用python写一个农夫过河的程序，并用集合表示农夫过河状态

好的，以下是用 Python 写的农夫过河程序，并用集合表示农夫过河状态：

# 定义初始状态
start = frozenset([('farmer', 'chicken', 'grain', 'fox')])

# 定义目标状态
goal = frozenset([])

# 定义可行状态
valid_states = set([
    frozenset([]),
    frozenset([('farmer',)]),
    frozenset([('farmer', 'chicken')]),
    frozenset([('farmer', 'grain')]),
    frozenset([('farmer', 'fox')]),
    frozenset([('farmer', 'chicken', 'grain')]),
    frozenset([('farmer', 'chicken', 'fox')]),
    frozenset([('farmer', 'grain', 'fox')])
])

# 定义移动规则
moves = {
    ('farmer', 'chicken'): 'chicken',
    ('farmer', 'grain'): 'grain',
    ('farmer', 'fox'): 'fox',
    ('farmer',): 'farmer'
}

# 定义农夫过河函数
def farmer_crossing(start, goal, valid_states, moves):
    visited = set()
    queue = [[start]]
    while queue:
        path = queue.pop(0)
        state = path[-1]
        if state == goal:
            return path
        for move, item in moves.items():
            if move[0] in state:
                new_state = set(state)
                new_state.remove(move[0])
                new_state.add(item)
                if frozenset(new_state) in valid_states and frozenset(new_state) not in visited:
                    new_path = list(path)
                    new_path.append(frozenset(new_state))
                    queue.append(new_path)
                    visited.add(frozenset(new_state))
    return None

# 执行农夫过河函数
path = farmer_crossing(start, goal, valid_states, moves)

# 输出结果
if path:
    for state in path:
        print(state)
else:
    print("无解")

在这个程序中，我们使用了集合来表示农夫过河的状态，其中每个元素代表一个物品或农夫的位置。移动规则定义了每个物品可以和农夫一起过河的情况。我们使用 BFS 算法来搜索可行的状态，直到找到目标状态或者无解。