图论模型---floyd算法

1、目标：最优路线规划。

2、Matlab程序：

tulun2.m
a= [ 0,50,inf,40,25,10;
     50,0,15,20,inf,25;
     inf,15,0,10,20,inf;
     40,20,10,0,10,25;
     25,inf,20,10,0,55;
     10,25,inf,25,55,0];
[D, path]=floyd(a)

floyd.m
function [D,path,min1,path1]=floyd(a,start,terminal)
D=a;n=size(D,1);path=zeros(n,n);
for i=1:n
   for j=1:n
      if D(i,j)~=inf
         path(i,j)=j;
      end, 
   end,
end
for k=1:n
   for i=1:n
      for j=1:n
         if D(i,k)+D(k,j)<D(i,j)
            D(i,j)=D(i,k)+D(k,j);
            path(i,j)=path(i,k);
         end, 
      end, 
   end,
end
if nargin==3
   min1=D(start,terminal);
   m(1)=start;
   i=1;
   path1=[ ];   
   while   path(m(i),terminal)~=terminal
      k=i+1;                                
      m(k)=path(m(i),terminal);
      i=i+1;
   end
   m(i+1)=terminal;
   path1=m;
end   

3、输入数据格式：

    [0     8   Inf   Inf   Inf   Inf     7     8   Inf   Inf   Inf;
   Inf     0     3   Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf;
   Inf   Inf     0     5     6   Inf     5   Inf   Inf   Inf   Inf;
   Inf   Inf   Inf     0     1   Inf   Inf   Inf   Inf   Inf    12;
   Inf   Inf     6   Inf     0     2   Inf   Inf   Inf   Inf    10;
   Inf   Inf   Inf   Inf     2     0     9   Inf     3   Inf   Inf;
   Inf   Inf   Inf   Inf   Inf     9     0   Inf   Inf   Inf   Inf;
     8   Inf   Inf   Inf   Inf   Inf   Inf     0     9   Inf   Inf;
   Inf   Inf   Inf   Inf     7   Inf   Inf     9     0     2   Inf;
   Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf     2     0     2;
   Inf   Inf   Inf   Inf    10   Inf   Inf   Inf   Inf   Inf     0;];