【Quant绿皮书】Q3 River crossing

Four people, A, B, C and D need to get across a river. The only way to cross the river is by an old bridge, which holds at most 2 people at a time. Being dark, they can't cross the bridge without a torch, of which they only have one. So each pair can only walk at the speed of the slower person. They need to get all of them across to the other side as quickly as possible. A is the slowest and takes 10 minutes to cross; B takes 5 minutes; C takes 2 minutes; and D takes 1 minute. What is the minimum time to get all of them across to the other side?

四个人，A、B、C 和 D，需要过河。唯一能过河的途径是通过一座古老的桥梁，这座桥每次最多只能承载两人。由于天色昏暗，他们没有手电筒无法过桥，而他们只有一支手电筒。因此，每两个人组成的小组只能以较慢者的速度前进。他们需要尽快让所有人安全到达对岸。A 是最慢的，需要 10 分钟才能过河；B 需要 5 分钟；C 需要 2 分钟；D 需要 1 分钟。让所有人安全到达对岸的最短时间是多少？

题目：过河
类型：脑筋急转弯
思路：
当前题目只设计了四个人，策略方案其实非常有限，问题聚焦于如何高效利用C和D的速度实现最短时间
最优策略->
C、D --> D回 （2+1）
A、B --> C回 （10+2）
C、D --> 结束（2）
这样最耗时的A和B只需要一次，而C和D各往返一次