农夫狼羊菜过河问题Python

农夫、狼、羊和菜过河问题是经典的计算机科学问题，也称为“吃人问题”或“四色问题”的变体。它描述了一个场景：一个农夫需要带着一只狼、一只羊和一棵菜过河，但是农夫每次只能带一样东西过河。如果农夫不在场，狼会吃羊，羊会吃菜。问题是找出一种安全的方法让它们全部过河。

在Python中解决这个问题通常通过递归回溯算法，也就是所谓的“搜索树”或“状态空间搜索”。程序会遍历所有可能的状态，并尝试每种状态下农夫可以带哪些物品过河，然后检查是否满足条件，如果找到可行的方案就记录下来。

这是一个简化版的伪代码：

def cross_the_river(items, farmer=None, wolf=None, sheep=None, cabbage=None, riverbank):
    # 初始化所有元素在起始岸上
    if not any([farmer, wolf, sheep, cabbage]):
        return [items, "Start"]

    # 检查当前状态是否允许过河
    if (wolf and not farmer) or (sheep and wolf) or (cabbage and sheep):
        return None  # 状态无效

    # 构造所有可能的转移
    for item in items:
        if farmer and item != wolf and item != sheep and item != cabbage:
            # 过河并更新状态
            new_items = items.copy()
            new_items.remove(item)
            new_farmer_side = {item: riverbank}
            next_state = cross_the_river(new_items, item, wolf, sheep, cabbage, True if riverbank == False else False)
            if next_state:
                yield next_state + [new_farmer_side]
        elif (not farmer and item == wolf) or (not farmer and item == sheep) or (not farmer and item == cabbage):
            # 农夫独自过河
            new_items = items.copy()
            new_farmer_side = {item: riverbank}
            next_state = cross_the_river(new_items, farmer, item, sheep, cabbage, True)
            if next_state:
                yield next_state + [new_farmer_side]

# 示例用法
solutions = list(cross_the_river(['wolf', 'sheep', 'cabbage'], farmer=True))