#HW 16 Nuray Kutlu
#OK TO POST


#C16.txt, March 18, 2024
Help:=proc(): print(`SR(INI,L,n), IsPer1(L,t), FindPer(L) `):end:

qSR:=proc(q,INI, L, n) local r, i,M,ng, IsSort:
r:=nops(L):
IsSort:=[]:
if nops(INI)<>L[-1][2] then
RETURN(FAIL):
fi:
for i from 1 to nops(INI) do:
 if INI[i]>(q-1) then
  RETURN(FAIL):
 fi:
od:
for i from 1 to nops(L) do:
 if L[i][1]>(q-1) then
  RETURN(FAIL):
 fi:
 IsSort:= [op(IsSort), L[i][2]]
od:

if not (type(L,list) and {seq(type(L[i][2],posint),i=1..nops(L))}={true} and sort(IsSort)=IsSort) then
   RETURN(FAIL):
fi:
if not type(n,posint) then
     RETURN(FAIL):
fi:
M:=INI:
while(nops(M))<n do
 ng:=add(L[i][1]*M[-L[i][2]], i=1..r) mod q:
 M:=[op(M),ng]:
od:
M:
end:

#FindPer(qSR(3, [1, 2, 1], [[1, 2], [2, 3]], 10000)) : 26
#FindPer(qSR(5, [1, 2, 4, 1, 2], [[1, 2], [2, 5]], 10000)) : 744
#FindPer(qSR(11, [3, 1, 2, 4, 3], [[1, 2], [2, 5]], 10000)) : 3660
#FindPer(qSR(5, [1, 0, 0, 0, 0, 0], [[3, 4], [2, 5], [3, 6]], 10000)): 744

#OLD CODE FROM CLASS:


#IsPer(L,t): Is L periodic of period t?
IsPer:=proc(L,t) local i:
if {seq(L[i]-L[i+t],i=1..nops(L)-t)}={0} then
  true:
else
 false:
fi:
end:

FindPer:=proc(L) local t:
for t from 1 to trunc(nops(L)/2) while not IsPer(L,t) do od:
if t=trunc(nops(L)/2)+1 then
RETURN(FAIL):
else
 RETURN(t):
fi:
end: