# Okay to post homework
# Ryan Badi, March 24, 2024, Homework 16

Help := proc(): print("qSR(q,INI,L,n), determine_period_length(qsr)"): end:

qSR := proc(q, INI, L, n) local r, i, M, ng:
  r := nops(L):

  if nops(INI) <> L[-1][2] then:
    return FAIL:
  fi:

  if not (sort(INI)[-1] < q and sort(INI)[1] >= 0) then:
    return FAIL:
  fi:

  if not (type(L, list) and {seq(type(L[i], list), i=1..nops(L))} = {true} and {seq(type(L[i][1], posint), i=1..nops(L))} = {true} and {seq(type(L[i][2], posint), i=1..nops(L))} = {true} and sort([seq(L[i][1], i=1..nops(L))])[-1] < q and sort([seq(L[i][1], i=1..nops(L))])[1] >= 0 and sort([seq(L[i][2], i=1..nops(L))]) = [seq(L[i][2], i=1..nops(L))]) 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:
  return M:
end:

determine_period_length := proc(qsr) local count, fail_count:
  fail_count := nops(qsr):
  count := 1:
  while qsr[1..count] <> qsr[count+1..2*count] do:
    count := count + 1:
	if count > fail_count then: return FAIL: fi:
  od:
  return count:
end:

printf("Period length of qSR(3,[1,2,1],[[1,2],[2,3]],10000): %a\n", determine_period_length(qSR(3, [1, 2, 1], [[1, 2], [2, 3]], 10000))):
printf("Period length of qSR(5,[1,2,4,1,2],[[1,2],[2,5]],10000): %a\n", determine_period_length(qSR(5,[1,2,4,1,2],[[1,2],[2,5]], 10000))):
printf("Period length of qSR(11,[3,1,2,4,3],[[1,2],[2,5]],10000): %a\n", determine_period_length(qSR(11,[3,1,2,4,3],[[1,2],[2,5]], 10000))):
printf("Period length of qSR(5,[1,0,0,0,0,0],[[3,4],[2,5],[3,6]],10000): %a\n", determine_period_length(qSR(5,[1,0,0,0,0,0],[[3,4],[2,5],[3,6]], 10000))):