最小生成树 Matlab Code

function [wSum StartPos EndPos] = MST_JunH(W_Matrix, headPos)
% W_Matrix' = W_Matrix : 表示权值矩阵
% headPos : 表示树头在W_Matrix的位置
% wSum : 表示得到的最小生成树的权值总和

% CopyRight : JunH 20130411

[row col] = size(W_Matrix);
if row ~= col
    error(' W_Matrix 不是权值矩阵， 因为不是对称矩阵');
end

wSum = 0;
StartPos = [];
EndPos = [];
TEset =[];

TEset = [TEset headPos];
TVMinQuene = [];
TEEndMinQuene = [];
TEStartMinQuene = [];
for R=1:row
    if 0 == isValueInSet(TEset, R)
        [TVMinQuene TEStartMinQuene TEEndMinQuene] = insertMinQuene(TVMinQuene, TEStartMinQuene, TEEndMinQuene, W_Matrix(headPos, R), headPos, R);
    end
end

for R=2:row
    wSum = wSum + TVMinQuene(1, 1);
    StartPos = [StartPos TEStartMinQuene(1, 1)];
    EndPos = [EndPos TEEndMinQuene(1, 1)];
    TEset = [TEset TEEndMinQuene(1, 1)];
   
    [TVMinQuene TEStartMinQuene TEEndMinQuene] = clearMinQuene(TVMinQuene, TEStartMinQuene, TEEndMinQuene, TEset(1, size(TEset, 2)));
    for RR=1:row
        if 0 == isValueInSet(TEset, RR)
            [TVMinQuene TEStartMinQuene TEEndMinQuene] = insertMinQuene(TVMinQuene, TEStartMinQuene, TEEndMinQuene, W_Matrix(TEset(1, size(TEset, 2)), RR), TEset(1, size(TEset, 2)), RR);
        end
    end
end
end

function [boolean] = isValueInSet(set, value)
boolean = 0;
len = size(set, 2);
for R=1:len
    if value == set(1, R)
        boolean = 1;
        break;
    end
end
end

function [TTVMinQuene TTEStartMinQuene TTEEndMinQuene] = clearMinQuene(TVMinQuene, TEStartMinQuene, TEEndMinQuene, Pos)
    len = size(TEEndMinQuene, 2);
    TTVMinQuene = [];
    TTEStartMinQuene = [];
    TTEEndMinQuene = [];
    for R=1:len
        if TEEndMinQuene(1, R) ~= Pos
            TTVMinQuene = [TTVMinQuene TVMinQuene(1, R)];
            TTEStartMinQuene = [TTEStartMinQuene TEStartMinQuene(1, R)];
            TTEEndMinQuene = [TTEEndMinQuene TEEndMinQuene(1, R)];
        end
    end
end

function [TVMinQuene TEStartMinQuene TEEndMinQuene] = insertMinQuene(TVMinQuene, TEStartMinQuene, TEEndMinQuene, value, startPos, endPos)
% 保持从小到大
len = size(TVMinQuene, 2);
for R=1:len
    if value < TVMinQuene(1, R)
        prior = TVMinQuene(1, 1:R-1);
        after = TVMinQuene(1, R:len);
        TVMinQuene = [prior value after];
       
        priorES = TEStartMinQuene(1, 1:R-1);
        afterES = TEStartMinQuene(1, R:len);
        TEStartMinQuene = [priorES startPos afterES];
       
        priorEE = TEEndMinQuene(1, 1:R-1);
        afterEE = TEEndMinQuene(1, R:len);
        TEEndMinQuene = [priorEE endPos afterEE];
        return;
    end
end

TVMinQuene = [TVMinQuene value];
TEStartMinQuene = [TEStartMinQuene startPos];
TEEndMinQuene = [TEEndMinQuene endPos];
end

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%最小生成树kruskal源程序

%c:原图的邻接矩阵

%v0:根节点

%c1:最小生成树的邻接矩阵

function c1=Krusk(c,v0)

[X,Y]=size(c);

if X~=Y

error('输入必须为方阵')

end

if v0>length(c(1,:))

error('不存在该顶点')

end

N=length(c(:,1));

con=0;

c(find(c==0))=inf;

c1=zeros(N,N);

comp=zeros(N,N);

comp(:,1)=[1:N]';

while con

clear min0;

min0=min(min(c));

[x,y]=find(c==min0);

X=x(1);

Y=y(1);

c(X,Y)=inf;

[i1,j1]=find(comp==X);

[i2,j2]=find(comp==Y);

if i1==i2

continue

else

l1=length(find(comp(i1,:)~=0));

l2=length(find(comp(i2,:)~=0));

comp(i1,[l1+1:l1+l2])=comp(i2,[1:l2]);

comp(i2,:)=0;

c1(X,Y)=min0;

con=con+1;

end

end

c1=c1';

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function [T,WT]=prim(A)

%Prim法求最小生成树

%A为无向图G={V，E}的权矩阵;

%T为A的最小生成树的权矩阵，WT为其权值。

n=length(A);

A(find(A==0))=inf;

T=zeros(n);WT=0;

V=2:n;%未通过点的集合

V1=1;%通过点的初始集合

p=1;%记录通过点的个数.

i=1;[y,k]=min(A(i,:));%{从以1为一个端点，以V中的点为另一个端点的所有边中，找出权值最小的边%}

p=p+1;V1(p)=k;%将找到的点加到V1中

V(k-1)=[];T(i,k)=y;T(k,i)=y;%将找到的点从V中删去，并把相应边加到T中。

WT=WT+y;A(i,k)=inf;A(k,i)=inf;

while p

   s=1;

for i=V1  %找出临跨V1和V的权值最小的边

   y(s)=min(A(i,V));s=s+1;

end

y=min(y);%y为找出的最小权值

for i=V1 %找出与y相关联的两个点

   for j=V

       if(A(i,j)==y)T(i,j)=y;T(j,i)=y;A(i,j)=inf;A(j,i)=inf;WT=WT+y;

        p=p+1;V1(p)=j;%将点加到V1中

        V(find(V==j))=[];%将通过点从V中删掉

       end

       break;end;end;end

end

可以在MATLAB中输入以下命令进行检验：

A=[inf 4 15 inf 7 inf 28;4 inf 9 inf infinf inf;15 9 inf 25 5 inf inf;inf inf 25 inf 32 16 12;7 inf 5 32 inf inf 30;infinf inf 16 inf inf 20;28 inf inf 12 30 20 inf]；

[T,WT]=prim(A)