CHAPTER 10FUN AND GAMES

Group 1: Xiangling Liu

PART IOverview of the

Chapter

OBJECT

How to use the binary search algorithm in word search puzzle problem to solve large instances of a word search in under 1 sec

How to use the alpha-beta pruning algorithm to speed up the recursive algorithm presented in Section7.7

How to use maps to increase the speed of the Tic-Tac-Toe algorithm

10.1 WORD SEARCH PUZZLES

The input to the word search puzzle problem is a two-dimensional array of characters and a list of words.

The object is to find the words in the grid. Words may be oriented in one of eight directions

(horizontal, vertical or diagonal).

10.1.1 THEORY The most direct algorithm is brute-force approach

as follows:− Algorithm

for each word W in the word list

for each row R

for each column C

for each direction D

check if W exists at row R, column

C in direction D− The algorithm requires 8WRC checks

10.1.1 THEORY (cont) An alternative algorithm searches from each point

in the grid in each direction for each word length and looks for the word in the word list. The lookups can be done by a binary search if the word list is sorted.− Algorithm for each row R

for each column C for each direction D for each word length L check if L chars starting at row R column C in direction D form a word

− The algorithm requires 8LRC checks

10.1.1 THEORY (cont) An further improved algorithm is to add an

assertion. If a character sequence is not a prefix of any word, we can stop that search and look in another direction.− Algorithm for each row R

for each column C for each direction D for each word length L check if L chars starting at row R column C in direction D form a word if they do not form a prefix break; //the innermost loop

− The prefix testing can also be done by binary search

10.1.2 JAVA IMPLEMENTATION

WordSearch class: to store the grid and word list, as well as the corresponding input streams.− A constructor. It merely opens and reads the two files

corresponding to the grid and the word list.− Private openFile method. It repeatly prompts for a file

until an open is successful.− Private readWords method. It reads the word list.− Private readPuzzle method reads the grid and is also

concerned with error handling.− Public solvePuzzle method nests the row, column and

direction loops and then calls the private method solveDirection for each possibility.

10.1.2 JAVA IMPLEMENTATION (cont)

− Private solveDirection method constructs a string by starting at the base row and colunm and extending in

the appropriate direction.− Private prefixSearch method performs the binary search

for word search. Main class is a simple routine for the word search

puzzle problem

10.2 THE GAME OF TIC-TAC-TOE A simple algorithm known as mininax strategy

allows the computer to select an optimal move in a game of Tic-Tac-Toe. It involves the following decisions.− A terminal position can immediately be evaluated, so if

the position is terminal, return its value.− Otherwise, if it is the computer’s turn to move, return the

maximum value of all positions reachable by making one move. The reachable values are calculated recursively.

− Otherwise, it is the human player’s turn to move. Return the minimum value of all positions reachable by making one move. The reachable values are calculated recursively.

10.2.1 ALPHA-BETA PRUNING The minimax strategy gives an optimal Tic-Tac-

Toe move, it performs more searching than necessary.

Alpha-beta pruning is the strategy of reducing the number of positions evaluated in a minimax search using refutation.

A refutation is a countermove that proves that a proposed move is not an improvement over moves previously considered. If a refutation found, we do not have to examine any more moves and the recursive call can return.

Alpha is the value that the human player has to

10.2.1 ALPHA-BETA PRUNING (cont)

refute and beta is the value that the computer has to refute.

Alpha-beta pruning requires only a few changes to chooseMove. − Both alpha and beta are passed as additional

parameters.− Add an assertion which provides for an immediate

return when a refutation is found.

10.2.2 TRANSPOSITION TABLES A transpostion table stores previously evaluated

positions. A map is used to implement the transposition

table. Often the underlying implementation is a hash table.

The chooseMove method has additional parameters, all of which have defaults.

The use of the transposition table in this tic-tac-toe algorithm can almost double the program’s speed by removing about half the positons from consideration.

10.2.3 COMPUTER CHESS Terminal positions cannot be searched in

computer chess. So we have to stop the search after a certain depth of recursion is reached.

In the best programs, considerable knowledge is built into the evaluation function.

PART IIOverview of TicTacToe

Program

WHAT HAVE BEEN REVISED Use a static final int SIZE to replace literal size of

the board in class TicTacToe Replace 3*3 board with 4*4 board Change the law of winning. If one side has

occupied 3 square in the diagonal or back-diagonal, the side wins the game

CLASSES OF THE PROGRAM Best class Position class TicTacToe class TicTacMain class TicTacPanel class

Best CLASS The class is to store the value, the row and

column corresponding to a position. Has two constructors

− public Best( int v ) − public Best( int v, int r, int c )

Position CLASS The class define a postion in the board and

define the equals of position and the hashcode

Has three methods− Constructor: initialize the board− equals: defines if the position is equal or not− hashCode: defines the hash value of the

board position in the hash table

TicTacToe CLASS

The class has eleven methods.− Constructor: clear the board of game− getBoard: get the board of the game− chooseMove with one parameter: choose the

optimal move− chooseMove with four parameter: choose the

optimal move− playMove: Play move, including checking

legality− clearBoard: clear the board of game

TicTacToe CLASS (cont)

− boardIsFull: check if the board is full− isAWin: check if the side wins the game− place: place the mark at a position in the

board− squareIsEmpty: checks if the square is empty− positionValue: computes static value of current

position (win, draw, etc.)

TicTacMain CLASS The class is to add TicTacPanel object and

windowAdapter show all actions. Has two methods and class TicTacPanel

− Constructor: add TicTacPanel object and windowAdapter

− main: a very simple main method

TicTacPanel CLASS The class is to set a GridLayout and make

every square listen to the action of button. Compute the value of the computer side and make a move. Calculate and show the game result.

Has five methods− Constructor: set a GridLayout and make every

square listen to the action of button. After each game, reset the board.

− resetBoard: reset the board and make each square of the board enable

TicTacPanel CLASS (cont)

− doCompMove: the computer side to choose best position and make a move

− resetIfDone: gives information of the game at the end of the game

− actionPerformed: performs a move corresponding to human's or compter's move and gives the result of the game

JAVA CODE AND RUNNING RESULTS

See the attached file Execute the program

Thank you all!