Consider a stack data structure into which we can PUSH and POP records. Assume that each record pushed in the stack has a positive integer key and that all keys are distinct. We wish to augment the stack data structure with an $\mathrm{O}(1)$ time MIN operation that returns a pointer to the record with smallest key present in the stack

1. without deleting the corresponding record, and

2. without increasing the complexities of the standard stack operations.

Which one or more of the following approach(es) can achieve it?

Consider the following algorithm someAlgo that takes an undirected graph $G$ as input. someAlgo ( $G$ )

1. Let $v$ be any vertex in $G$. Run BFS on $G$ starting at $v$. Let $u$ be a vertex in $G$ at maximum distance from $v$ as given by the BFS.

2. Run BFS on $G$ again with $u$ as the starting vertex. Let $z$ be the vertex at maximum distance from $u$ as given by the BFS.

3. Output the distance between $u$ and $z$ in $G$.

The output of someAlgo( $T$ ) for the tree shown in the given figure is $\qquad$ . (Answer in integer)

An audit of a banking transactions system has found that on an earlier occasion, two joint holders of account $A$ attempted simultaneous transfers of Rs. 10000 each from account $A$ to account $B$. Both transactions read the same value, Rs. 11000, as the initial balance in $A$ and were allowed to go through. $B$ was credited Rs. 10000 twice. $A$ was debited only once and ended up with a balance of Rs. 1000. Which of the following properties is/are certain to have been violated by the system?

Consider the following relational schema along with all the functional dependencies that hold on them.

$$\begin{aligned} & R 1(A, B, C, D, E):\{D \rightarrow E, E A \rightarrow B, E B \rightarrow C\} \\ & R 2(A, B, C, D):\{A \rightarrow D, A \rightarrow B, C \rightarrow A\} \end{aligned}$$

Which of the following statement(s) is/are TRUE?