python实现36数码问题（A*算法）

36数码问题是一种经典的搜索问题，其中一个3x3的九宫格中有1~9的数字和一个空格，目标是将数字移动到正确的位置，最终形成如下状态：

1 2 3
4 5 6
7 8

在此过程中，只能将数字移动到相邻的空格中，例如，如果空格在位置(1,1)，那么只能将数字2或者4移动到该位置，如果空格在位置(2,2)，那么可以将数字2、5或者8移动到该位置。

A*算法是一种启发式搜索算法，可以用于解决36数码问题。下面是使用Python实现36数码问题的A*算法的代码：

from queue import PriorityQueue

class Puzzle:
    def __init__(self, init_state, goal_state):
        self.init_state = init_state
        self.goal_state = goal_state

    def find_blank(self, state):
        for i in range(3):
            for j in range(3):
                if state[i][j] == 0:
                    return i, j

    def move_blank(self, state, move):
        blank_row, blank_col = self.find_blank(state)
        new_row = blank_row + move[0]
        new_col = blank_col + move[1]
        if new_row >= 0 and new_col >= 0 and new_row < 3 and new_col < 3:
            new_state = [row[:] for row in state]
            new_state[blank_row][blank_col], new_state[new_row][new_col] = new_state[new_row][new_col], new_state[blank_row][blank_col]
            return new_state
        return None

    def get_moves(self, state):
        moves = []
        moves.append((-1, 0))
        moves.append((1, 0))
        moves.append((0, -1))
        moves.append((0, 1))
        valid_moves = []
        for move in moves:
            new_state = self.move_blank(state, move)
            if new_state:
                valid_moves.append((new_state, move))
        return valid_moves

    def get_heuristic(self, state):
        distance = 0
        for i in range(3):
            for j in range(3):
                if state[i][j] != 0:
                    row = (state[i][j] - 1) // 3
                    col = (state[i][j] - 1) % 3
                    distance += abs(row - i) + abs(col - j)
        return distance

    def solve(self):
        queue = PriorityQueue()
        queue.put((self.get_heuristic(self.init_state), self.init_state, [], 0))
        visited = set()
        while not queue.empty():
            _, state, path, cost = queue.get()
            if state == self.goal_state:
                return path
            if tuple(map(tuple, state)) not in visited:
                visited.add(tuple(map(tuple, state)))
                for next_state, move in self.get_moves(state):
                    next_cost = cost + 1
                    next_path = path + [move]
                    priority = next_cost + self.get_heuristic(next_state)
                    queue.put((priority, next_state, next_path, next_cost))
        return None

if __name__ == '__main__':
    init_state = [[2, 3, 8], [1, 0, 4], [7, 6, 5]]
    goal_state = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]
    puzzle = Puzzle(init_state, goal_state)
    path = puzzle.solve()
    if path:
        for move in path:
            print(move)
    else:
        print('No solution')

在上面的代码中，Puzzle类表示36数码问题的状态和操作，包括查找空格、移动空格、获取有效移动、获取启发式函数等。solve()方法使用A*算法搜索最优解，并返回最佳路径。

在main()函数中，我们可以指定初始状态和目标状态，然后调用solve()方法求解最优路径并输出。如果没有解，则输出"No solution"。