蒙特卡洛算法uct 五子棋python

蒙特卡洛算法是一种基于随机模拟的算法，可以用于解决很多复杂的决策问题。在五子棋中，使用蒙特卡洛算法可以帮助计算机找到最佳的下棋策略。

在Python中，我们可以使用蒙特卡洛算法来实现五子棋的计算机对弈程序。使用UCT（Upper Confidence Bounds for Trees）算法结合蒙特卡洛树搜索，可以让计算机在搜索空间中快速找到最优解，提高计算机的下棋水平。

首先，我们需要编写一个五子棋的游戏引擎，实现下棋规则和胜负判断等功能。然后，我们可以编写一个基于蒙特卡洛算法的计算机对弈程序，通过大量的模拟来评估每一步的可能走法，根据评估结果选择最优的下棋策略。

在计算机和玩家对弈时，计算机可以利用蒙特卡洛算法来搜索可能的下棋位置，然后选择最优的下棋策略。通过不断的模拟和更新状态价值，计算机可以逐步提高对弈水平，最终实现与人类玩家有一定竞争力的对弈能力。

总之，利用蒙特卡洛算法和UCT算法实现五子棋的计算机对弈程序，可以帮助我们提高对弈水平，也可以作为一个很好的学习和实践项目。

相关问题

蒙特卡洛树搜索算法五子棋

### Monte Carlo Tree Search Algorithm Implementation for Gomoku

Monte Carlo Tree Search (MCTS) is a heuristic search algorithm often used in artificial intelligence applications, especially game playing. In the context of Gomoku or Five-in-a-Row, MCTS can be implemented to create an intelligent opponent that makes decisions based on simulations and evaluations.

#### Key Components of MCTS

The core components include selection, expansion, simulation, and backpropagation:

- **Selection**: Traverse nodes from root until reaching leaf node.
- **Expansion**: Add one or more child nodes to the leaf node selected during Selection phase.
- **Simulation**: Run random playouts starting at expanded node.
- **Backpropagation**: Update statistics up through tree hierarchy after Simulation completes.

import numpy as np
from copy import deepcopy

class TreeNode(object):
    def __init__(self, parent=None, prior_p=1.0):
        self._parent = parent
        self._children = {}  
        self._n_visits = 0
        self._Q = 0  
        self._u = 0   
        self._P = prior_p  

def select_action(node, c_param=5):
    """Select action with highest upper confidence bound."""
    best_value = float("-inf")
    best_actions = []
    
    for action, child_node in node._children.items():
        value = child_node.get_value(c_param)
        
        if value > best_value:
            best_value = value
            best_actions = [action]
        elif value == best_value:
            best_actions.append(action)

    return np.random.choice(best_actions)

def expand_and_evaluate(board_state, player_turn):
    available_moves = board_state.get_legal_moves()
    move = np.random.choice(available_moves)
    next_board_state = deepcopy(board_state).make_move(move, player_turn)
    
    new_node = TreeNode(parent=current_node)
    current_node._children[move] = new_node
    
    winner = next_board_state.check_winner()

    if winner != None:
        reward = 1 if winner == player_turn else -1
    else:
        reward = simulate_random_playout(deepcopy(next_board_state), player_turn)

    update_tree(current_node, reward)

def mcts_search(root_state, n_simulations=1000):
    root_node = TreeNode(None, 1.0)
    
    for _ in range(n_simulations):
        node = root_node
        
        while not node.is_leaf(): 
            node = select_child_with_highest_uct(node)
            
        if node.board_state.game_over():
            continue
            
        expand_and_evaluate(node.board_state, node.player_to_act())
        
    most_visited_nodes = sorted(
        [(child_node.n_visits, action) for action,
         child_node in root_node.children.items()], reverse=True)[:1]

    _, best_action = most_visited_nodes[0]
    
    return best_action

This code snippet provides a basic framework for implementing MCTS specifically tailored towards games like Gomoku where players aim to align five stones consecutively either horizontally, vertically, or diagonally before their opponents do so[^1].

