CG303 GAB+EO V5.40

-- adapted 2/27/13 by Crashguard 303 from CG303 GAB V4.701+EO
   -- some minor changes like function positioning.
   -- changed EO slider to checkbox, as flag can be only true or false

-- adapted 9/2/12 by jeff101 from CG303 GAB V4.70+EO


--[[
Genetic Bands III by Crashguard303

Inspired by cartoon Villain´s Script, I created this one, including freezing.
This script also works on not-very-best puzzle-states.

Random Creating:
 It creates a set of clusters (herd). Each cluster has a random set of bands,freezes and a drift value.
 There is a random list, which segments have already been banded or frozen, so it is guaranteed that all are tried.
 If all have been tried, this list is shuffled, all segments are tried again.
 The drift shows, in which directions banding or freezing segments can move.
 (-1 will increase current segment number by, +1 will increase segment number by 1, 0 won´t exist)

Then, for this puzzle state, all clusters are tried.
This means:

Pulling:
 Bands and freezes are applied (plus constant bands, if you want), the puzzle is wiggled for one iteration.

Releasing:
 Bands and freezes are removed.
 4 different subroutines similar to blue fuse run.
 They test different clashing-importance shake/wiggle combinations.
The best result of the fuse is stored to the cluster score.

Sorting:
 If all clusters were tried, they are sorted by the scores they created, double score results are moved to the end of the list.
 The best cluster is on top, the worst or and equal cluster is on bottom at the list.

Breeding:
 All clusters from BreedFirst to BreedLast are breeded, first best  with other random clusters, preferring good ones
 The cluster with the most bands is mom, cluster with fewer bands is dad.
 Bands of mom and drift value are copied at first,
 then a random crossover point is generated within the length of dad´s bands.
 Bands from 1 to inclusive crossover point from the new cluster are replaced by bands of dad, rest of mom
 The same happens to freezes.

Mutating:
 For each band or freeze:
  A random flag (Drift flag or multiplicator) (either 0 or 1)  is created, depending on mutation probability.
  If this flag is 1, drift value (-1 or +1) is added to the segment index, in other case, the segment index stays the same.
  Band length and strength are randomly changed between an amount of -0.1 to 0.1
  When mutating, all values are checked after they are changed, to guarantee that they don´t leave a legal value range.

Inverting:
 For each band or freeze:
  A random flag (inversion flag) (either o or 1) is created, depending on inverting probability.
  If this flag is 1, segment values are inverted, which means multiplying them by -1
  Negative segment values results banding or freezing skip, they are deactivated.
  If a segment has a negative value and is inverted, the value is positive and activated again

Filling:
 The rest of the herd (BreedLast+1 to HerdSize) is replaced by new random clusters, as described in Random Creating.

Restart:
  When new clusters have been breeded or replaced, the recent best puzzle state is loaded.
  and pulling is performed again.

END OF MAIN DESCRIPTION
P.S.: If you find typos, you can keep them ;)
]]--


function math.frandom(m,n,e)
 -- float random, e is number of remaining decimal digits
 local e2=10^e
 return math.random(m*e2,n*e2)/e2
end -- math.frandom()

function math.sgn(x)
 -- Signum function

 if x==nil then
   return nil
  elseif x>0 then
   return 1
  elseif x<-0 then
   return -1
  else
   return x
 end -- if
end -- math.sgn()

function CutOff(x,y)
 -- Keep only y digits after decimal point from x
 return math.floor(x*10^y)/10^y
end -- CutOff()

function UseSegIRange(UseList,A,B,StepSize,bool)
 -- In table "UseList", append or remove segment range A to B
 local UseList=UseList
 local A=A -- range start
 local B=B -- range end
 if A>B then A,B=B,A end -- Swap range start and end, if values are not okay
 local StepSize=StepSize
 local bool=bool -- True=append, false=remove

 local k=A
 repeat
  UseList=UseList_AR(UseList,k,bool)
  k=k+StepSize -- increase k by StepSize
 until k>B -- until k exceeds B
 return UseList
end -- UseSegIRange()

function UseSegIValues(UseList,field,bool)
 -- In table "UseList", append or remove segments listed in table "field"
 local UseList=UseList
 local field=field  -- table to add
 local bool=bool -- True=append, false=remove

 local k
 if #field>0 then -- If table to add is not empty
   for k=1,#field do -- cycle through all elements from table
    UseList=UseList_AR(UseList,field[k],bool)
   end -- k loop
 end -- if #field
 return UseList
end -- UseSegIValues()

function Use_ss(UseList,SSLetter,bool)
 -- In table "UseList", append or remove segments with secondary structure "SSLetter"
 local UseList=UseList
 local SSLetter=SSLetter
 local bool=bool -- True=append, false=remove

 local k
 for k=1,NumSegs do -- Cycle through all segment indices
  if structure.GetSecondaryStructure(k)==SSLetter then -- If current segment index has same ss as given
    UseList=UseList_AR(UseList,k,bool)
  end -- if get_ss
 end -- k loop
 return UseList
end -- Use_ss()

function Use_aa(UseList,AALetters,bool)
 -- In table "UseList", append or remove segments with amino-acid in table "AALetters"
 local UseList=UseList
 local AALetters=AALetters
 local bool=bool -- add or  remove

 if #AALetters>0 then -- Is there minimum one aa letter given?

  local k
  for k=1,NumSegs do -- Cycle through all segments
   local aa=get_aa(k) -- get current aa of segment index k

   local exit_condition=false
   local l=0
   repeat
    l=l+1 -- Cycle through all given aa letters
    if aa==AALetters[l] then -- If current segment k´s aa is equal to AALetters[l]
     UseList=UseList_AR(UseList,k,bool)
     exit_condition=true -- l loop can end here
    end -- if aa
    if l==#AALetters then exit_condition=true end
   until exit_condition==true
  end -- k loop
 end -- if AALetters
 return UseList
end -- Use_aa()

function Use_distance(UseList,MinDist,MaxDist,MinQuantity,MaxQuantity,bool)
 -- In table "UseList", append or remove segments which have
 -- MinQuantity to MaxQuantity neighbours within distance MinDist to MaxDist
 local MinDist=MinDist
 local MaxDist=MaxDist
 local MinQuantity=MinQuantity
 local MaxQuantity=MaxQuantity
 local bool=bool -- True=append, false=remove

 for k=1, NumSegs do -- Cycle through all segments
  local QCount=0
  for l=1,NumSegs do -- compare index k with all around
   if l~=k then -- Don´t count segment itself, only neighbours
    local Distance=structure.GetDistance(k,l) -- Measure distance from segment k to segment l
    if Distance>=MinDist then -- If equal or above min distance
     if Distance<=MaxDist then -- If equal or below max distance
      QCount=QCount+1 -- count this segment
     end -- if Distance
    end -- if Distance
   end -- if l
  end -- l loop
  if QCount<=MaxQuantity then -- If count is equal or below max quantity
   if QCount>=MinQuantity then -- If count is equal or above min quantity
    UseList=UseList_AR(UseList,k,bool) -- add or remove from list
   end -- if QCount
  end -- if QCount
 end -- k loop
 return UseList
end -- Use_distance()

function Use_close_ligand(UseList,MaxDist,bool)
 -- In table "UseList", append or remove segments which have
 -- a spatial distance of MaxDist or closer to ligand.
 local UseList=UseList
 local MaxDist=MaxDist
 local bool=bool -- True=append, false=remove
 local LigandIdx=NumSegs+1 -- Ligand Index

 local k
 for k=1,NumSegs do -- Cycle with k through all segments but not ligand
  local Distance=structure.GetDistance(k,LigandIdx) -- Check spatial distance of segment k to ligand
  if Distance<=MaxDist then -- If equal or below MaxDist
   UseList=UseList_AR(UseList,k,bool) -- add or remove from list
  end -- if
 end -- k loop
 return UseList
end -- Use_close_ligand()

function UseList_AR(UseList,value,bool)
 -- Append value "value" to UseList
 -- or remove all value´s out of UseList, depending on bool
 local UseList=UseList
 local value=value
 local bool=bool -- True=append, false=remove
 -- local OS=OS -- Temporary string for output

   if bool==true then
      UseList=UseList_Append(UseList,value)
      -- OS=OS.."In"
    else
      UseList=UseList_Remove(UseList,value)
      -- OS=OS.."Ex"
   end -- if bool
   -- OS=OS.."cluding segment index "..value
   -- print(OS)
 return UseList
end -- UseList_AR()

function UseList_Append(UseList,value)
 -- Adds content of "value" at end of UseList
 local UseList=UseList
 local value=value
 UseList[#UseList+1]=value
 return UseList
end -- UseList_Append()

function UseList_Remove(UseList,value)
 -- Creates new use list "UseList2" out of "UseList", but without all content of "value"
 local UseList=UseList
 local value=value
 local UseList2={} -- Initialize new uselist
 if #UseList>0 then -- if old
  for k=1,#UseList do -- Scan UseList
   if UseList[k]~=value then -- If "value" is not found
    UseList2[#UseList2+1]=UseList[k] -- append this content to new use list
   end -- if UseList
  end -- k loop
 end -- if UseList
 return UseList2
end -- UseList_Remove()

function CompactContent(OS,E,AS)
 --[[
 Adds string AS to temporary output string OS and counts number of added AS in E.
 If OS contents 10 elements, line is printed out

