Formal Language: check language with one stack and one queue - data-structures

Question

Write a pseudo code of method isL(w) which checks if the string w is an element of L using only 1 stack and 1 queue
L = {a^n⋅b^n⋅c^m⋅d^m | n≥1, m≥1} U {a^n⋅b^m⋅c^m⋅d^n | n≥1, m≥1}
(a^n is n-th power of a)
You can suppose that stack and queue is already implemented and use them with the variable stack and queue.
My code answering only half of this question is:
isL(w) {
for (each char ch in w) {
if (ch == 'a' || ch == 'c') {
stack.push( ch );
}
else if (ch == 'b' || ch == 'd') {
queue.enqueue( ch );
}
else return false; // no other letter than a,b,c,d
}
while (!queue.isEmpty()) {
if (stack.pop() == 'c' && queue.dequeue() == 'b')
continue;
else if (stack.pop() == 'a' && queue.dequeue() == 'd')
continue;
else
return false;
}
return true;
}
Though I targeted latter subset, it's still wrong for the latter too.
How do I implement the full answer that also checks the former subset?

Answer 1

isL(w) {
if (w[0] != 'a') return false
stack.push('a')
for ch in w{
if (!stack.isEmpty()) {
if (ch == 'a') stack.push(ch)
else if (ch == 'b') stack.pop()
else return false
}
else {
if (ch == 'c') queue.push(ch)
else if (!queue.isEmpty() && ch == 'd') queue.dequeue()
else return false
}
}
return true
}