FLOYD's ALGORITHM


       1 2 3 4 5 j 
       A B C D E    vertices       shortest(i,j, k)
 1  A  0 9 2 3 z                   vertex i to vertex j
 2  B  9 0 4 z 6                   using {1,2,3,...,k} 
 3  C  2 4 0 z z
 4  D  3 z z 0 z
 5  E  z 6 z z 0
 i
       k=0                         z = infinity


       1 2 3 4 5 j 
       A B C D E    vertices       shortest(i,j, k)
 1  A  0 9 2 3 z                   vertex i to vertex j
 2  B  9 0 4 z 6                   using {1,2,3,...,k} 
 3  C  2 4 0 z z
 4  D  3 z z 0 z
 5  E  z 6 z z 0
 i

       k=1                         shortest(i,j, k={none, 1})

              shortest(i,j,k) =
	              shortest(i,j, k-1)
               or     shortest(i,k, k-1) + shortest(k,j, k-1)

    example : 
             C - B : either   C - B  OR   C - A - B