 I only had to write this sub because there Lua standard library is not included.
 We neither can do some string manipulation nor use a print command without linebreaks at the moment :/
 ]]--

 local OS=OS -- Temporary string for output
 local AS=AS  -- String to add
 local E=E -- Element counter, how often AS was added

 E=E+1
 if AS<10 then -- Sorry for this, but there are no string operations possible at the moment
   OS=OS.."00"..AS
  elseif AS<100 then
   OS=OS.."0"..AS
  else
   OS=OS..AS
 end -- if AS

 if E<10 then -- If there are not 10 elements per line
   OS=OS.."   " -- add space
  else -- If there are 10 elements per line
   print(OS) -- print line out
   OS="" -- clear output string
   E=0 -- reset element counter
 end -- if E
 return OS,E
end -- CompactContent()

function CheckUselist(UseList)
 -- If there are fewer than 3 specific segments to work on given, take all
 local UseList=UseList
 if #UseList<=3 then
  print('No or too few specific segments to work on given.')
  print('Banding and freezing will now manipulate all puzzle segments.')
  UseList={}
  local k
  for k=1,NumSegs do -- Cycle through all segments
   UseList[#UseList+1]=k -- extend UseList by 1 and add segment index
  end -- k loop
 end -- if UseList
 print('Segment list is now:')
 local OS="" -- Initialize output string
 local E=0 -- Initialize element counter
 local k
 for k=1,#UseList do
   OS,E=CompactContent(OS,E,UseList[k])
 end -- k
 if E>0 then
  print(OS)
 end
 return UseList
end -- CheckUselist()

function shuffle2(ShuffleProb)
 -- Scrambles segment use list depending on ShuffleProb
 print('Shuffling segment list')

 local kend=#UseList-1
 local k
 for k=1,kend do -- Cycle through all UseList entries
  if math.random()<ShuffleProb then -- If random value<probability
  -- same as: if random_flag(ShuffleProb) then
   local l=math.random(k+1,#UseList) -- pick random list entry behind k
   UseList[k],UseList[l]=UseList[l],UseList[k] -- swap values of UseList index k with UseList index l
  end -- if random
 end -- k loop
 UsedSegments=0 -- After Shuffling, set list pointer to 0
end -- shuffle2()

function random_segment()
 -- Gets a random segment index out of UseList which has not been used so far

 UsedSegments=UsedSegments+1 -- Increase UseList pointer
 local Seg_result=UseList[UsedSegments] -- fetch segment index
 if UsedSegments==#UseList then shuffle2(ShuffleProb) end
 -- If this was the last value of UseList, shuffle list and reset pointer

 return Seg_result -- return random segment number
end -- random_segment()

function FillHerd(StartAt,EndAt,TimeStamp)
 local StartAt=StartAt -- First cluster index to generate (not cluster slot)
 if StartAt<=HerdSize then
  local EndAt=EndAt -- Last cluster index to generate (not cluster slot)
  local TimeStamp=TimeStamp -- "birth date"
  print('Generating Herd from '..StartAt..' to '..EndAt)

  local k2
  for k2=StartAt,EndAt do
   -- print('Cluster: '..k2)
   local k=ClusterPointer[k2] -- Fetch cluster slot by cluster index
   ClusterScore[k]=0
   ClusterDrift[k]=random_direction() -- Create value -1 or 1

   if (Mimic and k2==1) then -- If this is a Mimic band
     ClusterType[k]="mimic" -- set cluster information for Mimic
    else -- If this is not a Mimic band
     ClusterType[k]="random" -- set cluster information for random
   end -- if k2
   ClusterType[k]=ClusterType[k].."-"..TimeStamp.."@"..os.date() -- Stamp "birth date"

   if ClusterBands>0 then
   ClusterSegA[k]={}
   ClusterSegB[k]={}
   ClusterLength[k]={}
   ClusterStrength[k]={}

    local l
    for l=1,ClusterBands do
     if puzzle_is_ligand==false then -- If this is no ligand puzzle
       ClusterSegA[k][l]=random_segment() -- get random segment number
      else -- If this is a ligand puzzle
       ClusterSegA[k][l]=NumSegs+1 -- Segment A is always ligand
     end -- if puzzle_is_ligand

     if (Mimic==false or k2~=1) then -- If this is not a Mimic band
      if random_flag(InvBProb) then -- and random flag for inverting is given
       ClusterSegA[k][l]=-ClusterSegA[k][l] -- toggle cluster on/off by changing signum (+/-)
      end -- if random_flag
     end -- if k2

     repeat
      ClusterSegB[k][l]=random_segment()
      local IDistance=index_distance(ClusterSegA[k][l],ClusterSegB[k][l]) -- fetch index distance
      local SDistance=structure.GetDistance(math.abs(ClusterSegA[k][l]),ClusterSegB[k][l]) -- fetch spatial distance
     until IDistance>=MID_Game and SDistance<=MaxBL_Game
     -- Segments must have a minimum index distance
     -- and maximum spatial distance

     if (Mimic and k2==1) then -- If this is a Mimic band
       ClusterLength[k][l]=FactorByLength(ClusterSegA[k][l],ClusterSegB[k][l])
       ClusterStrength[k][l]=MaxBS
      else -- if k2
       ClusterLength[k][l]=math.frandom(0,1,6)
       ClusterStrength[k][l]=math.frandom(MinBS,MaxBS,3)
     end -- if k2

    end  -- l loop
   end -- if ClusterBands

   if ClusterFreezes>0 then
    ClusterFreeze[k]={}
    local l
    for l=1,ClusterFreezes do
     ClusterFreeze[k][l]=random_segment()
     if (Mimic and k2==1) or random_flag(InvFProb) then -- If this is a Mimic band or random flag for inverting freeze information is given
      ClusterFreeze[k][l]=-ClusterFreeze[k][l] -- toggle freeze on/off by changing signum (+/-)
     end -- if random_flag
    end -- l loop
   end -- if
  end -- k loop
 end -- if StartAt
end -- FillHerd()

function ShowHerd()
 local k2
 local l

 print('Clusters are:')
 for k2=1,HerdSize do
  local k=ClusterPointer[k2]
  print('Cluster:'..k2..' score:'..ClusterScore[k]..' drift:'..ClusterDrift[k])
  if ClusterBands>0 then
   local l
   for l=1,ClusterBands do
    print('Band '..l..': '..ClusterSegA[k][l]..' to '..ClusterSegB[k][l])
   end
  end -- if ClusterBands

  if ClusterFreezes>0 then
   local l
   for l=1,ClusterFreezes do
   print('Freeze '..l..': '..ClusterFreeze[k][l])
   end -- l
  end -- if
 end -- k loop
end -- ShowHerd()

function ShowHerdShort()
 print('Clusters are:')

 local k2
 for k2=1,HerdSize do
  local k=ClusterPointer[k2]
  print('Cluster:'..k2..'('..k..') score:'..ClusterScore[k])
  print('Drift:'..ClusterDrift[k])
 end -- k loop
end -- ShowHerdShort()

function ShowScoreList()
 local k2
 for k2=1,HerdSize do
  local k=ClusterPointer[k2]
  print('Cluster:'..k2..'('..k..') delta:'..ClusterScore[k])
 end -- k
end -- ShowScoreList()

function SortHerd()
 -- As we use pointers, we only have to swap the cluster "adresses" instead of copying all band/freeze values
 local Finish=HerdSize-1
 local k
 for k=1,Finish do
  local start=k+1
  local l
  for l=start,HerdSize do
   if ClusterScore[ClusterPointer[l]]>ClusterScore[ClusterPointer[k]] then
    -- print('Swapping cluster '..k..'('..ClusterPointer[k]..'):'..l..'('..ClusterPointer[l]..')')
    ClusterPointer[l],ClusterPointer[k]=ClusterPointer[k],ClusterPointer[l]
   end -- if
  end -- l
 end -- k
end -- SortHerd()

function CreateCrossoverPoint(x)
 -- create random crossover point

  if x==0 then
    return 0
   else -- if x ~=0
    -- return math.random(0,x) -- create random value between 0 and x
    return math.random(1,x-1) -- create random value between 1 and x-1
  end -- if x
end -- CreateCrossoverPoint()

function Breed(TimeStamp)
  -- Copy all clusters to another bank, same name for all cluster tables but with 2 at end
  -- Breed two clusters from bank 2 back to old bank to prevent breeding collision.
  -- If this wouldn´t be done, and (for example) cluster 1 and 2 would be breeded to cluster 3,
  -- cluster 3 couldn´t be used as breeding source again, as it would be overwritten already.

