井字棋英文名叫TicQ-Tac-Toe是一种在3*3格子上进行的连珠游戏和五子棋类似由于棋盘一般不画边框格线排成井字故得名。游戏需要的工具仅为纸和笔然后由分别代表O和X的两个游戏者轮流在格子里留下标记一般来说先手者为X任意三个标记形成一条直线则为获胜。最近学习了人工智能的博弈算法同时老师布置了相关算法的井字棋代码实现作业为了简便明了我将使用python进行程序编写算法使用了MinmaxAlpha-beta剪枝以及蒙特卡洛三种代码实现欢迎大家批评指正与交流学习。下面分部分进行代码讲解首先是算法部分的结构class JinZi: def __init__(self): #用于初始化井字棋数据 def full(self): #判断棋盘棋子是否满 def empty_pos(self): #判断位置为空 def winner(self,pos,qizi): #判断是否获胜 def moving(self,pos,turn): #通用落子函数 def minmax(self,depth,is_ai): #核心算法此处为最小最大算法 def ai_move(self): #ai计算落子 def human_move(self,pos): #玩家落子 def valid_move(self,pos): #判断落子位置是否合理 def reset(self): #重开接下来是UI部分结构class GameGUI: def __init__(self): #棋盘UI初始化 def draw_board(self): #绘制棋盘 def draw_status(self): #绘制棋子 def shift_mousepos(self,mouse_pos): #鼠标位置-棋盘位置转换 def reset_game(self): #重开 def run(self): #主循环下面是三个核心算发部分①最小最大算法AI同时站在自己和对手的角度计算自己要取得最大分而对手要失去最少的分因此在进行回溯时会一层max一层min进行比对def minmax(self,depth,is_ai): #到游戏结束的层就走 if (self.current_winner self.ai): return {position:None,score:10-depth} elif (self.current_winner self.human): return {position:None,score:depth-10} elif (self.full()): return {position:None,score:0} #初始化叶子值 if(is_ai): best {position:None,score:-math.inf} else: best {position:None,score:math.inf} #遍历落子 for pos in self.empty_pos(): turn self.ai if(is_ai) else self.human self.board[pos] turn temp_winner self.current_winner if(self.winner(pos,turn)): self.current_winner turn #递归求取最大胜利 result self.minmax(depth1,not is_ai) #取消模拟 self.board[pos] self.current_winner temp_winner #保留模拟记录 result[position] pos #实时更新最佳分数 if(is_ai): if(result[score] best[score]): best result else: if(result[score] best[score]): best result return best②alpha-beta剪枝算法这个算法算是最小最大算法的优化算法新增了alpha和beta两个参数并且在分数更新的同时更新alpha和beta的值并进行剪枝操作剪枝的条件是αβ即对相邻两层的节点进行比较如果满足条件则说明该节点及其后续节点没有扩展价值可以直接剪掉def minmax(self, depth, is_ai, alpha-math.inf, betamath.inf): # 到游戏结束的层就走 if (self.current_winner self.ai): return {position: None, score: 10 - depth} elif (self.current_winner self.human): return {position: None, score: depth - 10} elif (self.full()): return {position: None, score: 0} # 初始化叶子值 if (is_ai): best {position: None, score: -math.inf} else: best {position: None, score: math.inf} # 遍历落子 for pos in self.empty_pos(): turn self.ai if (is_ai) else self.human self.board[pos] turn temp_winner self.current_winner if (self.winner(pos, turn)): self.current_winner turn # 递归求取最大胜利传递alpha和beta参数 result self.minmax(depth 1, not is_ai, alpha, beta) # 取消模拟 self.board[pos] self.current_winner temp_winner # 保留模拟记录 result[position] pos # 实时更新最佳分数和alpha/beta值 if (is_ai): if (result[score] best[score]): best result # 更新alpha值 alpha max(alpha, best[score]) # Alpha-Beta剪枝如果alpha beta剪掉剩余分支 if alpha beta: break else: if (result[score] best[score]): best result # 更新beta值 beta min(beta, best[score]) # Alpha-Beta剪枝如果beta alpha剪掉剩余分支 if beta alpha: break return best③蒙特卡洛搜索树算法蒙特卡洛算法和前两者有本质区别它其实在井字棋上性能并不如前两种但对于更加复杂的难以计算得到的博弈情况蒙特卡洛算法则更具有优势。蒙特卡洛算法本质上是对概率的计算即进行大量实验以求得最有可能获胜的落子方式。可以使用UCT的蒙特卡洛决策算法:公式。下面展示的是蒙特卡洛搜索树算法class MCTSNode: def __init__(self, board, parentNone, posNone, turnX): self.board board.copy() # 棋盘状态 self.parent parent self.pos pos # 导致此节点的落子位置 self.turn turn # 当前轮到谁下棋 self.children [] self.visits 0 self.wins 0 self.untried_moves self.get_possible_moves() def get_possible_moves(self): return [i for i, value in enumerate(self.board) if value ] def is_terminal(self): return self.get_winner() is not None or len(self.untried_moves) 0 def get_winner(self): # 检查赢家 for i in range(0, 9, 3): if self.board[i] self.board[i1] self.board[i2] ! : return self.board[i] for i in range(3): if self.board[i] self.board[i3] self.board[i6] ! : return self.board[i] if self.board[0] self.board[4] self.board[8] ! : return self.board[0] if