[SOLVED] prolog代写：CUHK CSCI3230 Prolog Programming Assignment

CUHK CSCI3230

Prolog Programming Assignment – Pentago

Due date:: 23::559::559 (GGMT +008::000)),, 18 th November , 201 7

Introduction

Pentago is a two – player board game played on a 6×6 board divided into four 3××33 sub – boards (oor quadrants)) . This game is similar to tic – tac – toe.. One player owns the red playing pieces (ii..ee.. the red marbles)) and another one owns the black playing pieces (ii..ee.. the black marbles)).. In each turn,, the player place one o f their marble s and rotate a quadrant by 90 degrees . The goal of th is game is to create a vertical,, horizontal or diagonal row of five marbles.. This game is challenging and fun for both kids and adults..

In this assignment,, you are going to implement a simp le Pentago player program . T h is program can help you win the game .

Requirement

In this assignment,, you are required to implement Prolog predicate s :

threatening((BBoard,, Current Player , ThreatsCount )..

pentago_ai((BBoard,, CurrentPlayer , Best Move,, NextBoard))..

Board R epresentation

Pentago is a two – player ( say Black player vs.. Red player)) board game.. As shown in f igure 1,, the 6×6 board has 36 positions for the players to put their marbles on . Besides,, it has 4 quadrants which are labelled as top – left,, top – right,, bottom – left and bottom – right . These quadrants can be rotated separately (ssee f igure 2)) .

Figure 1.. An empty 6×6 board with 3×3 sub – boards

Figure 2.. An example for a rotation of 90 degrees on the bottom – right quadrant in anti – clockwise .

The holes on the 6×6 board are represented using a rectangular grid.. Each position i s labelled as shown in figure 3.. A position can only be in either one of the three states::

1.. Occupied by a black marble

2.. Occupied by a r ed marble

3.. Unoccupied (ii..ee.. no marble p ut on it))

We will use board((BBlackL,,RRedL)) to represent a board state.. BlackL is a list in Prolog and stores the positions occupied by black marbles;; RedL is a list in Prolog and stores the positions occupied by red marbles.. The unoccupied positions can be inferred from them.. For example,, board(([[]],,[[]])) represents the empty board in figure 1.. board(([[44,9,, 21,, 26 ],, [55,12,22,36 ])) represents the board in figure 4 .

Game F low

The goal of this game is to create a vertical,, horizontal or diagonal row of five marbles in your chosen color.. The game starts with an empty board.. The players take tur n during the game.. In every turn , a player are required to make the following two actions :

1.. Marble placement:: Place a marble of the chosen color on an unoccupied position

2.. Quadrant rotation:: Rotate a quadrant by 90 degrees either in anti – clockwise or clockwi se

The game ends when a ny player create s a vertical,, horizontal or diagonal row of five marbles of the same color ( either before or after the quadrant rotation in their move ).. Looking at the board in the ending state,, the player wins if he//sshe owns five marbles of the same color in a row.. As listed in the Appendix,, there are 32 ways to place the five marbles in a row on an empty board.. Some winning cases are shown in figure 5 . Note that it is possible for the two players to win this game a t the same

F i gure 3.. Coordinates of each position in the board

F i gure 4.. A position can only be in one of the three states..

time (ssee f igure 5 c)).. The players draw when neither of them make five marbles of the same color in a row.. Under this ending condition,, because marble placement never prevent s the current player from winning but quadrant rotation can (ssee figure 5 d,, if Black pla yer rotates top – right quadrant before putting a black marble,, Red player wins..)) , we assume that the player will always place a marble before quadrant rotation.. A move is a structure in Prolog::

move((PPosition,,DDirection,,QQuadrant))

where

Position refers to the place where the new marble will be put on the existing board,, {11,2,,……,,336}}

Direction refers to the direction of rotation of a quadrant,, {aanti – clockwise,, clockwise}}

Quadrant refers to the 4 possible quadrants,, {ttop – left,, top – right,, bottom – left,, bottom – rig ht}}

F igure 5 . (aa)) Five black marbles in a vertical row . (bb)) Five red marbles in a diagonal row . (cc)) Five black marbles in a diagonal row and at the same time f ive red marbles in a horizontal row.. (dd)) Nobody wins at the moment..

