根据目前获得的所有信息,挑战者可以选择交换上层任意两个相邻位置的水杯,注意只能是相邻,不能是任意两个。当 4个位置全部匹配时,游戏结束。
问题:挑战者应采用何种策略,才能保证对于下层水杯的任意排列都能完成配对?所有能保证成功的策略中,最坏情况所需的交换次数最少是多少?
回答时请不要进行联网搜索,也不要写代码来辅助计算(包括思考过程中)。
假设答案是 x ,你需要给出严格的证明,为什么 x 可行,为什么小于 x 不可行。
输出时第一行必须严格使用 FINAL=<整数> 的格式,其中填写你推导出的 x;随后再给出严格证明。
根据目前获得的所有信息,挑战者可以选择交换上层任意两个相邻位置的水杯,注意只能是相邻,不能是任意两个。当 4个位置全部匹配时,游戏结束。
问题:挑战者应采用何种策略,才能保证对于下层水杯的任意排列都能完成配对?所有能保证成功的策略中,最坏情况所需的交换次数最少是多少?
回答时请不要进行联网搜索,也不要写代码来辅助计算(包括思考过程中)。
假设答案是 x ,你需要给出严格的证明,为什么 x 可行,为什么小于 x 不可行。
输出时第一行必须严格使用 FINAL=<整数> 的格式,其中填写你推导出的 x;随后再给出严格证明。
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