Question $1$

Use the following definition of the union operation, assuming the sentinel of $x$ is not the same as the sentinel of

$y$ :

union $(x,y)=$ Make the sentinel of $x$ point to the sentinel of $y$

Imagine we start with an unconnected forest of nodes labeled $0$ through $7.$ Then, we perform the following

operations:

Assuming we are not performing any weighting optimizations $($i$.$e$.,$ don't use union$-$by$-$size or union$-$by$-$height$)$ and

assuming find does not perform any path compression, what is the array representation of our disjoint set?

Provide the array representation as space$-$separated numbers. For example, if you wanted to represent the initial

forest of nodes, your answer would look like the following: