#Please do not post homework
#Lucy Martinez, 04-27-2024, Assignment 26
read `ENGLISH.txt`:
with(combinat):

# Problem 2: Using the file ENGLISH.txt, where ENG() is a list of length 26
#  whose i-th entry is the list of words of length i, find:

#  Out of the 26^2=676 pairs of letters how many actualy show up as consecutive
#  two letters? (For example for the word [a,l,e,x] 
#  the pairs [a,l],[l,e],[e,x] showed up

#  ANSWER: 589 --- only counts words of length 3 or more (See Count1() below)


#  Out of the 26^3=175676 triples of letters how many actually show up as
#  consecutive three letters? (For example for the word [v,a,l,e,n,t,i,n,o]
#  the triples [v,a,l],[a,l,e],[l,e,n],[e,n,t],[n,t,i],[t,i,n],[i,n,o] showed up

#  ANSWER: 581 --- only counts words of length 4 or more (See Count2() below)


#chooseRepeat(L,m,k): Inputs a list L, and duplicates it k times, outputs
# a list of lists [xi,yi] where xi, yi is an element of L
chooseRepeat:= proc(L, m, k) local i,duplicated:
duplicated := [seq(op(L), i=1 .. k)]:
return choose(duplicated, m): 
end proc:


Count1:=proc() local allwords,ALPH,allpairs,i,current,w,S,j,curword:
allwords:=ENG():
#ALPH:=[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z]:
#allpairs:=chooseRepeat(ALPH, 2, 2):
S:={}:
for i from 3 to 26 do
 current:=allwords[i]: #this is the list of all words of length i
 for w in current do #looks at each word in all words of length i
  for j from 1 to nops(w)-1 do
   curword:=[w[j],w[j+1]]:
   S:=S union {curword}:
  od:
 od:
od:
nops(S):
end:


Count2:=proc() local allwords,ALPH,alltriples,i,current,w,S,j,curword:
allwords:=ENG():
#ALPH:=[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z]:
#alltriples:=chooseRepeat(ALPH, 3, 3):
S:={}:
for i from 4 to 26 do
 current:=allwords[i]: #this is the list of all words of length i
 for w in current do #looks at each word in all words of length i
  for j from 1 to nops(w)-2 do
   curword:=[w[j],w[j+1],w[j+1]]:
   S:=S union {curword}:
  od:
 od:
od:
nops(S):
end:





###################################C26.txt
#C26.txt, April 22, 2024
Help26:=proc(): 
 print(` FT(SetL), TM(SetL) `):
end:




#FT(SetL): The frequency table of all words whose length belobgs to SetL
#For example FT({3,4}) returns the randked frequency table for words of
#length 3 and 4
FT:=proc(SetL) local ALPH,T1,W,DB,C,B,FL,L,A,FL1,S1:
ALPH:=[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z]:
DB:=ENG():
C:=0:
for L in ALPH do
 T1[L]:=0:
od:

for A in SetL do
 for W in DB[A] do
  for B from 1 to nops(W) do
    T1[W[B]]:=T1[W[B]]+1:
    C:=C+1:
  od:
 od:
od:
FL:=evalf([seq(T1[ALPH[A]]/C,A=1..nops(ALPH))]):
FL1:=sort(FL,`>`):
for A from 1 to nops(ALPH) do
 S1[FL[A]]:=ALPH[A]:
 od:

FL1,[seq(S1[FL1[A] ],A=1..nops(ALPH))], [seq([FL1[A],S1[FL1[A]] ],A=1..nops(ALPH))] :

end:


#TM(SetL): The frequency table of all words whose length belobgs to SetL
#For example FT({3,4}) returns the randked frequency table for words of
#length 3 and 4
#AND the Transiton matrix 28x28 the first "letter" is ST and the last is EN
#NOT YET FINISHED
TM:=proc(SetL) local ALPH,T1,W,DB,C,B,FL,L,A,FL1,S1,T2,L1,L2,ST,EN,T3,ALPH1:
print(`Not yet finished`):
ALPH:=[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z]:
DB:=ENG():
C:=0:
for L in ALPH do
 T1[L]:=0:
od:

for L1 from 1 to nops(ALPH) do
 T2[ST,ALPH[L1]]:=0:
  T2[ALPH[L1],EN]:=0:
 for L2 from 1 to nops(ALPH) do
  T2[ALPH[L1],ALPH[L2]]:=0:
  od:
od:

for A in SetL do
 for W in DB[A] do
  for B from 1 to nops(W) do
    T1[W[B]]:=T1[W[B]]+1:

   C:=C+1:

    if B<nops(W) then
     T2[W[B],W[B+1]]:=T2[W[B],W[B+1]]+1:
     else
      T2[W[B],EN]:=T2[W[B],EN]+1:
     fi:

    if B=1 then
    T2[ST,W[1]]:=T2[ST,W[1]]+1:
    fi:
   
  od:
 od:
od:
FL:=evalf([seq(T1[ALPH[A]]/C,A=1..nops(ALPH))]):
FL1:=sort(FL,`>`):
for A from 1 to nops(ALPH) do
 S1[FL[A]]:=ALPH[A]:
 od:


for L1 from 1 to nops(ALPH) do

T3[ST,ALPH[L1]]:=evalf(T2[ST,ALPH[L1]]/C):
T3[ALPH[L1],EN]:=evalf(T2[ALPH[L1],EN]/C):
od:

for L1 from 1 to nops(ALPH) do
for L2 from 1 to nops(ALPH) do
 T3[ALPH[L1],ALPH[L2]]:=evalf(T2[ALPH[L1],ALPH[L2]]/C):
od:
od:
 

FL1,[seq(S1[FL1[A] ],A=1..nops(ALPH))], [seq([FL1[A],S1[FL1[A]] ],A=1..nops(ALPH))] , op(T3):

end: