Bai giai tri tue nhan tao tut 3

TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM Khoa Khoa học & Kỹ thuật Máy tính TUTORIAL SESSION 3 HEURISTIC SEARCH AND GAME PLAYING Question 1: Prove each of the following statements: refer wikiped

TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM Khoa Khoa học & Kỹ thuật Máy tính

TUTORIAL SESSION 3 HEURISTIC SEARCH AND GAME PLAYING

Question 1: Prove each of the following statements: (refer wikipedia for uniform-cost search algorithm)

a Breadth-first search is a special case of uniform-cost search

b Breadth-first search, depth-first search, and uniform-cost search are special cases of best-first search

c Uniform-cost search is a special case of A* search

Solution:

a When all step costs are equal, g(n) ~ depth(n), so uniform-cost search reproduces breadth-first search

b Breadth-first search is best-first search with f(n) = depth(n)

Depth-first search is best-first search with f(n) = - depth(n)

Uniform-cost search is best-first search with f(n) = g(n)

c Uniform-cost search is A* search with h(n) = 0

Question 2:

Consider the n blocks world in which only one block can be on another block or on the table And, possible actions including picking up a block from the table, putting a block down on the table,

stacking a block on another block, and unstacking a block from another block

Consider the problem of 3 blocks world with start and goal state in Figure 1

 Draw the search tree resulting from using best-first search with the heuristic function as the number of blocks not in the correct place as an estimate of the remaining distance to the goal For example, the heuristic value for start state is 2 since blocks A and C are not in the correct place (but block B is) relative to the goal state

 Repeat previous question with steepest ascent hill climbing Compare the number of

expanded nodes

 Draw the search tree resulting from using A-start with g being the number of operators executed and h being the same heuristic as about Give your opinion about this heuristic function

Notes:

 In the situation where we can’t decide which node to expand next Choose it randomly

 If the search tree resulting from using heuristic function, write node’s evaluation value beside it

 Each node of search tree will have the state representation as the node’s label For example, the

start state will be “(on(C,F), on(B,F), on(A,B))”

Figure 1 3 block world

Best first search

Steepest-ascent hill climbing

A star

Question 3:

A program is developed to play the Tic-Tac-Toe game using the Minimax algorithm Unfortunately, it is not easy to sharp out a good static function for such a game (you may try and see) So, a simple function

is then developed as follows:

 If the X’s player wins a board, the score for the board is 1

 If the O’s player wins a board, the score for the board is -1

 Otherwise, it returns 0

The function is, in fact, very straightforward and trivial, but it is quite natural In addition, we will empower its by another means: the Minimax is allowed to run with unlimited depth

Show that with the board given in Figure 2, the X’s player will win if played by the above-mentioned

program

Figure 2 An example board of Tic-Tac-Toe

Question 4:

Figure 3 presents a resultant Minimax-applied tree What are the corresponding resultant trees when the alpha-beta prunes are applied

Figure 3 A resultant Minimax-applied tree