(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
Algorithm 3