python实现的基于蒙特卡洛树搜索(MCTS)与UCT 的五子棋游戏的代码

好的，以下是一个基于Python实现的基于MCTS和UCT的五子棋游戏AI的代码示例：

import random
import math

class TreeNode:
    def __init__(self, state, parent=None):
        self.state = state
        self.parent = parent
        self.children = []
        self.visits = 0
        self.score = 0

def UCT(node):
    C = 1.4
    if node.visits == 0:
        return float('inf')
    return (node.score / node.visits) + C * math.sqrt(math.log(node.parent.visits) / node.visits)

def MCTS(state, iterations):
    root = TreeNode(state)
    for i in range(iterations):
        node = root
        # selection
        while node.children:
            node = max(node.children, key=UCT)
        # expansion
        if node.visits > 0:
            moves = node.state.get_moves()
            for move in moves:
                if move not in [c.state.last_move for c in node.children]:
                    child_state = node.state.apply_move(move)
                    child_node = TreeNode(child_state, node)
                    node.children.append(child_node)
        # simulation
        sim_node = node
        while sim_node.children:
            sim_node = random.choice(sim_node.children)
        score = simulate(sim_node.state)
        # backpropagation
        while node:
            node.visits += 1
            node.score += score
            node = node.parent
    return max(root.children, key=lambda c: c.visits).state.last_move

def simulate(state):
    player = state.get_current_player()
    while not state.is_terminal():
        move = random.choice(state.get_moves())
        state = state.apply_move(move)
        player = state.get_current_player()
    if state.get_winner() == player:
        return 1
    elif state.get_winner() == None:
        return 0.5
    else:
        return 0

class Board:
    def __init__(self, width=15, height=15, win_length=5):
        self.width = width
        self.height = height
        self.win_length = win_length
        self.board = [[None for y in range(height)] for x in range(width)]
        self.last_move = None

    def get_moves(self):
        moves = []
        for x in range(self.width):
            for y in range(self.height):
                if self.board[x][y] == None:
                    moves.append((x, y))
        return moves

    def apply_move(self, move):
        x, y = move
        player = self.get_current_player()
        new_board = Board(self.width, self.height, self.win_length)
        new_board.board = [row[:] for row in self.board]
        new_board.board[x][y] = player
        new_board.last_move = move
        return new_board

    def get_current_player(self):
        if sum(row.count(None) for row in self.board) % 2 == 0:
            return "X"
        else:
            return "O"

    def is_terminal(self):
        if self.get_winner() != None:
            return True
        for x in range(self.width):
            for y in range(self.height):
                if self.board[x][y] == None:
                    return False
        return True

    def get_winner(self):
        for x in range(self.width):
            for y in range(self.height):
                if self.board[x][y] == None:
                    continue
                if x + self.win_length <= self.width:
                    if all(self.board[x+i][y] == self.board[x][y] for i in range(self.win_length)):
                        return self.board[x][y]
                if y + self.win_length <= self.height:
                    if all(self.board[x][y+i] == self.board[x][y] for i in range(self.win_length)):
                        return self.board[x][y]
                if x + self.win_length <= self.width and y + self.win_length <= self.height:
                    if all(self.board[x+i][y+i] == self.board[x][y] for i in range(self.win_length)):
                        return self.board[x][y]
                if x + self.win_length <= self.width and y - self.win_length >= -1:
                    if all(self.board[x+i][y-i] == self.board[x][y] for i in range(self.win_length)):
                        return self.board[x][y]
        return None

    def __str__(self):
        return "\n".join(" ".join(self.board[x][y] or "-" for x in range(self.width)) for y in range(self.height))

if __name__ == "__main__":
    board = Board()
    while not board.is_terminal():
        if board.get_current_player() == "X":
            x, y = map(int, input("Enter move (x y): ").split())
            board = board.apply_move((x, y))
        else:
            move = MCTS(board, 1000)
            print("AI move:", move)
            board = board.apply_move(move)
        print(board)
    print("Winner:", board.get_winner())

该代码定义了一个 `TreeNode` 类来保存节点的状态和统计信息，实现了基于UCB公式的UCT算法和基于MCTS和UCT的五子棋AI。同时，代码还定义了一个 `Board` 类来表示五子棋游戏的状态和规则，并实现了判断胜负、获取可行落子位置等方法。在 `__main__` 函数中，代码通过交替输入玩家落子位置和调用AI选择落子位置的方式，实现了人机对战的功能。

希望这个代码对你有所帮助！