The A* algorithm is a pathfinding and graph traversal algorithm that finds the shortest path from the start node to a goal node using a priority queue. The priority of each node is determined by the function f(n) = g(n) + h(n), where:

• g(n) is the cost from the start node to node n.
• h(n) is the heuristic estimate of the cost from node n to the goal.

The node with the lowest f(n) value is expanded first.

Let's calculate the f(n) values for each node as they are expanded:

1. Start at S: f(S) = g(S) + h(S) = 0 + 6 = 6. Expand node S.
2. From S, generate A and E:
   • f(A) = g(A) + h(A) = 4 + 2 = 6.
   • f(E) = g(E) + h(E) = 1 + 6 = 7.
   Expand node A next as it has the lowest f(n) value.
3. From A, generate B:
   • f(B) = g(B) + h(B) = 6 + 2 = 8.
   Expand node E next because it was already generated and has the next lowest value (f(E) = 7).
4. From E, generate C:
   • f(C) = g(C) + h(C) = 3 + 6 = 9.
   Expand node B as it has f(B) = 8 which is the lowest among remaining nodes.
5. Continue to expand C, D, and finally G:
   • f(C) = 8 via path S-A-B-C.
   • f(D) = g(D) + h(D) = 9 + 2 = 11.
   • Goal G reached with f(G) = 8 (path: S-E-D-G).

Thus, the sequence of nodes expanded is S, A, E, B, C, D, G.