Consider the following algorithm which seeks to find a minimum spanning tree in a connected graph with positive weights on its edges. We start a modified version of DFS from an arbitrary node, initialize T $=\{\}$ and continue as follows:

A: From u$,$ the node where DFS currently is$,$ construct N$,$ the list of neighbors of u sorted by nondecreasing weight.

Find the first node v in N such that v has not already been visited.

If such a node does not exist backtrack.

else if such a node does exist

Add $\{$u$,$ v$\}$ to T$.$ Mark v as visited. If $|$T$|$ is n$-1$ return T else move o$=$to v and go to A$.$

Does this algorithm always find a minimum spanning tree? Explain or give a counter$-$example.