +
' 开发作者：成晓旭 ' + CHR( 13 ) + CHR( 10 ) +
' 完成时间：2003年01月23日 ' + CHR( 13 ) + CHR( 10 ) +
' 最后修改：2003年11月20日 ' + CHR( 13 ) + CHR( 10 ) +
' 联系方式：CXXSoft@163.com ' + CHR( 13 ) + CHR( 10 ) +
' 设计说明：本程序采用纯面向对象的分析、设计、实现。 ' +
' 也是本人的第一个运用 ' +
' 设计模式的作品。 ' + CHR( 13 ) + CHR( 10 ) +
' 发布说明：程序完成时，我将公布其源码<欢迎来信索取>。 ' ;
functionTfrmMain.ProcessRadioButton(isSort:Boolean):Integer;
const
space = 25 ;
var
aCtrl:TControl;
aChoose:TRadioButton;
// 点击的小球索引号,循环计数器,第一个RadioButton的Top属性,GroupBox中RadioCount的计数器(关键)
indexBall,I,aTop,RadioCount:Integer;
begin
indexBall: = - 1 ;
aTop: = 0 ;
RadioCount: = 0 ; // 注意:此处初值=-1是错误的
for I: = 0 togbConfig.ControlCount - 1 do
begin
aCtrl: = gbConfig.Controls[I];
if aCtrl.ClassType = TRadioButtonthen
begin
try
Inc(RadioCount);
aChoose: = TRadioButton(aCtrl);
if isSortthen
begin
if indexBall = - 1 then
aTop: = aChoose.Top
else
aChoose.Top: = aTop;
aChoose.Left: = (RadioCount - 1 ) * space + 8 ;
end
else
begin
if aChoose.Checkedthen
begin
indexBall: = RadioCount;
// ShowMessage('IndexBall='+IntToStr(indexBall));
break ; // 算法效率之关键
end;
end;
except

end;
end;
end;
Result: = indexBall;
end;

procedureTfrmMain.FormShow(Sender:TObject);
begin
ProcessRadioButton( true );
DrawSmallBall( false ,cbTrance.Checked);
end;

procedureTfrmMain.ChooseExceptBall();
var
index:Integer;
begin
index: = ProcessRadioButton( false );
if (index >= 0 )and(index <= BallNumber)then
ExceptBall: = SmallBall[index];
if cbEStyle.Checkedthen
begin
ExceptStyle: = esHeavy;
ExceptBallValue: = HeavyValue;
ExceptColor: = clRed;
end
else
begin
ExceptStyle: = esLight;
ExceptBallValue: = LightValue;
ExceptColor: = clFuchsia;
end;
ExceptBall.Weight: = ExceptBallValue;
ExceptBall.BgColor: = ExceptColor;
ExceptBall.TextColor: = clBlack;
SmallBall[index]: = ExceptBall;
end;

procedureTfrmMain.DrawSmallBall(withExceptBall:Boolean;isTrance:Boolean);
var
Loop:Integer;
begin
for Loop: = 1 toBallNumber do
begin
SmallBall[Loop].Order: = Loop;
SmallBall[Loop].Weight: = BallValue;
SmallBall[Loop].BgColor: = clBlue;
SmallBall[Loop].TextColor: = clRed;
end;
if withExceptBallthen
begin
ChooseExceptBall();
end;

Draw_Ball_Config(SmallBall,ImgConfig.Canvas,ClientRect,isTrance);
end;


procedureTfrmMain.RadioButton1Click(Sender:TObject);
begin
try
isTrance: = cbTrance.Checked;
except
isTrance: = NOTisTrance;
end;;
DrawSmallBall( true ,isTrance);
btnDemo.SetFocus();
end;

procedureTfrmMain.btnDemoClick(Sender:TObject);
begin
Serach_Error_Ball(SmallBall,imgMain.Canvas,ClientRect,isTrance);
Memo1.Lines.Text: = strLog1;
Memo2.Lines.Text: = strLog2;
Memo3.Lines.Text: = strLog3;
end;

procedureTfrmMain.FormCreate(Sender:TObject);
begin
// Width:=Screen.Width;
// Height:=Screen.Height;
Width: = 800 ;
Height: = 600 ;
Caption: = Soft_Name;
end;

procedureTfrmMain.ClearCanvas(aCanvas:TCanvas);
begin
aCanvas.Brush.Style: = bsSolid;
aCanvas.Brush.Color: = clWhite;
aCanvas.FillRect(ClientRect);
end;

procedureTfrmMain.btnSetNumberClick(Sender:TObject);
begin
Application.MessageBox(strSetNumber,Soft_Name,MB_ICONINFORMATION);
end;

procedureTfrmMain.btnAutoClick(Sender:TObject);
begin
Application.MessageBox(strAutoAnswer,Soft_Name,MB_ICONINFORMATION);
end;

procedureTfrmMain.btnAboutClick(Sender:TObject);
begin
Application.MessageBox(About_Soft_Info,Soft_Name,MB_ICONINFORMATION);
end;

end.