  local TimeStamp=TimeStamp -- "birth date"

  ClusterScore2={}
  -- ClusterType2={}
  ClusterDrift2={}

  ClusterSegA2={}
  ClusterSegB2={}
  ClusterLength2={}
  ClusterStrength2={}

  ClusterFreeze2={}

   local k
   for k=1,HerdSize do
    ClusterScore2[k]=ClusterScore[k]
    ClusterDrift2[k]=ClusterDrift[k]

    if ClusterBands>0 then
     ClusterSegA2[k]={}
     ClusterSegB2[k]={}
     ClusterLength2[k]={}
     ClusterStrength2[k]={}
     local l
     for l=1,ClusterBands do
       ClusterSegA2[k][l]=ClusterSegA[k][l]
       ClusterSegB2[k][l]=ClusterSegB[k][l]
       ClusterLength2[k][l]=ClusterLength[k][l]
       ClusterStrength2[k][l]=ClusterStrength[k][l]
     end -- l loop
    end -- if ClusterBands

     if ClusterFreezes>0 then
     ClusterFreeze2[k]={}
     local l
     for l=1,ClusterFreezes do
       ClusterFreeze2[k][l]=ClusterFreeze[k][l]
     end -- l loop
    end -- if ClusterFreezes
   end -- k loop

   FitnessOffset=ClusterScore[ClusterPointer[HerdSize]]
   -- Take worst cluster score as fitness offset reference
   -- By subtracting this score offset from each cluster score and adding 1,
   -- it is guaranteed that worst cluster score is always 1, all other scores are better.
   -- This will shift all cluster scores up, if worst cluster score is below 1, so there will be no values<1 for fitness calculation.
   -- It will pull all scores down, if worst cluster score is above 1, to guarantee maximum privilege by fitness.
   -- If all clusters would have similar big score values, they would be choosen equally.
   -- By shifting the scores making the last score be 1, other scores are always x-times higher than 1.

   Fitness=0
   local k
   for k=1,HerdSize do
    ClusterScore2[k]=ClusterScore2[k]-FitnessOffset+1 -- Shift cluster score copy by offset to met condition
   -- We can overwrite this table, because it is only needed for breeding, and it won´t affect the original table.
   -- Original score will remain untouched.
    Fitness=Fitness+ClusterScore2[k] -- Calculate fitness by adding all scores (offset included)

   end -- k loop

   local k
   for k=BreedFirst,BreedLast do
    ClusterBreed(k,TimeStamp)
   end -- k loop
end -- Breed()

function Roulette()
 -- Returns a random cluster index (not slot), the better their score, the more often they will appear
 local TValue=math.random()*(Fitness+1) -- Target fitness value, which will stop the wheel
 local CValue=0 -- Current value, where single cluster points will be added
 local Wheel=math.random(1,HerdSize) -- Random initial wheel position
 repeat
  Wheel=Wheel+1 -- Spin Wheel
  if Wheel>HerdSize then Wheel=1 end -- If Wheel made a full turn, it starts at 1 again
  CValue=CValue+ClusterScore2[ClusterPointer[Wheel]]
  -- Increase current value by score of cluster at wheel position
 until CValue>TValue
 return Wheel
end -- Roulette()

function ClusterBreed(indexClusterB,TimeStamp)
 local indexClusterB=indexClusterB -- Target cluster
 local TimeStamp=TimeStamp -- "birth date"

 local indexClusterA1 -- Source cluster 1
 if Parent1isRoulette==false then
   indexClusterA1=indexClusterB-BreedFirst+1 -- Choose best, starting with 1
  else
   indexClusterA1=Roulette() -- Choose one by fitness roulette, the better the score, the more often it can be chosen
 end -- if Parent1isRoulette

 local indexClusterA2 -- Source cluster 2
 if Parent2isRoulette==true then
   repeat
    indexClusterA2=Roulette() -- Choose one by fitness roulette, the better the score, the more often it can be chosen
   until indexClusterA2~=indexClusterA1 -- clusters must be different
  else
   indexClusterA2=indexClusterA1+1 -- Take next to Parent 1
   if indexClusterA2>HerdSize then indexClusterA2=1 end
 end -- if Parent2isRoulette

 local ClusterB=ClusterPointer[indexClusterB] -- Fetch save slot for target cluster
 local ClusterA1=ClusterPointer[indexClusterA1] -- Fetch load slot for source cluster 1 (dad)
 local ClusterA2=ClusterPointer[indexClusterA2] -- Fetch load slot for source cluster 2 (mom)

 print('Breeding '..indexClusterA1..'('..ClusterA1..') and '..indexClusterA2..'('..ClusterA2..') to '..indexClusterB..'('..ClusterB..')')

 ClusterType[ClusterB]="breeded".."-"..TimeStamp.."@"..os.date() -- Stamp "birth date"

 ClusterDrift[ClusterB]=ClusterDrift2[ClusterA1] -- Take drift information always from dad, preventing change in drift when breeding

  if ClusterBands>0 then -- We only need to copy if there are any bands
   local CrossoverEnd
   if MultiCrossOver== false then
    CrossoverEnd=CreateCrossoverPoint(ClusterBands) -- Create
    print('Band crossover point: '..CrossoverEnd) -- and show crossover point
   end -- if MultiCrossOver

   ClusterSegA[ClusterB]={}
   ClusterSegB[ClusterB]={}
   ClusterLength[ClusterB]={}
   ClusterStrength[ClusterB]={}

   local BandsChild
   local l
   for l=1,ClusterBands do -- Is crossover point reached?
    if CrossOverCheck(CrossoverEnd,l) then
      BandsChild=ClusterA2 -- Take mom after crossover point
     else
      BandsChild=ClusterA1 -- Take dad until crossover point
    end -- if CrossoverEnd
    ClusterSegA[ClusterB][l]=ClusterSegA2[BandsChild][l]
    ClusterSegB[ClusterB][l]=ClusterSegB2[BandsChild][l]
    ClusterLength[ClusterB][l]=ClusterLength2[BandsChild][l]
    ClusterStrength[ClusterB][l]=ClusterStrength2[BandsChild][l]
   end -- l loop
  end -- if ClusterBands

  if ClusterFreezes>0 then -- We only need to copy if there are any freezes
  local CrossoverEnd
   if MultiCrossOver== false then
    CrossoverEnd=CreateCrossoverPoint(ClusterFreezes) -- Create
    print('Freeze crossover point: '..CrossoverEnd) -- and show crossover point
   end -- if MultiCrossOver

   ClusterFreeze[ClusterB]={}

   local FreezesChild
   local l
   for l=1,ClusterFreezes do -- For all freezes
    if CrossOverCheck(CrossoverEnd,l) then -- Is crossover point reached?
      FreezesChild=ClusterA2 -- Take mom after crossover point
     else
      FreezesChild=ClusterA1 -- Take dad until crossover point
    end -- if CrossoverEnd
    ClusterFreeze[ClusterB][l]=ClusterFreeze2[FreezesChild][l]
   end -- l loop
  end -- if ClusterFreezes

  -- Cluster mutating starts here
  -- Secondary cluster set not needed anymore
  -- Mutation is directly performed on target cluster

  if ClusterBands>0 then
  local l
   for l=1,ClusterBands do
    if puzzle_is_ligand==false then -- only on non-ligand-puzzles mutate segment A
     if random_flag(DriftProb) then
      ClusterSegA[ClusterB][l]=drift_segment(ClusterSegA[ClusterB][l],ClusterDrift[ClusterB])
     end -- if random_flag
    end -- if puzzle_is_ligand

    if random_flag(InvBProb) then
     ClusterSegA[ClusterB][l]=-ClusterSegA[ClusterB][l] -- invert
    end -- if random_flag

    repeat
     if random_flag(DriftProb) then
      ClusterSegB[ClusterB][l]=drift_segment(ClusterSegB[ClusterB][l],ClusterDrift[ClusterB])
     end -- if random_flag
     local Distance=index_distance(ClusterSegA[ClusterB][l],ClusterSegB[ClusterB][l])
    until Distance>=MID_Game -- Segments must have a minimum index distance

    if random_flag(DriftProb) then -- mutation allowed
     ClusterLength[ClusterB][l]=drift_band_attribute(ClusterLength[ClusterB][l],1,3,0,1,6)
     -- change bandlength by value + or - randomly 10e-[1 to 3 randomly]
     -- keep bandlength between 0 and 1
     -- if error occurs, generate new bandstrength value with 6 decimal digits
    end -- if random_flag

    if random_flag(DriftProb) then -- mutation allowed
     ClusterStrength[ClusterB][l]=drift_band_attribute(ClusterStrength[ClusterB][l],1,3,MinBS,MaxBS,3)
     -- change bandstrength by value + or - randomly 10e-[1 to 3 randomly]
     -- keep bandstrength between MinBS and MaxBS
     -- if error occurs, generate new bandlength value with 3 decimal digits
    end -- if random_flag
   end  -- l loop
  end -- if ClusterBands

  if ClusterFreezes>0 then
   local l
   for l=1,ClusterFreezes do
    if random_flag(DriftProb) then
    ClusterFreeze[ClusterB][l]=drift_segment(ClusterFreeze[ClusterB][l],ClusterDrift[ClusterB])
    end -- if random_flag

    if random_flag(InvFProb) then
     ClusterFreeze[ClusterB][l]=-ClusterFreeze[ClusterB][l] -- invert
    end -- if random_flag
   end -- l loop
  end -- if
end -- ClusterBreed()

function drift_segment(Segment,Drift)
 local Drift=Drift
 local Seg2=Segment

 local Seg2sgn=math.sgn(Seg2)
 Seg2=math.abs(Seg2)+Drift

 if Seg2<1 then
   Seg2=NumSegs
  elseif Seg2>NumSegs then
   Seg2=1
 end -- if Seg2

