CYK算法自顶向下设计，带有记忆功能

Question

我运行CYK算法，但是，我试图将其作为自顶向下设计（memoization），任何帮助吗？

bool canDerive(nonterminal S, string w) {
    return canDeriveRec(S, w, 0, w.size());
}

/* Can you derive the substring [start, end) of w from S? */
bool canDeriveRec(nonterminal S, string w, int start, int end) {
    /* Base case: Single characters */
    if (end - start == 1) {
        return whether there is a production S -> a, where a = w[start];
    }

    /* Recursive case: Try all possible splits */
    for (each production S -> AB) {
        for (int mid = start + 1; mid < end; mid++) {
            if (canDeriveRec(A, w, start, mid) &&
                canDeriveRec(B, w, mid, end)) {
                return true;
            }
        }
    }
    return false;
}