Consider the (incomplete) pseudocode snippet SOLVE().

function SOLVE($G=(V,E,w)$, $s$, $t$) 1 $P = V$ // Initializes a set with all vertices. 2 Set $A[s]=0$ and $A[x]=\infty$ for all $x \ne s$. // Initializes an array $A$. 3 while $P \ne \emptyset$ do 4 $x = \arg\min_{x \in P}\{A[x]\}$ // Chooses a vertex. 5 $P = P - \{x\}$ // Removes the vertex. 6 for each $y \in P$ such that $(x,y) \in E$, do 7 ($\star$) 8 return ($\star\star$)

You have realized that this code snippet can be used to solve different problems by filling the blanks in different ways. Here are three problems we consider:

• In the ST-DISTANCE problem, you are given a graph $G$ with non-negative weights, and two vertices $s,t \in V$. The goal is to compute the shortest distance between $s$ and $t$.
• In the ST-BOTTLENECK problem, you are given a graph $G$ with non-negative weights, and two vertices $s,t \in V$. The goal is to compute the smallest possible weight $wgt$ such that there exists at least one path from $s$ to $t$ using only edges whose weights are less than or equal to $wgt$.
• In the MST problem, you are given an undirected, weighted, and connected graph $G$. The goal is to compute the total weight of a minimum spanning tree.

Select all correct statement(s) below.