Consider the following recurrence relation:
$$T(n) = \begin{cases} \sqrt{n} T(\sqrt{n}) + n & \text{for } n \ge 1, \\ 1 & \text{for } n = 1. \end{cases}$$
Which one of the following options is CORRECT?
Which of the following is/are Bottom-Up Parser(s)?
Consider the following syntax-directed definition (SDD).
| S → DHTU | { S.val = D.val + H.val + T.val + U.val; } |
| D → “M” D1 | { D.val = 5 + D1.val; } |
| D → ε | { D.val = –5; } |
| H → “L” H1 | { H.val = 5 * 10 + H1.val; } |
| H → ε | { H.val = –10; } |
| T → “C” T1 | { T.val = 5 * 100 + T1.val; } |
| T → ε | { T.val = –5; } |
| U → “K” | { U.val = 5; } |
Consider the following grammar $G$, with $S$ as the start symbol. The grammar $G$ has three incomplete productions denoted by (1), (2), and (3).
$$S \rightarrow d a T \mid \underline{\ (1)}$$
$$T \rightarrow a S \mid b T \mid \ \underline{(2)}$$
$$R \rightarrow \underline{(3)} \mid \epsilon$$
The set of terminals is $\{a, b, c, d, f\}$. The FIRST and FOLLOW sets of the different non-terminals are as follows.
FIRST($S$) = $\{c, d, f\}$, FIRST($T$) = $\{a, b, \epsilon\}$, FIRST($R$) = $\{c, \epsilon\}$
FOLLOW($S$) = FOLLOW($T$) = $\{c, f, \#\}$, FOLLOW($R$) = $\{f\}$
Which one of the following options CORRECTLY fills in the incomplete productions?