(a) generate: Generate multiple copies of all the combinations as . Append 
as the position numbers of . Then append and to store the energies. 
(b) energy: Compute the dissimilarities of the possible clusters and store in energy. 
(c) find: Find the best solution. 
(d) count: Count the number of clusters. 
Now we present algorithms to implement the above procedures. 
(a) Generation of all the possible solutions. Append values in order to store the energies. 
generate 

for to do 
for to 

endfor 
for to 

endfor 
for to 

endfor 
for downto 

endfor 
endfor 

. 
for to 

endfor 
. 
(b) Energy computation. The problem is to compute totals of energy for those where . 
Hence and . The total energy is stored in . At the same time, 
the counting number of each bin is stored in the following stickers. 
energy 
for to do 

endfor 
for to do 
for to do 



if yes then 

endif 
endfor 
endfor 
for to do 
for to do 
for to do 

endfor 
endfor 


endfor 
(c) The next step is to find the best solution with least energy. If yes in the final step, 
then we get the optimal solution. The final number of clusters in stored in the last sticker. 
find 
, 
for to do 
, 
if no then 

else 

endif 
endfor 
. 
(d) The final step is to count the number of clusters. It is stored in the last sticker while in the variable . 
count 

for to do 

if yes then 


endif 
endfor 