THIS IS THE PROBLEM DONE IN CLASS on January 31.
The example comes from Figure 3.2
To reduce unproductive moves we did not add to OPEN the parent of any node.  
We do not prune states already visited.

1. START: arad 
   generate zerind (75)
            timisoara (118)
            sibiu (140)
2. expand zerind (75)
   generate oradea (75+71=146)
3. expand timisoara (118)
   generate lugoj (118+111=229)
4. expand sibiu (140)
   generate rimnicu (140+80=220)
            fagaras (140+99=239)
	    oradea (140+151=291)* -- already reached on shorter path
5. expand oradea (146)
   generate sibiu (146+151=297)* -- already reached on shorter path 
6. expand rimnicu (220)
   generate pitesti (220+97=317)
            craiova (220+146=366)
7. expand lugoj (229)
   generate mehadia (229+70=299)
8. expand fagaras (239)
   generate bucharest (239+211=450)  -- goal but not cheapest state

Nodes in OPEN:
  oradea(291)* sibiu(297)* mehadia(299) pitesti(317) craiova(366) bucharest(450)

9. expand oradea (291)*
   generate zerind (291+71=362)* -- already reached on shorter path
10.expand sibiu (297)*
   generate rimnicu (297+80=377)* -- already reached on shorter path 
            fagaras (297+99= 396)* -- already reached on shorter path
11.expand mehadia (299)
   generate dobreta (299+75=374)
12.expand pitesti (317)
   generate bucharest (317+101=418) -- already reached on longer path
	    craiova (317+138=455)*-- already reached on shorter path

Nodes in OPEN:
   zerind(362)* craiova(366) drobeta(374) rimnicu(377)* fagaras(396)* 
   bucharest(418) bucharest(450) craiova(455)* drobeta(486)* 

For simplicity, from here on we stop expanding the nodes already seen

13.expand craiova (366)
   generate pitesti (366+138=504)* -- already reached on shorter path
14.expand dobreta (374)
   generate craiova (374+120=494)
15.expand bucharest (418)
   GOAL reached