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].