 Seg2=Seg2*Seg2sgn

 return Seg2
end -- drift_segment()

function drift_band_attribute(Target,RndE1,RndE2,Min,Max,RndE3)
 -- apply random drift on variable Target resulting Target2 (Target2=Target+random value)
 -- drift value can be positive or negative
 -- and is 10^-[RndE1 to RndE2 randomly]
 -- for example if RndE1 is 1 and RndE2 is 3, resulting value can be 10^-1,10-2 or 10^-3

 -- If Min or Max is exceeded, value of Target2 is ring-wrapped (moebius transformation, no clamping):
 -- If maximum is exceeded, the amount of exceedment (Target2-Value) is applied to minimum
 -- If minimum is exceeded, the amount of exceedment (Target2-Value) is applied to maximum

 local Target2=Target

 local Target2=Target2+random_direction()*10^-math.random(RndE1,RndE2)

 if Target2>Max then
   Target2=Min+(Target2-Max)
  elseif Target2<Min then
   Target2=Max+(Target2-Min)
 end -- if Target2

 if Target2>Max or Target2<Min then
  Target2=math.frandom(Min,Max,RndE3)
 end -- if Target2

 return Target2
end -- drift_band_attribute()

function CrossOverCheck(CrossoverEnd,Pos)

 if MultiCrossOver then
   if random_flag(0.5) then
     return true
    else
     return false
   end -- if random_flag
  else -- if MultiCrossOver is false
   if Pos>CrossoverEnd then
     return true
    else
     return false
   end -- if Pos
 end -- if
end -- CrossOverCheck()

function random_flag(Prob)
 -- Returns false or true randomly
 -- how often true appears depends on probability Prob
 local Prob=Prob

 if math.random()<Prob then
   return true
  else
   return false
 end -- if random
end -- random_flag()

function random_direction()
 -- returns either -1 or 1
 return math.random(0,1)*2-1
end -- random_direction()

function structure.WiggleBackbone(iter)
 structure.WiggleAll(iter,true,false)
end -- structure.WiggleBackbone()

function structure.WiggleSidechains(iter)
 structure.WiggleAll(iter,false,true)
end -- structure.WiggleSidechains()

function xtool(method,iter,tL2)
  -- unifies score-conditional shake and wiggle into one function
  local OS=""
  local iter=iter
  local tL2=tL2
  if iter>0 then
    OS="max iter:"..iter
  end -- if
  -- print('Method:'..method..' '..OS..' threshold:'..tL2)
  local curr_iter=0
  local exit_condition=false
  repeat
   curr_iter=curr_iter+1
   -- print(' Testing with iterations: '..curr_iter)
   local tempScore=current.GetEnergyScore()
   if method=="s" then
     structure.ShakeSidechainsAll(curr_iter)
    elseif method=="wb" then
     structure.WiggleBackbone(curr_iter)
    elseif method=="ws" then
     structure.WiggleSidechains(curr_iter)
    else
     structure.WiggleAll(curr_iter)
   end -- if method
   local tempScore2=current.GetEnergyScore()
   local rDelta=(tempScore2-tempScore)/curr_iter
   -- print(' Rel. change: '..rDelta..' pts/iteration')
   if curr_iter==iter then exit_condition=true end
   if math.abs(rDelta)<tL2 then exit_condition=true end
  until exit_condition==true
end -- xtool()

-- Inspired by vertex´s blue fuse script
-- You may want to tweak this function

function PinkFuse()
    save.Quicksave(3) -- store state before fuse
     print('Release 1')

     behavior.SetClashImportance(0.1)
     xtool("s",Shakes,ScoreThreshold)
     BestScoreCheck()
     behavior.SetClashImportance(0.7)
     xtool("wa",Wiggles,ScoreThreshold)
     BestScoreCheck()
    FuseEnd()

    save.Quickload(3) -- load state before fuse
     print('Release 2')

     behavior.SetClashImportance(0.3)
     xtool("s",Shakes,ScoreThreshold)
     BestScoreCheck()
     behavior.SetClashImportance(0.6)
     xtool("wa",Wiggles,ScoreThreshold)
     BestScoreCheck()
    FuseEnd()

    save.Quickload(3) -- load state before fuse
     print('Release 3')

     behavior.SetClashImportance(0.2)
     xtool("s",Shakes,ScoreThreshold)
     BestScoreCheck()
     behavior.SetClashImportance(0.5)
     xtool("wa",Wiggles,ScoreThreshold)
     BestScoreCheck()
    FuseEnd()

    save.Quickload(3) -- load state before fuse
     print('Release 4')

     behavior.SetClashImportance(0.4)
     xtool("s",Shakes,ScoreThreshold)
     BestScoreCheck()
     behavior.SetClashImportance(0.3)
     xtool("wa",Wiggles,ScoreThreshold)
     BestScoreCheck()
    FuseEnd()
end -- PinkFuse()

function FuseEnd()
    -- Fuse try finishing with CI=1
    behavior.SetClashImportance(1)
    xtool("wa",Wiggles,ScoreThreshold)
    xtool("s",Shakes,ScoreThreshold)
    xtool("wa",Wiggles,ScoreThreshold)
    BestScoreCheck()
end -- FuseEnd()

function BestScoreCheck()
   local TempScore=current.GetEnergyScore()

   if LastBest then
    if TempScore>ACS5 then
     save.Quicksave(5) -- Set best cluster result for this generation
     ACS5=TempScore
     -- print('ACS5 is '..ACS5)
    end -- if TempScore
   end -- if LastBest

    if TempScore>ACS4 then
     save.Quicksave(4) -- Set best cluster result for current cluster
     ACS4=TempScore
    end -- if TempScore

   if TempScore>BestScore then
    -- recentbest.Save()
    BestScore=TempScore
    print('New best total score: '..BestScore)
    BSChange=true
   end -- if
end -- BestScoreCheck()

function PullDownEqualResults()
 print('Checking for double results')
 -- Compare all cluster points with next in list
 -- If next has the same score, move this cluster to end.

 local kEnd=HerdSize-1
 local k
 for k=1,kEnd do
  while ClusterScore[ClusterPointer[k]]==ClusterScore[ClusterPointer[k+1]] do
  -- If next has the same score
   ClusterScore[ClusterPointer[k+1]]=ClusterScore[ClusterPointer[HerdSize]]-1
   -- make its score more worse then the baddest cluster
   SortHerd() -- so it is placed at the end when sorting by score
  end -- while ClusterScore
 end -- k
end -- PullDownEqualResults()

function InitializeClusterData()
 ClusterScore={}
 ClusterType={}
 ClusterDrift={}

