This question refers to Uniform Cost Search algorithm, S is the start satet and G$1,$ G$2,$ and G$3$ are the goal states. Lastly, clearly indicate the path cost from the start node to the goal node and the path taken within the solution tree.

For Step $2$: I get this answer however I$\text{'}$m confused about how N$,$E$,$W comes into this situation since they are not in the picture above. Also as to how the sorted list get numbered. Can somebody help me understand this part?

Expand node S:

Connections from S: N $(1),$ E $(1),$ W $(1)$

Sorted list: N $(1),$ E $(1),$ W $(1)$

Solution state space: $\{$S$,$ N$,$ E$,$ W$\}$

Step $3$:

Expand node N:

Connections from N: G$1(2),$ G$2(4)$

Sorted list: E $(1),$ W $(1),$ G$1(2),$ G$2(4)$

Solution state space: $\{$S$,$ N$,$ E$,$ W$,$ G$1,$ G$2\}$

Step $4$:

Expand node E:

Connections from E: G$2(3)$

Sorted list: W $(1),$ G$1(2),$ G$2(3)$

Solution state space: $\{$S$,$ N$,$ E$,$ W$,$ G$1,$ G$2\}$

Step $5$:

Expand node W:

Connections from W: G$3(6)$

Sorted list: G$1(2),$ G$2(3),$ G$3(6)$

Solution state space: $\{$S$,$ N$,$ E$,$ W$,$ G$1,$ G$2,$ G$3\}$

Step $6$:

Expand node G$1$:

Goal node G$1$ is reached.