module Project where

studentInput  = [["1", "MmcG", "","",""], ["2", "CM", "GE", "", ""],
                 ["3", "BG", "CM", "GE", "JN"], ["4", "JC", "CM", "GE", 
"JN"],
		 ["5", "GE", "DF", "TC", ""], ["6", "BG", "MH", "MH", "JG"],
		 ["7", "JC", "JN", "JN", "JH"], ["8", "JS", "GE", "CM", "RR"],
		 ["9", "NM", "JS", "AM", "JC"], ["10", "MM", "JC", "TS", "GE"],
		 ["11", "JC", "AM", "DF", "MT"], ["12", "CM", "JN", "JH", "DF"],
		 ["13", "BG", "MM", "CM", "AM"], ["14", "CM", "AM", "DF", "GE"],
		 ["15", "DF", "JC", "CM", "JS"], ["16", "MM", "CM", "BG", "AM"],
		 ["17", "GE", "CM", "DF", "AM"], ["18", "JC", "JS", "CM", "JS"],
		 ["19", "JS", "RR", "DF", "JS"], ["20", "CM", "GE", "RR", "JN"],
		 ["21", "CM", "MM", "GE", "GP"], ["22", "", "", "", ""],
		 ["23", "GE", "AM", "CM", "JC"], ["24", "CT", "CT", "CT", "JS"],
		 ["25", "CT", "JH", "", ""], ["26", "JN", "JH", "JN", "JH"],
		 ["27", "JN", "JH", "JH", "MH"], ["28", "JoC", "JN", "", ""],
		 ["29", "JC", "JN", "JN", "JH"], ["30", "JN", "JS", "JoC", "MH"],
		 ["31", "JN", "MH", "JS", "TH"], ["32", "MH", "JN", "MH", ""],
		 ["33", "MH", "JN", "JH", "DoR"], ["34", "JN", "JN", "JN", "JN"],
		 ["35", "JoC", "JoC", "JoC", "CT"], ["36", "MH", "DoR", "AK", "MH"],
		 ["37", "MH", "CT", "JN", "JH"], ["38", "CT", "", "", ""],
		 ["39", "MH", "", "", "CT"], ["40", "CT", "JN", "MH", ""],
		 ["41", "JN", "JN", "JN", "JH"], ["42", "RR", "JC", "AM", "AM"],
		 ["43", "GE", "", "", ""], ["44", "MH", "MH", "RR", "NM"],
		 ["45", "", "", "", ""], ["46", "RR", "JS", "JC", "GP"],
		 ["47", "JS", "JN", "JN", ""], ["48", "JS", "JN", "JN", "JN"],
		 ["49", "TH", "TH", "TH", "TH"], ["50", "JC", "RR", "RR", ""]
		]

staffInput    = ["GE", "GE", "MmcG", "BG", "RD", "TC", "JB", "JB", "JM", 
"JM", "CM", "CM", "CM",
		 "NM", "NM", "TS", "MT", "MoC", "AM", "AM", "DF", "DF", "MM", "JW", "JW", 
"GP",
		 "GP", "CT", "CT", "CT", "JH", "JH", "JoC", "JoC", "JC", "JC", "TH", "TH", 
"MH",
		 "MH", "DoR", "DoR", "JN", "JN", "AK", "AK", "RR", "RR", "JS", "JS"]

--For Staff input there is 50 names but some are repeated since there is
--not enough staff to accomdate all the students. The staffInput is given
--by their initials

numberOfStudents = length studentInput

studentName i = (studentInput !! (i-1)) !! 0
staffName i   = (staffInput !! (i-1))
firstChoice i = (studentInput !! (i-1)) !! 1
secondChoice i   = (studentInput !! (i-1)) !! 2
thirdChoice i = (studentInput !! (i-1)) !! 3
fourthChoice i  = (studentInput !! (i-1)) !! 4
initialState i = i

--initialstate is the position of the students relative to the staffInput
--i.e student 1 will have GE and student 5 would have RD and so on

weight(i,j)   =
  if firstChoice i == staffName j
    then 0
    else if secondChoice i == staffName j
      then 4
      else if thirdChoice i == staffName j
	then 8
	else if fourthChoice i == staffName j
	  then 12
	  else 16

--Each staffName is given a weighting according to the student ranking

successor s i = s (i+1)

--This is to map it onto the next element let s i = initialstate i

position i s  = if i== (s 1)  then 1
	        else 1+(position i (successor s))

--Finds position of student relative to the staffInput
--Try position 9 initialstate initialstate

studentiAssignedToStaff i s = staffName (position i s)

--Shows staffName at a certain position

stWeight s n = if (n==1) then weight((s 1),((numberOfStudents -n) +1))
               else (weight ((s 1), ((numberOfStudents -n) +1))) +
                                      (stWeight  (successor s) (n-1) )

stateWeight s = stWeight s numberOfStudents

--stateWeight is the sum of i=1 to 50 weight(initialstate i, i) or
--it can be the transposition of initialstate

tr i j x = if (and [i/=x,j/=x]) then x
           else
                  if (i==x) then j
                  else i

myMod k n = if ((mod k n)==0) then n
            else mod k n

myDiv k n = if ((mod k n)==0) then (div k n) -1
            else div k n

trans k x= tr (1+(myDiv k numberOfStudents)) ((myMod k numberOfStudents)) x

--These four lines above transposes two elements in the list i.e our 
initialstate is
--[1,2,...,49,50] it will be continously transposed so get a desirable 
assignment

gFunction s k = if (k==(numberOfStudents*numberOfStudents)) then s
                else if (stateWeight s)>(stateWeight (s.(trans k)))
                            then (s.(trans k))
                     else gFunction s (k+1)

--gFunction is the state obtained from s by interchanging the ith & jth
--enteries of initialstate such that {stateweight initialstate > stateweight 
transpose initialstate}


nextState s = gFunction s 1

--start at initialstate and compute initialstate, gFunction(initialstate),
--gFunction(gFunction(initialstate)) etc

finalState s = if ((stateWeight s) == (stateWeight (nextState s))) then s
               else finalState (nextState s)

--Output when stateWeight initialstate == stateweight (nextstate 
initialstate)

studentsSupervisor i = studentiAssignedToStaff i (finalState initialState)

--Last line outputs what is the particular students supervisor