  ClusterSegA={}
  ClusterSegB={}
  ClusterLength={}
  ClusterStrength={}

  ClusterFreeze={}

 ClusterPointer={}
 local k
 for k=1,HerdSize do
  ClusterPointer[k]=k
 end -- k
end -- InitializeClusterData()

function PrintStartingTests()
 print()
 local OS=" "
 if Runs==1 then
   OS=OS.."1 run"
  else
   if Runs>1 then
     OS=OS..Runs
    else
     OS=OS.."infinite"
   end -- if
   OS=OS.." runs"
 end -- if
 OS="Starting cluster tests for "..OS.."."
 print(OS)
end -- PrintStartingTests()

function select_close_ligand()
 local LigandSegment=NumSegs+1
 local k
 for k=1,NumSegs do
  if structure.GetDistance(k,LigandSegment)<=MutateLigandDistance then
   selection.Select(k)
   -- print(k," is close enough to ligand for mutating.")
  end -- if get_segment_distance
 end -- k loop
end -- select_close_ligand()

function SetRebuildWorst()
 -- Acitvate rebuild worst if forced or condidtions are met
 if RebuildForce==nil then
   --[[
   if BSChange then
     RebuildWorst=false
    else
     RebuildWorst=true
   end -- if BSChange
   ]]--
   RebuildWorst=BSValueCheck()
  else
   RebuildWorst=RebuildForce
 end -- if RebuildForce
end -- SetRebuildWorst()

function BSValueCheck()
 -- Returns true if current generation´s best cluster didn´t do much
 local ChangeTooSmall=false
 if BSValue>=0 then -- If last generation´s best cluster score is better than at generation start
   if BSValue<SCPT then -- but below limit
    ChangeTooSmall=true
   end -- if BSValue
  else -- if BSValue<0  -- If last generation´s best cluster score is not better than at generation start
   if BSValue>SCNT then  -- but above limit
    ChangeTooSmall=true
   end -- if BSValue
 end -- if BSValue
 return ChangeTooSmall
end -- BSValueCheck()

function SetBreedFirstCurrent(BreedFirstCurrent)
 -- Changes first cluster to test if forced or conditions are met
 local BreedFirstCurrent=BreedFirstCurrent
 if BreedFirstCurrentForce==nil then -- If we don´t force BreedFirstCurrent do a special value
   if (LastBest==false) and (RecentUse==false) then -- if we load initial state
      BreedFirstCurrent=BreedFirst
   else -- If we don´t load initial state
     if BSChange or BSValueCheck()==false then -- If there was a considerable change
        BreedFirstCurrent=1 -- check all clusters again in next generation
     else -- If there was no considerable change
        BreedFirstCurrent=BreedFirstCurrent+1 -- increase start cluster for this generation (don´t test best again)
        if BreedFirstCurrent>BreedFirst then
           BreedFirstCurrent=BreedFirst
        end -- but not further than BreedFirst
     end -- if BSChange
   end -- if LastBest==false and RecentUse=false then
 else -- if BreedFirstCurrentForce not nil
   BreedFirstCurrent=BreedFirstCurrentForce
 end -- if BreedFirstCurrentForce
 return BreedFirstCurrent
end -- SetBreedFirstCurrent()

function GAB()
 -- save.Quickload(1): Puzzle state at GAB Start
 -- save.Quickload(2): Puzzle state at generation start
 -- save.Quickload(3): Puzzle state at fuse start
 -- save.Quickload(4): Best result for current cluster
 -- save.Quickload(5): Best result for current generation

 print('Starting GAB.')

 UseList=CheckUselist(UseList)
 shuffle2(ShuffleProb) -- Shuffle UseList and reset pointer

 InitializeClusterData()

 FillHerd(1,HerdSize,1) -- From 1 to HerdSize

 -- ShowHerd()

 band.DeleteAll() -- clean bands
 freeze.UnfreezeAll() -- and freezes
 behavior.SetClashImportance(1)
 selection.DeselectAll()
 recentbest.Save()

 save.Quicksave(1) -- Save initial puzzle state
 BestScore=current.GetEnergyScore() -- initialize best score (ACS1)

 PrintStartingTests(Runs)

 local BreedFirstCurrent=1
 CRun=0 -- set CRun to 0, counting up after each cluster generation
 repeat -- seems start of main loop 9/2/12
  CRun=CRun+1 -- Increase current run value
  if CRun>1 then -- If this is not the first run
   if RecentHybrid>0 then -- If RecentHybrid>0, tweak RecentUse
     if (CRun-1)%RecentHybrid==0 then -- Each RecentHybrid runs
       RecentUse=true -- use recent best
      else -- If not
       RecentUse=false -- don´t use recent best
     end -- if CRun
   end -- if RecentHybrid
   if LastBest then
     print('Loaded last generation´s best.')
     save.Quickload(5) -- Load best cluster result of last generation
    else -- If Lastbest is false
     if RecentUse then
       print('Loaded recent best.')
       recentbest.Restore() -- Load best result so far
      else
       print('Loaded initial state.')
       save.Quickload(1) -- Load initial state
     end -- if RecentUse
   end -- if LastBest
   SetRebuildWorst()
   BreedFirstCurrent=SetBreedFirstCurrent(BreedFirstCurrent)
  end -- if CRun

  if RebuildWorstGen then -- If rebuild is requestet at geneartion start
   rebuild_worst() -- do it
  end

  BSChange=false -- Reset improvement information

  save.Quicksave(2) -- Set this state as start state for current generation
  ACS2=current.GetEnergyScore() -- Get score at start for this generation
  print()
  print('Score now: '..ACS2)

  local k2 -- Cluster counter (cluster number not in braces)
  for k2=BreedFirstCurrent,HerdSize do
   local k=ClusterPointer[k2] -- fetch slot number(adress) resulting from k2 (cluster number in braces)
   print()
   print('Gen.:'..CRun..' cluster:'..k2..'('..k..')/'..HerdSize..' drift:'..ClusterDrift[k]..' type:'..ClusterType[k])

   if k2>BreedFirstCurrent then
      -- print('Loaded Quicksave 1.')
      save.Quickload(2)
   end -- if k2

   band.DeleteAll() -- remove all bands, because recent best can contain some
   freeze.UnfreezeAll() -- and freezing to apply others

   if ClusterBands>0 then
    local l -- Band counter
    for l=1,ClusterBands do
     if ClusterSegA[k][l]>0 then
       band.AddBetweenSegments(ClusterSegA[k][l],ClusterSegB[k][l])
       local TempBandCount=band.GetCount()
       -- fetch current band number index to make setting its length and strength possible

       local Length=LengthWithFactor(ClusterSegA[k][l],ClusterSegB[k][l],ClusterLength[k][l])

       if (Mimic==false or l~=1) then -- If this is not a Mimic band
        if Length>structure.GetDistance(ClusterSegA[k][l],ClusterSegB[k][l]) then -- and random generated target length is bigger than actual distance
          Length=Length+BLchangeUpPush -- add push up value
          -- print('Pushed up.')
          if Length>MaxBL_Game then
           Length=MaxBL_Game
          end -- if Length>MaxBL_Game
         else -- if random generated target length is smaller or equal than actual distance
          Length=Length+BLchangeDownPush -- add push down value
          -- print('Pushed down.')
          if Length<MinBL_Game then
           Length=MinBL_Game
          end -- if Length<MinBL_Game
        end -- if Length>structure.GetDistance
       end -- if (Mimic==false or l~=1)

       local Length1R=CutOff(ClusterLength[k][l],3) -- Cut after 3 decimal digits before displaying
       local Length2R=CutOff(Length,3) -- Cut after 3 decimal digits before displaying

       local OS="Band "..l..": "..ClusterSegA[k][l]..":"..ClusterSegB[k][l]
       OS=OS.." L:"..Length1R.."="..Length2R
       if ShowBF then
        OS=OS.." S:"..ClusterStrength[k][l]
       end -- if
       print(OS)

       band.SetGoalLength(TempBandCount,Length) -- Set current band length
       band.SetStrength(TempBandCount,ClusterStrength[k][l]) -- Set current band strength

      else -- if ClusterSegA[k][l] is <0, which means band is deactivated
      if ShowBF then
       print('Band '..l..': off')
      end -- if
     end -- if ClusterSegA
    end -- l loop
   end -- if ClusterBands

   if RebuildWorstGen==false then rebuild_worst() end

   selection.DeselectAll() -- Before freezing, so we can select segments to freeze

   if ClusterFreezes>0 then -- if there are segments to freeze
    local l -- Freeze counter
    for l=1,ClusterFreezes do  -- select all segments to freeze
     if ClusterFreeze[k][l]>0 then
       if ShowBF then
        print('Freeze '..l..': '..ClusterFreeze[k][l])
       end -- if
       selection.Select(ClusterFreeze[k][l])
      else
      if ShowBF then
       print('Freeze '..l..': off')
      end -- if
     end -- if ClusterFreez
    end -- l loop
   end -- if ClusterFreezes

   if puzzle_is_ligand then -- if this is a ligand puzzle
     selection.Select(NumSegs+1) --  select ligand for freezing
     freeze.FreezeSelected(true,true) -- freeze backbone and sidechains
    else -- if this is not a ligand puzzle
      if ClusterFreezes>0 then -- but there are segments to freeze
       freeze.FreezeSelected(true,false) -- freeze backbone only
      end -- if ClusterFreezes
   end -- if puzzle_is_ligand

   if ConstantBands==true then
    add_constant_bands() -- You can add some bands or freezes in this routine, which should appear each try
   end -- if

   print('Pulling...')
   behavior.SetClashImportance(CI_pull)
   selection.SelectAll () -- Select all segments to wiggle
   structure.WiggleAll(PWiggles) -- Just a small pull

   band.DeleteAll() -- clean up bands before saving
   freeze.UnfreezeAll() -- clean up freezes before saving

   if LastBest then -- If LastBest Mode
    if k2==BreedFirstCurrent then -- and this is the first try of current generation
     ACS5=current.GetEnergyScore()
     -- initialize current generation best score
    end -- if k2
   end -- if LastBest

   save.Quicksave(4) -- Initialize this state as reference for current cluster best score
   ACS4=current.GetEnergyScore() -- and initialize current cluster best score
   BestScoreCheck() -- raise BestScore ACS4, if result is better

   xMutate(Mutating1) -- including BestScoreCheck

   Release() -- including Fuse and BestScoreCheck

   xMutate(Mutating2) -- including BestScoreCheck

   ClusterScore[k]=ACS4-ACS2 -- Store best score minus start score for this try as cluster score
   print('Difference to start: '..ClusterScore[k]..' = '..(math.floor(ACS4*1000)/1000)..' - '..(math.floor(ACS2*1000)/1000))
  end -- k loop, take next cluster

  print('\nSorting Cluster list by score')
  SortHerd() -- Sort herd by score difference
  ShowScoreList()

