Consider the following graph representing the state space and operators of a navigation problem.

The path cost is shown by the number on the links; the heuristic evaluation is shown by the number in the box.

• There are two goal states at G and F
• Unless there is an order required by the algorithm, when placing expanded child nodes on a queue, assume that the child nodes are placed in alphabetical order (i.e. if node S is expanded the queue will be: A B).
• Assume that we never generate child nodes that appear as ancestors of the current node in the search tree.

1. 1. What is the order that best first search will expand the nodes?
2. 2. What is the order that hill-climbing search will expand the nodes?
3. 3. What is the order that uniform cost search will expand the nodes? Give each steps state and elements in the Queue and draw the search tree.
4. 4. What is the order that A* search will expand the nodes? Give each steps state and elements in the Queue and draw the search tree.
5. 5. What is the order that IDA* search will expand the nodes, using the cost limit sequence {5, 7, 8}? Give each steps state and elements in the Queue.