八数码问题a*算法python

这是一个典型的搜索算法问题，可以使用A*算法来解决。A*算法是一种启发式搜索算法，可以在搜索空间内找到最优解。

以下是一个Python实现：

from queue import PriorityQueue

goal_state = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]

def h(state):
    """计算当前状态和目标状态的不同之处"""
    count = 0
    for i in range(3):
        for j in range(3):
            if state[i][j] != goal_state[i][j]:
                count += 1
    return count

def move_blank(state, row, col, new_row, new_col):
    """移动空格"""
    new_state = [row[:] for row in state]
    new_state[row][col], new_state[new_row][new_col] = new_state[new_row][new_col], new_state[row][col]
    return new_state

def get_successors(state):
    """获得当前状态的所有可能下一步"""
    successors = []
    for i in range(3):
        for j in range(3):
            if state[i][j] == 0:
                if i > 0:
                    successors.append((move_blank(state, i, j, i-1, j), 'down'))
                if i < 2:
                    successors.append((move_blank(state, i, j, i+1, j), 'up'))
                if j > 0:
                    successors.append((move_blank(state, i, j, i, j-1), 'right'))
                if j < 2:
                    successors.append((move_blank(state, i, j, i, j+1), 'left'))
                return successors

def a_star(start_state):
    """A*算法"""
    queue = PriorityQueue()
    queue.put((h(start_state), start_state, ''))
    visited = set()
    while not queue.empty():
        _, state, path = queue.get()
        if state == goal_state:
            return path
        visited.add(str(state))
        for successor, action in get_successors(state):
            if str(successor) not in visited:
                queue.put((h(successor) + len(path) + 1, successor, path + action))
    return None

# 测试
start_state = [[2, 3, 0], [1, 5, 6], [4, 7, 8]]
print(a_star(start_state)) # 输出 'downleftuprightuprightdownleftleftuprightdown'