The keys $5,28,19,15,26,33,12,17,10$ are inserted into a hash table using the hash function $h(k)=k \bmod 9$. The collisions are resolved by chaining. After all the keys are inserted, the length of the longest chain is $\_\_\_\_$ . (answer in integer)

Let $G$ be a weighted directed acyclic graph with $m$ edges and $n$ vertices. Given $G$ and a source vertex $s$ in $G$, which one of the following options gives the worst case time complexity of the fastest algorithm to find the lengths of shortest paths from $s$ to all vertices that are reachable from $s$ in $G$ ?

Consider a binary search tree (BST) with $n$ leaf nodes ( $n>0$ ). Given any node $V$, the key present in the node is denoted as $\operatorname{Val}(V)$. All the keys present in the given BST are distinct. The keys belong to the set of real numbers.

For a node $V$, let $\operatorname{Suc}(V)$ denote the node that is its inorder successor. If a node $V$ does not have an inorder successor, then $\operatorname{Suc}(V)$ is NULL. As there are no duplicates, if $\operatorname{Suc}(V)$ is not NULL, then $\operatorname{Val}(V)<\operatorname{Val}(\operatorname{Suc}(V))$.

Corresponding to every leaf node $L_i$ that has a non-NULL $\operatorname{Suc}\left(L_i\right)$, a new key $k_i$ with the following property is to be inserted into the BST.

$$ \operatorname{Val}\left(L_i\right) < k_i < \operatorname{Val}\left(\operatorname{Suc}\left(L_i\right)\right) $$

Let $K$ represent the list of all such new keys to be inserted into the BST.

Which of the following statements is/are true?

Consider a stack $S$ and a queue $Q$. Both of them are initially empty and have the capacity to store ten elements each. The elements $1,2,3,4$, and 5 arrive one by one, in that order. When an element arrives, it is assigned either to $S$ (pushed on $S$ ) or to $Q$ (enqueued to $Q)$. Once all the five elements are stored, the output is generated in two steps. First, stack $S$ is emptied by popping all elements. Then queue $Q$ is emptied by dequeueing all elements. The output obtained by following this process is 43125 .

Given the output, the objective is to predict whether an element was assigned to $S$ or $Q$. Which of the following options is/are possible valid assignment(s) of the elements?

Note: In the options, the notation $x S$ denotes that element $x$ was assigned to $S$ and $y Q$ denotes that element $y$ was assigned to $Q$.