Threatening

This section describes the Prolog predicate

threaten ing (BBoard,, Current Player , ThreatsCount )..

As listed in the Appendix,, there are only 32 ways to place the five marbles in a row on an empty board . We call each of these ways as a winning row . The current state of the board is stored in Board , in board((BBlackL,,RRedL)) structure . CurrentP layer player is threatened when any of the winning rows is filled with exactly 4 opponent’s marbles with 1 empty slot 1 , which we call each of them as a threatening row . From the perspective of the Current Player player,, the

1 We ignore the formation of threatening rows after rotation of the quadrants..

a

b

c

d

degree of the threat is defined as the number of threatening rows produced on a board by the opponent and is stored in ThreatsCount . Refer to figure 6 , the number of threatening rows with respect to Black player is 3,, i..ee.. [11,8,15,22,29]] , [ 8,15,22,29 ,33 6 ] and [55,11,17,23,29]] . T he number of threatening rows with respect to Red player is 0 (ii..ee.. not threatened)).. T he more threatening rows you create for the opponent , the higher the chance of winning.. In your turn,, the less threatening rows you encounter,, the higher the chance of winning..

F i gure 6 . Coordinates of each position in the board..

On Choosing the Best M o ve

In this assignment,, we will implement a greedy strategy in the Pentagon AI program on choosing the best move((ss)) by using the predicate::

pentago_ai((BBoard,, CurrentPlayer ,BBestMove,,NNextBoard))..

Your program will search the states of the board one step ahead ( e . g . Black player’s turn  Red player’s tur n)).. The choice of the move by CurrentPlayer player is stored in BestMove represented in move structure.. We denote the two turns as T n and T n++11 respectively , hence three layers of board states . A ssume it is CurrentPlayer player’s turn..

The goal of CurrentPlayer player is to win this game as soon as possible given the current board state Board . CurrentPlayer player always executes a winning move if it exists in turn T n . If not,, CurrentPlayer player will think one turn ahead and prevent the rational o pponent from winning in turn T n++11 unless both players win at the same time.. The opponent will try his//hher best to win the game and threaten CurrentPlayer player.. CurrentPlayer player prefers a draw over a loss and will choose any move as BestMove if he//ssh e must los e the game..

When neither of players wins after turn T n++11 ends,, CurrentPlayer player will reduce threat s made by the op ponent as much as possible.. How to count t he threat s has been discussed in the previous section.. After deciding the BestMove , it will be executed a give the new board NextBoard . The partial search tree formed by your program is shown in figure 7..

N ote that if the player can only win by placing a marble and without quadrant rotation,, the program should produce a NextBoard containing five marbles in a row.. Only the P osition of BestMove will be checked in this case while Direction and Quadrant will be ignored .

Figure 7.. Search tree by the AI program..

Illustration

Example 1

? – threatening((bboard(([[ 3,, 4 ,99,10,21,26,27 ,333 ],,[[55 ,88,11,15,17,, 22,, 29,3 1 ])),, black , S )..

S = 3 .

? – threatening((bboard(([[33,4,9,10,21,26,27 ,333 ],,[[55,8,11,15,17,, 22,, 29,3 1]])),,rred,,SS))..

S = 0..

Example 2

Note that the solution for this problem may not be unique..

? – pentago_ai((bboard(([[ 2,4 ,110,16,2 1 ,226,27 ],,[[55,8,12,15,, 24,29 ])),, red , BestMove,,NNextBoard))..

BestMove = move(( 34,,aanti – clockwise,, bottom – right )..

NextBoard = board(([[ 2,, 4,10,16,21,26,2 7 ],,[[55,8,12,15,, 22,, 29,, 36 ])) .

Board

Board