读书时,饭间看青年报,上面每期都有9*9的九宫阵.心血来潮,编写了matlab程序,将之求解完毕.

输入数据为9*9的数组.

思路是,首先根据规则,确定每个方格中可能值,首先确定唯一可能值,进行试探时,也选取可能性小的那个方格进行处理.走不通时,退栈,更新数值,重新试探.

程序源代码如下:(很多有些记不清楚了)

function [JGTNData]=JGZ()
clear;
JGZ=zeros(9,9);
AllData(1:9)=3;
JGTData=zeros(9,9,11);
for i=1:9
    for j=1:9
        for k=1:9
            JGTData(i,j,k)=k;
        end
        JGTData(i,j,10)=9;
        JGTData(i,j,11)=0;
    end
end

   % Inputdata=[1,1,6;1,2,9;1,4,2;1,8,3;2,1,7;2,3,5;2,4,8;2,8,2;3,2,3;3,3,2;3,4,5;3,8,8;4,1,2;4,3,4;4,9,5;5,2,6;5,5,9;5,9,3;6,6,2;6,8,7;7,1,5;7,2,4;7,5,7;8,3,9;8,5,2;8,9,1;9,4,9;9,7,8]   ;
   %Inputdata=[1,1,8;1,4,1;1,5,4;1,7,7;2,1,7;2,6,8;2,8,1;2,9,6;3,4,6;3,5,9;3,8,8;3,9,3;4,2,5;4,5,2;5,1,3;6,3,8;6,6,4;6,8,6;6,9,5;7,3,5;7,9,2;8,1,4;9,2,2;9,4,9;9,5,1;9,7,8];
   %Inputdata=[1,3,6;1,5,2;1,7,7;1,8,8;2,2,1;2,4,9;2,6,7;2,9,6;3,6,6;3,7,3;4,2,9;4,4,8;5,3,4;5,5,6;5,8,2;6,1,2;6,6,1;6,7,8;6,8,9;7,3,3;7,8,5;8,2,4;8,4,2;8,9,8;9,1,1;9,4,6;9,6,5;9,7,4];
%   Inputdata=[1,1,6;1,4,8;2,1,5;2,8,2;3,6,5;3,7,1;4,1,3;4,6,2;4,8,8;4,9,7;5,3,2;5,4,7;5,7,3;5,9,9;6,2,4;6,5,3;6,9,6;7,1,7;7,4,4;7,5,9;7,7,6;8,2,6;8,5,5;8,6,8;8,8,7;9,3,5;9,5,1;9,9,4];
   Inputdata=[1,1,6;1,4,8;2,1,5;2,8,2;3,6,5;3,7,1;4,1,3;4,6,2;4,8,8;4,9,7;5,3,2;5,4,7;5,7,3;5,9,9;6,2,4;6,5,3;6,9,6;7,1,7;7,4,4;7,5,9;7,7,6;8,2,6;8,5,5;8,6,8;8,8,7;9,3,5;9,5,1;9,9,4];
    xsize=size(Inputdata);
    for i=1:xsize(1)
        tempi=Inputdata(i,1);
        tempj=Inputdata(i,2);
        JGZ(tempi,tempj)=Inputdata(i,3);
        AllData(JGZ(tempi,tempj))=AllData(JGZ(tempi,tempj))-1;
        JGTData(tempi,tempj,1:9)=0;
        JGTData(tempi,tempj,JGZ(tempi,tempj))=JGZ(tempi,tempj);
        JGTData(tempi,tempj,10)=1;
        JGTData(tempi,tempj,11)=JGZ(tempi,tempj);
    end

JGZ;
JGTData;

[JGZ1,JGTData1]=PDDJGT(JGZ,JGTData);
JGZ=JGZ1;
JGTData=JGTData1;

%%%%%%%%%%判断是否有可以确定的数
for i=1:9
    for j=1:9
        if JGTData(i,j,10)==1 & JGTData(i,j,11)==0%可以确定
            JGZ(i,j)=max(JGTData(i,j,1:9));
            JGTData(i,j,11)=JGZ(i,j);
        end
    end
end
JGZ;
JGTData(:,:,10);
%%%%%%%%

 

 

JGTPD=zeros(9,9);
while max(max(JGTPD~=JGTData(:,:,10)))
    JGTPD=JGTData(:,:,10);
    %%%%%%%%%%%第二次
    [JGZ1,JGTData1]=PDDJGT(JGZ,JGTData);
    JGZ=JGZ1;
    JGTData=JGTData1;

    %%%%%%%%%%判断是否有可以确定的数
    for i=1:9
        for j=1:9
            if JGTData(i,j,10)==1 & JGTData(i,j,11)==0%可以确定
                if max(JGTData(i,j,1:9))>0   %有错
                    JGZ(i,j)=max(JGTData(i,j,1:9));
                    JGTData(i,j,11)=JGZ(i,j);
                end
            end
        end
    end
    JGZ;
    JGTData(:,:,10);

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%加入一个试探值
NTData=1;
ForT=0;
TFT=0;%有无错
%xsize=find(JGTPD==2);
%xsize=xsize(1);
%while xsize
while NTData>=1 & ForT==0
    NTData=1;
    JGTN=1;
    JGTNData(JGTN,:,:)=zeros(9,9);
while max(max(JGTPD~=ones(9,9))) & TFT==0
 while max(max(JGTPD~=ones(9,9))) & TFT==0
    xsize=find(JGTPD==2);
    if xsize~=[]
    xsize=xsize(1);
   
    tempi=mod(xsize,9);
    if tempi==0
        tempi=9;
        tempj=floor(xsize/9);
    else
        tempj=floor(xsize/9)+1;
    end
    tempsize=find(JGTData(tempi,tempj,1:9)>0);
   
