Figure I below is a maze with tile A as the starting point and tile G as the goal. Using A* search, the solution path is given as A-B-C-D-E-F-G (white tiles). Yellow tile represent the node in open list and red tile is the node in closed list. Gray tile is the wall where no movement is allowed. Based from the Figure 1, please answer the following questions. 9 341 h 500 f841 g 482 g 441 g 482 9 582 h 500 h 400 19 682 h 300 h 200 h 300 f 982 f 841 f782 f 782 f 982 Ig 300 9 341 9 441 19 541 h 400 19 641 h 300

all where no movement is allowed. Based from the Figure 1, please answer the following questions. 9 341 h 500 f841 g 482 g 441 g 482 9 582 h 500 h 400 19 682 h 300 h 200 h 300 f 982 f 841 f782 f 782 f 982 Ig 300 9 341 9 441 19 541 h 400 19 641 h 300 h 200 h 100 f 780 h 200 f641 Df641 E F 641 F f 841 9 200 9 241 9 682 h 300 h 200 h 100 f 500 G f 782 9 100 g 141 h 400 h 300 f 500 9 241 h 400 f641 f 441 c g 141 h 500 f641 f441 B 9 100 g 100 h 600 f 700 go no f h 400 500 g 141 h 700 f 841 g

Manhattan distance (n) Cost of n from A, g(n) f(n) = n(n) + g(n) O 0 A-B 300 A-B-C A-B-C-D A-B-C-D-E A-B-C-D-E-F A-B-C-D-E-F-G o Assume g=100 b) Show that the heuristic is admissible or not admissible The heuristic is because Manhattan distance never the cost to reach the goal. The solution path is A-B-C-D-E-F-G with cost equal to and h*(A) is the cost of tile A to tile G showing that heuristic fulfills the condition QUESTION B Consider the maze problem below in which the white boxes are available paths and gray boxes are blocked (no movement allowed). S is the start point and is the goal.

provided that a valid move is available. X is the current maze position while A, B and C are the next possible moves. Please answer all the questions. S B A X G a) When X is the current node, which node(s) are in the corresponding list? When X is the current node, are the children node where in the visited list while in the yet to visit list QUESTION C An A* search is used to solve the 8-puzzle problem game with heuristic h(n) as the number of tiles out of place. Please answer all the following questions a) The heuristic h(n) is admissible when h(n) =>