The AND-OR-GRAPH-SEARCH algorithm in Figure 4.11 checks for repeated states only on the path from the root to the current state. Suppose that, in addition, the algorithm were to store every visited state and check against that list. (See BREADTH-FIRST-SEARCH in Figure 3.11 for an example.) Determine the information that should be stored and how the algorithm should use that information when a repeated state is found. 

Figure 4.11

Figure 3.11

function AND-OR-GRAPH-SEARCH(problem) returns a conditional plan, or failure OR-SEARCH(problem.INITIAL-STATE, problem, []) function OR-SEARCH(state, problem, path) returns a conditional plan, or failure if problem.GOAL-Test(state) then return the empty plan if state is on path then return failure for each action in problem.ACTIONS(state) do plan - AND-SEARCH(RESULTS(state, action), problem, [state | path]) if plan + failure then return [action | plan] return failure function AND-SEARCH(states, problem, path) returns a conditional plan, or failure for each s; in states do plan; - OR-SEARCH($;, problem, path) if plan; = failure then return failure return [if s1 then plan, else if s2 then plan, else ...if sn-1 then plann-1 else plan,] function BREADTH-FIRST-SEARCH( problem) returns a solution, or failure node - a node with STATE = problem.INITIAL-STATE, PATH-COST = 0 if problem.GOAL-TEST(node.STATE) then return SOLUTION(node) frontier - a FIFO queue with node as the only element explored an empty set loop do if EMPTY?(frontier) then return failure node - POP( frontier) * chooses the shallowest node in frontier */ add node.STATE to erplored for each action in problem.ACTIONS(node.STATE) do child CHILD-NODE(problem, ode, action) if child.STATE is not in explored or frontier then if problem.GOAL-TEST(child.STATE) then return SOLUTION(child) frontier INSERT(child, frontier)