    TData(NTData,1:4)=[tempi,tempj,(JGTData(tempi,tempj,tempsize(1))),(JGTData(tempi,tempj,tempsize(2)))];%加入值同时保留另外一个值
    TAData(NTData,1:9,1:9,1:11)=JGTData;
    TAJGZ(NTData,1:9,1:9)=JGZ;
    JGZ(tempi,tempj)=TData(NTData,3); 
    JGTData(tempi,tempj,1:9)=0;
    JGTData(tempi,tempj,JGZ(tempi,tempj))=JGZ(tempi,tempj);
    JGTData(tempi,tempj,10)=1;
    JGTData(tempi,tempj,11)=JGZ(tempi,tempj);
    NTData=NTData+1;
    TFT=0;
    %%%%%%%%%%%%%重新判断
    JGTPD=zeros(9,9);
    while max(max(JGTPD~=JGTData(:,:,10)))
        JGTPD=JGTData(:,:,10);
        %%%%%%%%%%%第二次
        [JGZ1,JGTData1]=PDDJGT(JGZ,JGTData);
        JGZ=JGZ1;
        JGTData=JGTData1;

        %%%%%%%%%%判断是否有可以确定的数
        for i=1:9
            for j=1:9
                if JGTData(i,j,10)==1 & JGTData(i,j,11)==0%可以确定
                    if max(JGTData(i,j,1:9))>0   %有错
                        JGZ(i,j)=max(JGTData(i,j,1:9));
                        JGTData(i,j,11)=JGZ(i,j);
                    else
                        TFT=1;%有错
                    end
                end
            end
        end
        JGZ;
        JGTData(:,:,10);

    end%%%while
    if min(min(JGTPD))==0
        TFT=1;
    end
  else%%%%%%%%%%%无法填写
       TFT=1;%有错
  end
       
 end%%%%%while
 if TFT==1 %%因为有错退出
    if NTData>0
            NTData=NTData-1;
            tempi=TData(NTData,1);
            tempj=TData(NTData,2);
            for i=1:9
                for j=1:9
                    JGTData(i,j,1:11)=TAData(NTData,i,j,1:11);
                    JGZ(i,j)=TAJGZ(NTData,i,j);
                end
            end
%    JGTData=TAData(NTData,1:9,1:9,1:11);
    JGZ(tempi,tempj)=TData(NTData,4); 
    JGTData(tempi,tempj,1:9)=0;
    JGTData(tempi,tempj,JGZ(tempi,tempj))=JGZ(tempi,tempj);
    JGTData(tempi,tempj,10)=1;
    JGTData(tempi,tempj,11)=JGZ(tempi,tempj);
    JGTPD=JGTData(:,:,10);
    TFT=0;
 else
    JGTPD=ones(9,9);
 end%%if   
end%%%if

end%%%while
JGTNData(JGTN,:,:)=JGZ;
JGTN=JGTN+1;
if TFT==1 %%因为有错退出
    if NTData>1
            NTData=NTData-1;
            tempi=TData(NTData,1);
            tempj=TData(NTData,2);
            for i=1:9
                for j=1:9
                    JGTData(i,j,1:11)=TAData(NTData,i,j,1:11);
                    JGZ(i,j)=TAJGZ(NTData,i,j);
                end
            end
%    JGTData=TAData(NTData,1:9,1:9,1:11);
    JGZ(tempi,tempj)=TData(NTData,4); 
    JGTData(tempi,tempj,1:9)=0;
    JGTData(tempi,tempj,JGZ(tempi,tempj))=JGZ(tempi,tempj);
    JGTData(tempi,tempj,10)=1;
    JGTData(tempi,tempj,11)=JGZ(tempi,tempj);
    JGTPD=JGTData(:,:,10);
    TFT=0;
 else
    JGTPD=ones(9,9);
    ForT=1;
 end%%if   
end%%%if
JGTPD=zeros(9,9);
NTData;
JGZ;
end%%while NData==0

 

function [JGZ2,JGTData2]=PDDJGT(JGZ1,JGTData1)
%%%%%%%%%%%%%%%%%%%%%判断横
for i=1:9
    for j=1:9
        if JGZ1(i,j)>0 %有数据，清除其他中这个数据
            for k=1:9%横
                if j~=k
                    if JGTData1(i,k,JGZ1(i,j))>0
                        JGTData1(i,k,JGZ1(i,j))=0;
                        JGTData1(i,k,10)=JGTData1(i,k,10)-1;
                    end
                end
            end
            for k=1:9%列
                if i~=k
                    if JGTData1(k,j,JGZ1(i,j))>0
                        JGTData1(k,j,JGZ1(i,j))=0;
                        JGTData1(k,j,10)=JGTData1(k,j,10)-1;
                    end
                end
            end
            %%%%%%%%%%%%%%%%%%%%小格
            for i1=(ceil(i/3)-1)*3+1:(ceil(i/3)-1)*3+3
                for j1=(ceil(j/3)-1)*3+1:(ceil(j/3)-1)*3+3
                    if i1~=i & j1~=j
                        if JGTData1(i1,j1,JGZ1(i,j))>0
                            JGTData1(i1,j1,JGZ1(i,j))=0;
                            JGTData1(i1,j1,10)=JGTData1(i1,j1,10)-1;
                        end
                    end
                end
            end
        end
                  
       
    end

end
JGTData2=JGTData1;
    JGZ2=JGZ1;
end

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