#OK to post homework
#GLORIA LIU, Apr 20 2024, Assignment 25

read `C26.txt`:

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#1. Continue to work on your project due May 1, 11:00pm

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#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] shosed up.
#Out of the 26^2=676 pairs of letters how many show up up as consecutive two lettersmore than ten times?
#Out of the 26^3=175676 triples of letters how many actualy 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)

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]:

pairs:=proc() local DB,S,I1,Table,L,Letter,Letter2,length,W:
DB:=ENG():
S:={}:
for Letter in ALPH do
 for Letter2 in ALPH do
  Table[Letter,Letter2]:=0:
 od:
od:
for L in DB do
 for W in L do
  length:=nops(W):
  for I1 from 1 to length-1 do
   S:=S union {[W[I1],W[I1+1]]}:
   Table[W[I1], W[I1+1]]:=Table[W[I1], W[I1+1]]+1:
  od:
 od:
od:
S,op(Table):
end:

result:=pairs():
nops(result[1]);
Table:=result[2]:
count:=0:
for Letter in ALPH do
 for Letter2 in ALPH do
  if Table[Letter,Letter2]>=10 then
   count:=count+1:
  fi:
 od:
od:
count;

#I got that there were 593 pairs in total, and 500 of them appeared 10 times or more

triples:=proc() local DB,S,I1,L,length,W:
DB:=ENG():
S:={}:
for L in DB do
 for W in L do
  length:=nops(W):
  for I1 from 1 to length-2 do
   S:=S union {[W[I1],W[I1+1],W[I1+2]]}:
  od:
 od:
od:
S:
end:

nops(triples());
#I got that there were 6639 triples

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#3. Finish up procedure TM(SetL) that should output a 28 by 28 matrix (in decimals) where the order is 
#ALPH1:=[ST,a,b,c ..., z, EN], and the [i,j] entry is the probability that if you are currently at letter ALPH1[i] that the 
#letter after that is ALPH1[j]. The last row should of course be all zeores.
#Skipped