  BSValue=ClusterScore[ClusterPointer[1]] -- Fetch best score difference

  PullDownEqualResults() -- Move duplicate results to end of herd

  -- call breeding, if needed
  -- replace clusters with index BreedFirst to BreedLast by breeded ones
  if EOMode==0 then -- if we do genetic and not extremal optimization, breed and replace some clusters
   -- if EOMode is >0, breeding is skipped
   Breed(CRun+1) -- Range: BreedFirst to BreedLast
  end -- if EOMode

  -- check if we have to increase herd size
  local incBreedLastFlag=false
   -- flag for increasing breedable clusters by 1
   -- performed when herd size was increased by 2
  if BSValueCheck() or BSValue<=0 then -- If generation´s best cluster has low or negative score difference
   print('No or few improvement for this generation.')
   if HerdSize<IncHerdSize then -- and herd size increasing is allowed
    print('Increasing herd size.')
    local k
    for k=1,2 do -- increase herd size by 2 clusters
     HerdSize=HerdSize+1 -- increase herd size
     ClusterPointer[HerdSize]=HerdSize -- and number of cluster save slots; set them to its own value
    end -- k loop
    incBreedLastFlag=true
    -- remind that 1 of these 2 new clusters can be breeded next generation
    -- but at first we need 2 random ones extra,
    -- which was done by increasing herd size by 2, now executing herd filling below
   end -- if incHerdSize
  end -- if BSChange

  -- after eventually breeding and increasing herd size
  -- replace worst clusters by new random ones by filling (like it was done in the beginning)
  if EOMode<2 then
   FillHerd(BreedLast+1,HerdSize,CRun+1)
   -- generate random clustes behind breeded ones
  else
   FillHerd(BreedFirst,HerdSize,CRun+1)
   -- generate random clustes instead of breeding them and behind
  end -- if EOMode<2

  if incBreedLastFlag then -- if we have increased herd size
     -- 1 of these 2 new clusters can be breeded next generation
     BreedLast=BreedLast+1 -- increase breed slots by 1
  end -- if incBreedLastFlag

  -- ShowHerdShort()

 until CRun==Runs -- seems end of main loop 9/2/12
end -- GAB()

function FactorByLength(SegA,SegB)
 -- As mimic doesn´t use random band lengths (with random factor) but tries to imitate current puzzle state,
 -- we have not to generate but to calculate the factor value
 -- This is the opposite of function LengthWithFactor

 local Min=SpatLimit(SegA,SegB,BLchangeDown)
 local Max=SpatLimit(SegA,SegB,BLchangeUp)

 return (structure.GetDistance(SegA,SegB)-Min)/(Max-Min)
end -- FactorByLength()

function LengthWithFactor(SegA,SegB,Factor)
 -- Apply length factor to range between minimum allowed band length and maximum allowed band length
 -- Factor=0 results minimum allowed band length
 -- Factor=1 results maximum allowed band length

 local Min=SpatLimit(SegA,SegB,BLchangeDown)
 local Max=SpatLimit(SegA,SegB,BLchangeUp)

 -- print('Length range without push: '..CutOff(Min,3)..':'..CutOff(Max,3))

 return Factor*(Max-Min)+Min
end -- LengthWithFactor()

function SpatLimit(SegA,SegB,Distance)

 local Distance2=structure.GetDistance(SegA,SegB)+Distance

 if Distance2<MinBL_Game then
   Distance2=MinBL_Game
  elseif Distance2>MaxBL_Game then
   Distance2=MaxBL_Game
 end -- if Distance2

 return Distance2
end -- SpatLimit()

function index_distance(SegA,SegB)
 -- Fetch segment index distance

 return math.abs(math.abs(SegA)-SegB)
end -- index_distance()

function Release()
  if Releasing then
    -- print('Score after pulling: '..ACS4)
    print('Releasing...')
    save.Quickload(4) -- load best cluster result so far
    selection.SelectAll ()
    if Fuse then
      PinkFuse() -- save.Quicksave(4), raise BestScore and ACS4, if result is better
     else
      behavior.SetClashImportance(1)
      structure.ShakeSidechainsAll(1)
      structure.WiggleAll(12)
      BestScoreCheck() -- save.Quicksave(4), raise BestScore and ACS4, if result is better
    end -- if fuse
   end -- if Releasing
end -- Release()

function rebuild_worst()
 if RebuildWorst then
  print('Rebuilding worst...')
  selection.DeselectAll()

  local WorstScore=current.GetSegmentEnergyScore(1)
  local WorstIndex=1

  local k
  for k=2,NumSegs do
   local SegmentScore=current.GetSegmentEnergyScore(k)
   if SegmentScore<WorstScore then
    WorstScore=SegmentScore
    WorstIndex=k
   end -- if SegmentScore
  end -- k

  if (WorstIndex-RebuildRange)<1 then
    WorstIndex=1+RebuildRange
   elseif (WorstIndex+RebuildRange)>NumSegs then
    WorstIndex=NumSegs-RebuildRange
  end -- if

  local SegA=WorstIndex-RebuildRange
  local SegB=WorstIndex+RebuildRange

  for k=SegA,SegB do
   selection.Select(k)
  end -- k loop
  structure.RebuildSelected(RebuildIter)
  selection.DeselectAll()
 end -- if RebuildWorst
end -- rebuild_worst()

function xMutate(Mutating)
   if Mutating then
    save.Quickload(4) -- load best result for this cluster so far
    print('Mutating...')
    if puzzle_is_ligand then
      selection.DeselectAll() -- clear selection
      select_close_ligand() -- select all segments close as MutateLigandDistance or less to ligand
     else
      selection.SelectAll ()
    end -- if puzzle_is_ligand
    do_mutate(1)
    BestScoreCheck() -- Check if it made an improvement
   end -- if Mutating
end -- xMutate()

function detect_ligand(flag)
 --[[
 ligand puzzle detection
 normally, segments have a secondary structure of "E", "H" or "L"
 and they always have a spatial distance of about 3.75 to 3.85 to their next index neighbour.
 a ligand is more far away.

 this function should respond true if this is a ligand puzzle, and false if it is not.
 if flag is nil, ligand auto-detection is enabled, distance of last two segments is checked
 if flag is not nil, ligand auto-detection is disabled, result is flag

 It also returns the last segment index which is no ligand
 ]]--

 local flag=flag

 local LastPos=structure.GetCount() -- fetch very last segment index number

 if flag==nil then -- Only if flag is nil, detect if there is a ligand and change flag
   print('Detecting if there is a ligand.')
   local ss=structure.GetSecondaryStructure(LastPos)
   flag=not(ss=="L" or ss=="H" or ss=="E" )
   -- if last segment´s ss is neither "l" nor "h" nor "e"
   flag=flag or (structure.GetDistance(LastPos-1,LastPos)>=3.9)
   -- or distance to second last segment is bigger or equal than 3.9
 end -- if

 local OS="This should be "
 if flag then
   OS=OS.."a"
   LastPos=LastPos-1
  else
   OS=OS.."no"
 end -- if flag
 OS=OS.." ligand puzzle."
 print(OS)

 return flag,LastPos
end -- detect_ligand()

function create_UseList(flag)
 -- Creates segment use list depending on which puzzle-type is there

