| Item number | Weight (in Kgs) |
Value (in Rupees) |
|---|---|---|
| 1 | 10 | 60 |
| 2 | 7 | 28 |
| 3 | 4 | 20 |
| 4 | 2 | 24 |
The task is to pick a subset of these items such that their total weight is no more than $$11$$ $$Kgs$$ and their total value is maximized. Moreover, no item may be split. The total value of items picked by an optimal algorithm is denoted by $$V$$opt. A greedy algorithm sorts the items by their value-to-weight ratios in descending order and packs them greedily, starting from the first item in the ordered list. The total value of items picked by the greedy algorithm is denoted by $$V$$greedy.
The value of $$V$$opt $$β$$ $$V$$greedy is ____________.
Choose a value for $$x$$ that will maximize the number of minimum weight spanning trees $$(MWSTs)$$ of $$G.$$ The number of $$MWSTs$$ of $$G$$ for this value of $$x$$ is ______.
$$\eqalign{ & {T_1}:\,\,\,a?{\left( {b|c} \right)^ * }a \cr & {T_2}:\,\,\,b?{\left( {a|c} \right)^ * }b \cr & {T_3}:\,\,\,c?{\left( {b|a} \right)^ * }c \cr} $$
Note that $$'x?'$$ means $$0$$ or $$1$$ occurrence of the symbol $$x.$$ Note also that the analyzer outputs the token that matches the longest possible prefix.
If the string $$bbaacabc$$ is processed by the analyzer, which one of the following is the sequence of tokens it outputs?
Which one of the following is correct for the given parse tree?