self.board[2] self.board[4] self.board[6] ! : return self.board[2] return None def expand(self): if self.untried_moves: pos random.choice(self.untried_moves) self.untried_moves.remove(pos) new_board self.board.copy() new_board[pos] self.turn next_turn O if self.turn X else X child_node MCTSNode(new_board, self, pos, next_turn) self.children.append(child_node) return child_node return None def simulate(self): board self.board.copy() current_turn self.turn while True: # 检查是否结束 winner self.get_winner_from_board(board) if winner is not None: return 1 if winner X else 0 # X是AI if not in board: return 0.5 # 平局 # 随机落子 empty [i for i, v in enumerate(board) if v ] pos random.choice(empty) board[pos] current_turn current_turn O if current_turn X else X def get_winner_from_board(self, board): for i in range(0, 9, 3): if board[i] board[i1] board[i2] ! : return board[i] for i in range(3): if board[i] board[i3] board[i6] ! : return board[i] if board[0] board[4] board[8] ! : return board[0] if board[2] board[4] board[6] ! : return board[2] return None def backpropagate(self, result): self.visits 1 self.wins result if self.parent: self.parent.backpropagate(result) def is_fully_expanded(self): return len(self.untried_moves) 0 def best_child(self, exploration_weight1.41): best_score -float(inf) best_child None for child in self.children: if child.visits 0: uct_score float(inf) else: exploitation child.wins / child.visits exploration exploration_weight * math.sqrt(math.log(self.visits) / child.visits) uct_score exploitation exploration if uct_score best_score: best_score uct_score best_child child return best_child --------------------------------------------------------------------------------- def mcts_search(self, iterations1000): root MCTSNode(self.board, turnself.ai) for _ in range(iterations): node root # Selection while node.is_fully_expanded() and not node.is_terminal(): node node.best_child() # Expansion if not node.is_terminal(): node node.expand() # Simulation result node.simulate() # Backpropagation node.backpropagate(result)下面是MinMax的完整代码示例import math import pygame import sys import time sun_time 0 class JinZi: def __init__(self): self.board[ for _ in range(3*3)] self.aiX self.humanO self.current_winnerNone self.think_time 0 def full(self): return not in self.board def empty_pos(self): return [i for i,value in enumerate(self.board) if(value )] def winner(self,pos,qizi): rowpos // 3 colpos % 3 #行 win_rall(qizi temp_row for temp_row in self.board[row*3:row*33]) #列 win_call(qizi self.board[coli*3] for i in range(3)) if(win_r or win_c): return True #斜 if(pos % 2 0): return all(qizi self.board[i] for i in [0,4,8]) or all(qizi self.board[i] for i in [2,4,6]) return False def moving(self,pos,turn): if(self.board[pos] ): self.board[pos] turn if(self.winner(pos,turn)): self.current_winner turn return True return False def minmax(self,depth,is_ai): #到游戏结束的层就走 if (self.current_winner self.ai): return {position:None,score:10-depth} elif (self.current_winner self.human): return {position:None,score:depth-10} elif (self.full()): return {position:None,score:0} #初始化叶子值 if(is_ai): best {position:None,score:-math.inf} else: best {position:None,score:math.inf} #遍历落子 for pos in self.empty_pos(): turn self.ai if(is_ai) else self.human self.board[pos] turn temp_winner self.current_winner if(self.winner(pos,turn)): self.current_winner turn #递归求取最大胜利 result self.minmax(depth1,not is_ai) #取消模拟 self.board[pos] self.current_winner temp_winner #保留模拟记录 result[position] pos #实时更新最佳分数 if(is_ai): if(result[score] best[score]): best result else: if(result[score] best[score]): best result return best def ai_move(self): start_time time.time() move self.minmax(0,True) end_time time.time() self.think_time end_time - start_time global sun_time sun_time self.think_time if(move[position] ! None): self.moving(move[position],self.ai) print(f本次思考时间:{self.think_time}) return True return False def human_move(self,pos): if(self.current_winner is None): if(not self.full()): return self.moving(pos,self.human) return False def valid_move(self,pos): return self.board[pos] def reset(self): global sun_time print(f总耗时:{sun_time}) sun_time 0 self.board [ for _ in range(9)] self.current_winner None class GameGUI: def __init__(self): pygame.init() self.width 600 self.height 700 self.screen pygame.display.set_mode((self.width,self.height)) pygame.display.set_caption(井字棋) #time self.ai_delay 200 self.ai_timer 0 #/time #color #/color self.game JinZi() self.gameover False self.turn self.game.human #front self.font pygame.font.SysFont(Arial,48) #/front self.cell_size self.width // 3 self.line_width 5 self.button_rect pygame.Rect(self.width//2 - 100,self.height-80,200,50) def draw_board(self): self.screen.fill([28, 170, 156]) for i in range(1,3): pygame.draw.line(self.screen,[255,255,255],(i*self.cell_size,0),(i*self.cell_size,self.width),self.line_width) pygame.draw.line(self.screen,[255,255,255],(0,i*self.cell_size),(self.width,i*self.cell_size),self.line_width) for i in range(9): x (i%3) * self.cell_size self.cell_size // 2 y (i//3) * self.cell_size self.cell_size // 2 x_line x - self.cell_size // 4 y_line y - self.cell_size // 4 if(self.game.board[i] O): pygame.draw.circle(self.screen,[239, 231, 200],(x,y),self.cell_size//4,self.line_width5) elif(self.game.board[i] X): pygame.draw.line(self.screen,[84,84,84],(x_line,y_line),(xself.cell_size // 4,yself.cell_size // 4),self.line_width5) pygame.draw.line(self.screen,[84,84,84],(xself.cell_size // 4,y_line),(x_line,yself.cell_size // 4),self.line_width5) def draw_status(self): y self.height - 30 if(self.game.current_winner): text (fWinner:{self.game.current_winner}) elif(self.game.full()): text (fDraw!) else: text (fTurn:{self.turn}) #显示对局情况 text_status self.font.render(text,True,(255,255,255)) self.screen.blit(text_status,(0,0)) #绘制重来按钮 pygame.draw.rect(self.screen,(200,200,200), self.button_rect) pygame.draw.rect(self.screen, (255,255,255), self.button_rect, 2) button_text self.font.render(New Game, True, (255,255,255)) button_rect button_text.get_rect(centerself.button_rect.center) self.screen.blit(button_text, button_rect) def shift_mousepos(self,mouse_pos): x,ymouse_pos if(yself.width): return None row y // self.cell_size col x // self.cell_size return row*3col def reset_game(self): self.game.reset() self.gameover False self.turn self.game.human def run(self): clock pygame.time.Clock() ai_turn False while(True): dt clock.tick(60) for event in pygame.event.get(): if(event.type pygame.QUIT): pygame.quit() sys.exit() if(event.type pygame.MOUSEBUTTONDOWN and not self.gameover): #人回合 if(self.turn self.game.human and not ai_turn): pos self.shift_mousepos(event.pos) if(pos is not None and self.game.valid_move(pos)): if(self.game.human_move(pos)): if(self.game.current_winner or self.game.full()): self.gameover True else: self.turn self.game.ai ai_turn True self.ai_timer self.ai_delay if(event.type pygame.MOUSEBUTTONDOWN): if(self.button_rect.collidepoint(event.pos)): self.reset_game() self.ai_timer 0 if(self.turn self.game.ai and not self.gameover and not self.game.current_winner and not self.game.full()): self.ai_timer - dt if(self.ai_timer 0): if(self.game.ai_move()): self.turn self.game.human if(self.game.current_winner or self.game.full()): self.gameover True ai_turn False #更新界面 self.draw_board() self.draw_status() pygame.display.flip() clock.tick(60) if __name__ __main__: gui GameGUI() gui.run() print(f总耗时:{sun_time})以上便是本次全部内容感谢各位鉴赏。