 local flag=flag

 UseList={}
                      -- Initialize list of segments to use
                      -- UseList extensions (true) are applied to list, so multiple selected segments will appear more often
 if flag==false then -- If this is no ligand puzzle
   UseList=UseSegIRange(UseList,1,NumSegs,1,true)
                      -- Set every segment index from 1 to puzzle size as bandable
   UseList=Use_distance(UseList,0,8,10,1200,false)
                      -- Consider all segments which have min 10 to max 1200 neighbours
                      -- over a distance of 0 to 8 as non-solitary and remove them from list
   UseList=UseSegIRange(UseList,1,NumSegs,1,true)
                      -- Add a complete segment set again to make sure that distance check didn´t erase all
   UseList=Use_ss(UseList,"L",true)
                      -- Add segments with this secondary structure
                        -- "L"=loop
                        -- "H"=helix
                        -- "E"=sheet
   -- UseList=UseSegIRange(UseList,1,NumSegs,2,false)
                      -- Set every 2nd segment index between 1 to puzzle size as not bandable, example
   -- UseList=UseSegIValues(UseList,{1;3;9},true)
                      -- Include these single segments as bandable, example
   -- UseList=UseSegIValues(UseList,{2;5;10},false)
                      -- Exclude these single segments as bandable, example
   -- UseList=Use_aa(UseList,{"g";"a"},true)
                      -- Set this amino acid as bandable, example
  else -- If this is a ligand puzzle
   UseList=Use_close_ligand(UseList,20,true)
                      -- Set segments which have a maximum spatial distance of 20 to ligand as bandable
 end -- if flag
end -- create_UseList()

function LastBandLengthStrength(Length,Strength)
 -- sets length and strength of the very last band to default values
 local TempBandCount=band.GetCount()
 band.SetGoalLength(TempBandCount,Length)
 band.SetStrength(TempBandCount,Strength)
end -- LastBandLengthStrength()

function add_constant_bands()
 -- Add some constant bands to fix parts of the puzzle here
 -- and/or freeze some parts

 band.AddBetweenSegments(40,15)
 LastBandLengthStrength(5,0.1)

 --[[
 selection.DeselectAll()
 for k=10,11 do
  selection.Select(k)
 end -- k
 freeze.FreezeSelected(true,false)
 ]]--
end -- add_constant_bands()

function showss()
 -- below will show the sequence and secondary structure
 -- adapted 9/2/12 from randforce4d3.txt
 -- adapted 2/27/13 from randforce4d3.txt

 local j,aa,ss
 local aastr="AAs="
 local ssstr="SSs="
 local tot=structure.GetCount()
 print('Puzzle has '..tot..' residues with AAs and SSs as below:')
 for j=1,tot do
  aa=structure.GetAminoAcid(j)
  ss=structure.GetSecondaryStructure(j)
  aastr=(aastr..aa)
  ssstr=(ssstr..ss)
  if j==10*math.floor(j/10) and j<tot then
     aastr=(aastr..' ') -- add blank space after every 10th one
     ssstr=(ssstr..' ')
  end -- if j
 end -- for j
 print(aastr)
 print(ssstr)
end -- showss()

function altervalues()
 local qflag=0
 while qflag==0 do
   local ask=dialog.CreateDialog('CG303 GAB V5')
   ask.Input1=dialog.AddSlider("EOMode",EOMode,0,2,0)
   ask.Label1a=dialog.AddLabel(" ")
   ask.Label1b=dialog.AddLabel("\n0 = don't use Extremal Optimization,\n     breed clusters\n1 = use EO,\n     (don't breed, just leave clusters as they are)\n2 = use EO,\n     (don't breed, replace clusters by random ones)")
   ask.Label1c=dialog.AddLabel(" ")
   ask.Label1d=dialog.AddLabel(" ")

   ask.Input2=dialog.AddTextbox("randstr ",randstr)
   ask.Label2a=dialog.AddLabel("\nBlank     = use best randomization\nNumber = use same sequence of random numbers.")
   ask.Label2b=dialog.AddLabel(" ")
   ask.Label2c=dialog.AddLabel(" ")

   ask.Input3=dialog.AddSlider("HerdSize ",HerdSize,4,14,0)
   ask.Label3a=dialog.AddLabel("Initial number of clusters for one generation")
   ask.Label3b=dialog.AddLabel(" ")

   ask.Input4=dialog.AddSlider("IncHerdSize ",IncHerdSize,4,32,0)
   ask.Label4a=dialog.AddLabel("Maximum herdsize - allow herd growing to this size")
   ask.Label4b=dialog.AddLabel(" ")

   ask.OK = dialog.AddButton("OK", 1)
   dialog.Show(ask)

   EOMode=ask.Input1.value
   randstr=ask.Input2.value
   HerdSize=ask.Input3.value
   IncHerdSize=ask.Input4.value
   qflag=1
 end -- while

 print ('Extremal Optimization Mode: '..EOMode)

 for tmpval in string.gmatch(randstr,'[%s%a]*([%d%-%+]+)') do
  RNDseed=tmpval+0 -- force RNDseed to be a number
 end
 print('As randstr='..randstr..': set RNDseed to '..RNDseed..'.')
 math.randomseed(RNDseed) -- initialize random seed

 if IncHerdSize<HerdSize then
    IncHerdSize=HerdSize
 end -- if IncHerdSize<HerdSize
 print ('Herdsize: '..HerdSize)
 print ('Herdsize increasable to: '..IncHerdSize)

qflag=0
 while qflag==0 do

   local Keep=0
   if (HerdSize%2)==0 then
   -- If number of cluster is even
    Keep=2
    -- Keep 2 clusters
   else
   -- If number of cluster is not even
    Keep=3
    -- Keep 3 clusters
   end -- if (HerdSize%2)==0
   local Breed=(HerdSize-Keep)/2
   -- After subtracting kept clusters,
   -- divide the rest by 2
   -- first half for breeding
   BreedFirst=Keep+1
   BreedLast=Keep+Breed
   -- other half for creating new

   local ask=dialog.CreateDialog('Breed settings')
   ask.Input1=dialog.AddSlider("BreedFirst",BreedFirst,1,HerdSize,0)
   ask.Label1a=dialog.AddLabel("First cluster # beeing a breeded one\nAll before are kept as parents")
   ask.Label1b=dialog.AddLabel(" ")

   ask.Input2=dialog.AddSlider("BreedLast",BreedLast,1,HerdSize,0)
   ask.Label2a=dialog.AddLabel("Last cluster # beeing a breeded one\nAll behind are created new")
   ask.Label2b=dialog.AddLabel(" ")

   ask.Label3=dialog.AddLabel("\nBreed settings are also used by EO as orientation")

   ask.OK = dialog.AddButton("OK", 1)
   dialog.Show(ask)

   BreedFirst=ask.Input1.value
   BreedLast=ask.Input2.value

   qflag=1
 end -- while

 if BreedFirst>BreedLast then
  BreedFirst,BreedLast=BreedLast,BreedFirst
 end -- if BreedFirst>BreedLast
 print ('First cluster to breed: '..BreedFirst)
 print ('Last cluster to breed: '..BreedLast)
end -- altervalues()

 Runs=0
                     -- Number of runs (generations), integer value
                       -- Set to <1 to run infinitely
 puzzle_is_ligand,NumSegs=detect_ligand()
                     -- puzzle_is_ligand: Ligand flag, boolean value
                       -- true for ligand puzzle
                       -- false for non-ligand-puzzle
                     -- NumSegs: Last segment index which is no ligand, integer value
                     -- detect_ligand(): Ligand auto detection.
                       -- If it fails, use detect_ligand(true) to declare that this is a ligand puzzle
                       -- and detect_ligand(false) to declare that this is a no ligand puzzle
 create_UseList(puzzle_is_ligand)
                      -- Initialize segment working list
                      -- Depending on puzzle type
                      -- Advanced Users: see function create_UseList for description of uselist creating features
 MID_Game=3
                       -- Minimum index distance of segment indices, integer value >=2
                       -- As the game doesn´t allow banding the segments with themselves or the nearest neighbour,
                       -- This value is needed to prevent game errors,
                       -- but you can also use it to prevent sharp backbone turns.
 MinBL_Game=3.8
                       -- Minimum band length limiter, float value >=0 and <=MaxBL_Game
                       -- Opposite of MaxBL_Game
                       -- Prevents bands getting too short
 MaxBL_Game=10000
                       -- Maximum band length limiter, float value <=10000 and >=MinBL_Game
                       -- In rough, values about 20 or lower tend to compress the puzzle, values above 20 allow decompressing (stretching)
                       -- Maximum expedient value for a puzzle is about (number of segments-1)*3.8,
                        -- which would stretch the region between connected segments completely out.
 BLchangeDown=-3.8*2
                       -- Maximum band change down, float value <=0
                       -- Generated bands have a minimum length of [current segment distance]+BLchangeDown+BLchangeDownPush
 BLchangeDownPush=-3.8/2
                       -- Value added to BLchangeDown, float value <=0
                       -- This value is added to non-mimic bands if they are shorter or equal current segment distance to guarantee a certain change in length
 BLchangeUp=3.8*1.5
                       -- Maximum band change up, float value >=0
                       -- Generated bands have a maximum length of [current segment distance]+BLchangeUp+BLchangeUpPush
 BLchangeUpPush=3.8/2
                       -- Value added to BLchangeUp, float value >=0
                       -- This value is added to non-mimic bands if they are longer than current segment distance to guarantee a certain change in length
 BreedFirst=3
                      -- First cluster to change by breeding, integer value
                      -- All clusters before this index will be kept as good solution and as potential parents for breeding new solutions
                        -- Setting this to 1 is not a good idea, because you will loose good clusters as breeding parents (some kind of incest), but should work, too
 BreedLast=5
                      -- Last cluster to change by breeding, integer value >=BreedFirst and <=HerdSize
                      -- All clusters after this index to HerdSize will be generated randomly
                      -- This value will be increased if no better solution was found

