Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given by the entry $${W_{ij}}$$ in the matrix $$W.$$ $$$W = \left[ {\matrix{ 0 & 2 & 8 & 5 \cr 2 & 0 & 5 & 8 \cr 8 & 5 & 0 & X \cr 5 & 8 & X & 0 \cr } } \right]$$$

The largest possible integer value of $$x,$$ for which at least one shortest path between some pair of vertices will contain the edge with weight $$x$$ is _________________.

An operator $$delete(i)$$ for a binary heap data structure is to be designed to delete the item in the $$i$$-th node. Assume that the heap is implemented in an array and i refers to the $$i$$-th index of the array. If the heap tree has depth $$d$$ (number of edges on the path from the root to the farthest leaf), then what is the time complexity to re-fix the heap efficiently after the removal of the element?

The attributes of three arithmetic operators in some programming language are given below.

Operator	Precedence	Associativity	Arity
+	High	Left	Binary
_	Medium	Right	Binary
*	Low	Left	Binary

The value of the expression $$2 - 5 + 1 - 7 * 3$$ in this language is _______________.

Consider the following Syntax Directed Translation Scheme $$(SDTS),$$ with non-terminals $$\left\{ {S,A} \right\}$$ and terminals $$\left\{ {A,B} \right\}.$$
$$S \to aA$$ $$\,\,\,\,\,$${ print $$1$$ }
$$S \to a$$ $$\,\,\,\,$$$$\,\,\,\,\,$${ print $$2$$ }
$$A \to Sb$$ $$\,\,\,\,\,$${ print $$3$$ }

Using the above $$SDTS,$$ the output printed by a bottom-up parser, for the input $$aab$$ is: