经典面试问题：12小球问题算法(源码)

(文档请参考：http://blog.csdn.net/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);

ifA2=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;
withbCmpParado
begin
Pre_LNumber:=4;
Fro_LNumber:=1;
SetLength(Pre_Latency,Pre_LNumber);
SetLength(Fro_Latency,Fro_LNumber);
forLoop:=0toPre_LNumber-1do
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);

ifA3=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;
ifA2>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);

ifA3=B3then
begin
vErr_Ball_Order:=A[3];
vIsHeavy:=A2<B2;
end
else
begin
ifA2>B2then
begin
ifA3>B3then
vErr_Ball_Order:=A[1]
else
vErr_Ball_Order:=A[2];
//IsHeavy:=True;
end
else
begin
ifA3>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);
ifA2=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);

ifA3=B3then
begin
vErr_Ball_Order:=A[4];
vIsHeavy:=IsAdyB;
end
else
begin
ifIsAdyBthen
begin
ifA3>B3then
vErr_Ball_Order:=B[4]
else
vErr_Ball_Order:=B[3];
//IsHeavy:=NOTIsAdyB;
end
else
begin
ifA3>B3then
vErr_Ball_Order:=B[3]
else
vErr_Ball_Order:=B[4];
//IsHeavy:=NOTIsAdyB;
end;
vIsHeavy:=NOTIsAdyB;
end;
end
else
begin
ifA2>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);
ifA3=B3then
begin
vErr_Ball_Order:=B[2];
vIsHeavy:=NOTIsAdyB;
end
elseifA2>B2then
begin
ifA3>B3then
vErr_Ball_Order:=A[1]
else
vErr_Ball_Order:=A[2];
vIsHeavy:=IsAdyB;
end
elseifA2<B2then
begin
ifA3>B3then
vErr_Ball_Order:=A[2]
else
vErr_Ball_Order:=A[1];
vIsHeavy:=IsAdyB;
end;
end
elseif((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);
ifA3=B3then
begin
vErr_Ball_Order:=B[1];
vIsHeavy:=NOTIsAdyB;
end
elseifA3>B3then
begin
ifIsAdyBthen
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
ifIsAdyBthen
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;
forLoop:=1to4do
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;
forLoop:=5to8do
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);
forLoop:=0tobNumber-1do
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);

ifA=Bthen
begin
strLog1:=strLog1+strAXDB;
str:=proHead;
forLoop:=1to4do
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;
forLoop:=1to8do
BufT[Loop]:=AllBall[Loop].Order;
withbCmpParado
begin
Pre_LNumber:=12;
Fro_LNumber:=4;
SetLength(Pre_Latency,Pre_LNumber);
SetLength(Fro_Latency,Fro_LNumber);
forLoop:=0toPre_LNumber-1do
Pre_Latency[Loop]:=AllBall[Loop+1];
forLoop:=0toFro_LNumber-1do
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);

ifSearchBall_At4(AllBall,BufC,BufT,bOrder,bHeavy,ACanvas,bShowTrace)then
begin
FoundBall.Ball:=AllBall[bOrder];
FoundBall.IsHeavy:=bHeavy;
ifFoundBall.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
ifA>Bthen
strLog1:=strLog1+strADYB
else
strLog1:=strLog1+strAXYB;
str:=proHead;
forLoop:=1to8do
str:=str+IntToStr(AllBall[Loop].Order)+',';
str:=str+']'+preTail1+'【排4余8】';
strLog1:=strLog1+str;
forLoop:=1to4do
begin
BufA[Loop]:=AllBall[Loop].Order;
BufB[Loop]:=AllBall[4+Loop].Order;
BufG[Loop]:=AllBall[8+Loop].Order;
end;
withbCmpParado
begin
Pre_LNumber:=12;
Fro_LNumber:=4;
SetLength(Pre_Latency,Pre_LNumber);
SetLength(Fro_Latency,Fro_LNumber);
forLoop:=0toPre_LNumber-1do
Pre_Latency[Loop]:=AllBall[Loop+1];
forLoop:=0toFro_LNumber-1do
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);

ifSearchBall_At8(AllBall,A>B,BufA,BufB,BufG,bOrder,bHeavy,ACanvas,bShowTrace)then
begin
FoundBall.Ball:=AllBall[bOrder];
FoundBall.IsHeavy:=bHeavy;
ifFoundBall.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
withaCanvasdo
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
ifbDrawOrderthen
strDrawText:=IntToStr(bAbstractBall.Order)
else
strDrawText:=IntToStr(bAbstractBall.Weight);
ifbColorChangedthen
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);
ifw>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*1414div1000,bStartPoint.Y+r*1414div1000);
if(Length(strDrawText)=1)then
bCanvas.TextOut(bStartPoint.X+r*414div1000,bStartPoint.Y+r*207div1000,strDrawText)
elseif(Length(strDrawText)=2)then
bCanvas.TextOut(bStartPoint.X+r*214div1000,bStartPoint.Y+r*228div1000,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
withACanvasdo
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;
ifbWeightA>bWeightBthen//[A>B]
bDelta:=bDelta
elseifbWeightA=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,Ddiv2,H,0);
X2:=X0+D+H;
Y2:=Y0-H-bDelta;
DrawTray(bCanvas,X2,Y2,Ddiv2,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);
forLoop:=0tocbCmpPara.Pre_LNumber-1do
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;
forLoop:=0tocbCount-1do
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);
forLoop:=0tocbCmpPara.Fro_LNumber-1do
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);
forLoop:=0tocbCount-1do
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;
ifpPartA[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*1414div1000;
//下面的计算公式有点难
pPartA[Loop].bStartPoint.X:=cbPPartA.X-(cbCountdiv2)*r-r*5*(cbCountmod2)div10+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);
forLoop:=0tocbCount-1do
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;
ifpPartB[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*1414div1000;
pPartB[Loop].bStartPoint.X:=cbPPartB.X-(cbCountdiv2)*r-r*5*(cbCountmod2)div10+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);
forLoop:=0toOneCmp.cbCount-1do
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
forLoop:=Low(AllBall)toHigh(AllBall)-1do
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
forI:=0togbConfig.ControlCount-1do
begin
aCtrl:=gbConfig.Controls[I];
ifaCtrl.ClassType=TRadioButtonthen
begin
try
Inc(RadioCount);
aChoose:=TRadioButton(aCtrl);
ifisSortthen
begin
ifindexBall=-1then
aTop:=aChoose.Top
else
aChoose.Top:=aTop;
aChoose.Left:=(RadioCount-1)*space+8;
end
else
begin
ifaChoose.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];
ifcbEStyle.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
forLoop:=1toBallNumberdo
begin
SmallBall[Loop].Order:=Loop;
SmallBall[Loop].Weight:=BallValue;
SmallBall[Loop].BgColor:=clBlue;
SmallBall[Loop].TextColor:=clRed;
end;
ifwithExceptBallthen
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.