5. Problem solving by search Represent the problem as STATES and OPERATORS that transform one state into another state. A solution to the problem is an OPERATOR SEQUENCE that transforms the INITIAL STATE into a GOAL STATE . Finding the sequence requires SEARCHING the STATE SPACE by GENERATING the paths connecting the two.

7. Example: Measuring problem! A c B A B C 0 0 0 3 0 0 3 0 3 0 0 6 3 0 6 0 3 6 3 3 6 1 5 6 0 5 7 3 l 5 l 9 l

21. Tree for water jug problem (0,0,0) (0,3,0) (4,0, 0) (0,0,0) (1,3,0) (4,3,0) (0,0,0) (3,0,0) (0,3,0) (1,0,0) (4,0,0) (4,3,0)     (4,3,0)

35. Breath-first search Expand the tree in successive layers, uniformly looking at all nodes at level n before progressing to level n+1 function Breath-First-Search( problem ) returns solution nodes := Make-Queue(Make-Node(Initial-State( problem )) loop do if nodes is empty then return failure node := Remove-Front (nodes) if Goal-Test[ problem ] applied to State( node ) succeeds then return node new-nodes := Expand (node, O perators [problem])) nodes := Insert-At-End-of-Queue (new-nodes) end

36. Another Breath-first search S A D B D A E C E E B B F D F B F C E A C G G C G F 14 19 19 17 17 15 15 13 G 25 11

39. Depth-first

47. Depth first search Dive into the search tree as far as you can, backing up only when there is no way to proceed function Depth-First-Search( problem ) returns solution nodes := Make-Queue(Make-Node(Initial-State( problem )) loop do if nodes is empty then return failure node := Remove-Front (nodes) if Goal-Test[ problem ] applied to State( node ) succeeds then return node new-nodes := Expand (node, O perarors [problem])) nodes := Insert-At-Front-of-Queue (new-nodes) end

48. Depth-first search S A D B D A E C E E B B F D F B F C E A C G G C G F 14 19 19 17 17 15 15 13 G 25 11