📄 12345.m
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clear
a=[61 53 47 56 52 44 53 55 55 41 44 59 47 47 53 52;
61 58 44 57 52 47 52 57 55 41 38 55 41 44 52 52;
61 58 44 57 52 47 52 57 55 41 38 55 41 44 52 52;
60 57 39 57 51 54 51 57 60 48 51 57 45 54 51 51;
60 57 39 57 51 54 51 57 60 48 51 57 45 54 51 51;
58 52 41 54 50 47 50 54 55 44 47 55 44 50 50 50;
58 52 41 54 50 47 50 54 55 44 47 55 44 50 50 50;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];
a1=max(max(a'));
% 第一步
a=abs(a-a1);
b=a; %b表示始矩
mina=min(a');
for row =1:16 %row表示行
for col =1:16 %col表示列
a(row,col)=a(row,col)-mina(row) ;
end
end
mina=min(a);
for col =1:16 %col表示列
for row =1:16 %row表示行
a(row,col)=a(row,col)-mina(row) ;
end
end
%初始化标矩阵
zerobznum=0;
for row=1:16
for col =1:16
if a(row,col)~=0
bz(row,col)=3;
else
bz(row,col)=0;
zerobznum=zerobznum+1;
end
end
end
% 第2步：求最优解
while zerobznum>0
for row =1:16 %row表示行
zeronum=0; %zeronum表示每行0的个数
zerocol=0;
for col =1:16 %col表示列
if a(row,col)==0
zeronum=zeronum+1;
zerocol=col;
end
end
if zeronum==1
bz(row,zerocol)=1;
a(row,zerocol)=1;
zerobznum=zerobznum-1;
for rowbz=1:16
if a(rowbz,zerocol)==0 & rowbz~=row
bz(rowbz,zerocol)=-1; %如果该列有0则划去
a(rowbz,zerocol)=-1;
zerobznum=zerobznum-1;
end
end
end
end
for col =1:16 %col表示列
zeronum=0; %zeronum表示每列0的个数
zerorow=0;
for row =1:16 %row表示行
if a(row,col)==0 & bz(row,col)~=1
zeronum=zeronum+1;
zerorow=row;
end
end
if zeronum==1
bz(zerorow,col)=1;
a(zerorow,col)=1;
zerobznum=zerobznum-1;
for colbz=1:16
if a(zerorow,colbz)==0 & colbz~=col & a(zerorow,colbz)~=1
bz(zerorow,colbz)=-1; %如果该列有0则划去
a(zerorow,colbz)=-1;
zerobznum=zerobznum-1;
end
end
end
end
%如果zerobznum>=0
%求出0个数最少的行
if zerobznum>0
zerorownum1=zeros(1,16)
for row=1:16
zerorownum0=0;
for col=1:16
if a(row,col) ==0
zerorownum0=zerorownum0+1;
end
end
if zerorownum0>=2
zerorownum1(1,row)=zerorownum0;
end
end
mi=99999;
mr=0;
for r=1:16
if zerorownum1(r)~=0 zerorownum1(r)<mi
mi=zerorownum1(r) ;
mr=r ;%0最少的行
end
end
zerocolnum1=zeros(1,16)
for c=1:16
if a(mr,c)==0
n=0 %该列0的个数
for r=1 :16
if a(c,r)==0
n=n+1;
end
end
zerocolnum1(1,c)=n;
end
end
mm=99999;
mc=0;
for i=1:16
if zerocolnum1(i)~=0 zerocolnum1(i)<mm
mm=zerorownum1(r) ;
mc=i ;%0最少的行
end
end
%把该行该列上的作标记
bz(mr,mc)=1;
a(mr,mc)=1;
zerobznum=zerobznum-1;
%划掉行
for i=1:16
if a(mr,i)==0
bz(mr,i)=-1;
a(mr,i)=-1 ;
zerobznum=zerobznum-1;
end
end
%划掉列
for i=1:16
if a(i,mc)==0
bz(i,mc)=-1;
a(i,mc)=-1 ;
zerobznum=zerobznum-1;
end
end
zerorownum1=zeros(1,16) ;
end
end
%第三步
azeronum=0;
for row=1:16
for col=1:16
if bz(row,col)==1
azeronum=azeronum+1;
end
end
end
%如果0原索的个数等于系数矩阵的阶乘，本题为7那么帮助bz就是最优解
if azeronum==7
bz
else
%第三步的程序
grow=zeros(1,16);
gcol=zeros(1,16);
for row=1:16
growbz=0;
for col=1:16
if bz(row,col)==1
growbz=growbz+1;
end
end % growbz=growbz+1;
if growbz~=1
grow(1,row)=1 ;
for icol=1:16
if bz(row,icol) ==-1
gcol(1,icol)=1 ;
for irow=1:16
if bz(irow,icol)==1
grow(1,irow)=1;
end
end
end
end
end
end
end
%第四步
%还员a
for row=1:16
for col=1:16
if a(row,col)==1 || a(row,col)==-1
a(row,col)=0;
end
end
end
%找出没划线的最小直
min4=99999;
for row=1:16 %
if grow(row)==1
for col=1:16
if gcol(col)==0 & min4>a(row,col)
min4=a(row,col) ;
end
end
end
end
%行减最小直
for row=1:16
if grow(1,row)==1
for col=1:16
a(row,col)=a(row,col)-min4 ;
end
end
end
%列家最小直
for col=1:16
if gcol(1,col)==1
for row=1:16
a(row,col)=a(row,col)+min4 ;
end
end
end ⌨️ 快捷键说明
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