lingo最小生成树问题代码

最小生成树：
MODEL:
sets:
cities/1..10/:level; !level(i)= the level of city;
link(cities, cities):
distance, !The distance matrix;
x; ! x(i,j)=1 if we use link i,j;
endsets
data: !Distance matrix, it need not be symmetirc;
distance = 0 8 5 9 12 14 12 16 17 22
8 0 9 15 16 8 11 18 14 22
5 9 0 7 9 11 7 12 12 17
9 15 7 0 3 17 10 7 15 15
12 16 9 3 0 8 10 6 15 15
14 8 11 17 8 0 9 14 8 16
12 11 7 10 10 9 0 8 6 11
16 18 12 7 6 14 8 0 11 11
17 14 12 15 15 8 6 11 0 10
22 22 17 15 15 16 11 11 10 0;
enddata
n=@size(cities); !The model size;
! Minimize total distance of the links;
min=@sum(link(i,j)|i #ne# j: distance(i,j)*x(i,j));
!There must be an arc out of city 1;
@sum(cities(i)|i #gt# 1: x(1,i))>=1;
!For city i, except the base (city 1);
@for(cities(i) | i #gt# 1 :
! It must be entered;
@sum(cities(j)| j #ne# i: x(j,i))=1;
! level(j)=levle(i)+1, if we link j and i;
@for(cities(j)| j #gt# 1 #and# j #ne# i :
level(j) >= level(i) + x(i,j)
- (n-2)*(1-x(i,j)) + (n-3)*x(j,i);
);
! The level of city is at least 1 but no more n-1,
and is 1 if it links to base (city 1);
@bnd(1,level(i),999999);
level(i)<=n-1-(n-2)*x(1,i);
);
! Make the x's 0/1;
@for(link : @bin(x));
END