 HerdSize= 8
                      -- Number of clusters, integer value >=BreedLast (alterable by InputBox)
                      -- This value will be increased if no better solution was found
 IncHerdSize= 16
                       -- Increase herdsize, integer value (alterable by InputBox)
                        -- Allows increasing the herdsize if no better solution was found (will generate more clusters)
                        -- if >HerdSize, allow increasing herdsize until this amount
                        -- if <=HerdSize, no increasing

 EOMode=0
                      -- Extremal Optimization mode, integer value (alterable by InputBox)
                        -- 0 (default) = No EO. Script uses genetic algorithm with breeding
                          -- clusters with index BreedFirst...BreedLast are breeded for next generation
                          -- clusters with index behind BreedLast are re-generated randomly
                        -- 1 = EO (light)
                          -- clusters with index BreedFirst...BreedLast are kept as they are
                          -- clusters with index behind BreedLast are re-generated randomly
                        -- 2 = EO (hard, closer to paradigma)
                          -- All clusters with index at BreedFirst and behind are re-generated randomly
 ShowBF=true
                      -- Shows band and freeze details, boolean value
                        -- true (default) = segments which are banded or frozen are shown by text
                        -- false = no text for these actions
 ClusterBands=4
                      -- Maximum Bands to create per cluster, integer value >=0
 ClusterFreezes=3
                      -- Maximum segments to freeze by random, integer value >=0
 MinBS=0.8
                      -- Minimum strength per (random chosen) band, float value
                        -- Use decimal number between .1 and 10
 MaxBS=1.2
                      -- Minimum strength per (random chosen) band, float value
                        -- Use decimal number between .1 and 10 and >=MinBS
 Shakes=1
                      -- Number of iterations for fuse-shake, integer value
 Wiggles=4
                      -- Number of iterations for fuse-wiggle, integer value
 PWiggles=1
                      -- Number of iterations for pulling, integer value
 CI_pull=1
                      -- Clashing importance for pulling, float value >=0 and <=1
                        -- Default is 1
                        -- Reduce this to make pulling more drastic
 Releasing=true
                      -- Release flag, boolean value
                        -- true (default) = After pulling, releasing is performed.
                        -- false = releasing is skipped (and Fuse, too)
 Fuse=true
                      -- Fuse flag, boolean value
                        -- true (default) = After pulling, Fuse (requires Releasing=true) is performed.
                        -- false = after pulling, just a shake(1) and wiggle_all(12) with CI=1 is performed
 MutateLigandDistance=15
                      -- Radius length for selection sphere around ligand, where mutating is performed.
                        -- Selects only segments which are this or more close to the ligand for mutating.
 ScoreThreshold=0.5
                      -- Threshold value for shake and wiggles, float value >=0
                        -- This won´t repeat some w/s, if absolute score change per itertation is below this
 MultiCrossOver=true
                      -- Multi crossover flag, boolean value
                        -- false (default) = One crossover point for each breeding is generated.
                        -- true = Each gene can be from mom or dad
 Parent1isRoulette=false
                      -- Roulette flag for breeding parent 1, boolean value
                        -- false (default) = parent is cluster with best score and downwards
                          -- use this to force good clusters for breeding
                        -- true = parent is chosen by fitness roulette
 Parent2isRoulette=true
                      -- Roulette flag for breeding parent 2, boolean value
                      -- true (default) = parent is chosen by fitness roulette
                      -- false = parent is next to parent 1
                        -- use this to force good clusters for breeding
 DriftProb=0.3
                      -- band drift (cluster mutation) probability, float value >=0 and <1
                        -- Probability, if drift is added or not
 InvBProb=0.2
                      -- Inverting (deactivating/reactivating) probability for bands, float value >=0 and <1
                        -- Makes inversion happen depending on this probability value
 InvFProb=0.3
                      -- Inverting (deactivating/reactivating) probability for freezes, float value >=0 and <1
                        -- Makes inversion happen depending on this probability value
 ShuffleProb=0.9
                      -- Shuffle rate, float value >=0 and <=1
                        -- Used to scramble random segment list, where bands are applied
                        -- 0 lets the list be as it is
                        -- 1 swaps all list entries with a random one behind them in list
 RecentUse=true
                        -- recent best flag, boolean value
                          -- true = recent best puzzle state is used for each generation
                          -- false = initial puzzle state is used for each generation
                            -- prevents getting stuck on local maximum (recommended for endgame)
                          -- If using RecentHybrid or LastBest, this value will be set automatically
 RecentHybrid=0
                        -- Hybrid behaviour between RecentUse=false/true, integer value >=0
                          -- ==0 = regular behaviour as set in RecentUse
                          -- >0 = use intial puzzle state but recent best state each RecentHybrid´s generations
                           -- (counting from generation 2)
                          -- 1 would have the same effect as RecentUse=true
                          -- I recommend values>=2 when using it
 LastBest=false
                        -- Flag for using best cluster of current generation, boolean value
                        -- false (default) = use recent best or initial puzzle state (as set in RecentUse/RecentHybrid)
                        -- true = neither recent best nor initial puzzle state are loaded, but best result of current generation,
                        -- allowing unimproving the puzzle to get out of local maximum
                        -- Try this, you are really stuck on a puzzle.
 BreedFirstCurrentForce=nil
                       -- Loop start cluster force flag, integer value
                         -- nil (default) = best clusters will only be tested again
                           -- if there was an improvement in last generation
                         -- >0 = start at this cluster after first generation
                           -- 1 = test all clusters again (also good ones)
                           -- If BreedFirst, test only new generated clusters
 SCPT=1
                        -- Score change positive tolerance, float value >=0
                          -- Activates rebuild (if allowed)
                          -- if current generation start score and best cluster score difference
                          -- is below this positive value (not good enough)
 SCNT=-10
                        -- Score change negative tolerance, float value <=0
                          -- Activates rebuild (if allowed)
                          -- if current generation start score and best cluster score difference
                          -- is above this negative value (not bad enough)
 RebuildWorstGen=true
                        -- Rebuild worst at generation start flag, boolean value
                          -- true = rebuild worst is executed once for current generation
                          -- false = rebuild worst is executed for each cluster (not recommended)
                          -- nil = rebuild is never executed.
 RebuildWorst=false
                        -- Rebuild flag at script start, boolean value
                          -- true = rebuild is executed in first generation
 RebuildForce=nil
                        -- Force RebuildWorst, boolean value
                        -- Sets how RebuildWorst is changed.
                          -- nil (default) = worst segment is only rebuilt
                            -- if there was no improvement in last generation
                          -- true = worst segment is always rebuilt before pulling
                          -- false = worst segment is never rebuilt before pulling
 RebuildRange=2
                        -- Rebuild range, integer value>=1
                          -- For example, if 1 and worst segment is 3, segments from 2 to 4 are rebuilt.
                          -- if 2 and worst segment is 3, segments from 1 to 5 are rebuilt.
 RebuildIter=1
                      -- Iterations for rebuild worst, integer value>0
 Mutating1=puzzle_is_ligand
                      -- if true, puzzle segment mutating after pulling is performed
 Mutating2=false
                      -- if true, puzzle segment mutating after releasing is performed
 ConstantBands=false
                      -- Add constant bands flag, boolean value
                        -- if true, adds user-defined bands and freezes of add_constant_bands function above
                        -- before regular test-cluster is applied
 Mimic=false
                        -- Mimic flag, boolean value
                          -- if true, first cluster tries to imitate initial puzzle state

 randstr=' '
                      -- Random Seed (input box), String value (alterable by InputBox)
                        -- if not empty, it will change RNDseed

 RNDseed=os.time()+recipe.GetRandomSeed()
                      -- Random Seed (resulting), integer value
                        -- Here, the initial value is set to system time plus the game´s random seed, so we get different random numbers
                        -- for each PC and each time the script is started.
                        -- If you want the same numbers (for testing purposes/results), enter a value in randstr.

 altervalues()
 -- alter some of the default values given above via InputBox
 print('\nDoing puzzle '..puzzle.GetName()..' with ID '..puzzle.GetPuzzleID()..'.')
 -- show puzzle details
 showss()
 -- show AA and SS
 GAB()
 -- call main program