秘书问题
Miss Moneypenny
题目详情
Miss Moneypenny You need to hire a secretary. There are n possible candidates to interview and you want to find thebest, the most talented. The problem is that there is great demand for secretaries, so if you want to make sure that you get one you' ll have to offer her the job on the spot. Once she walks out of the door she's gone. You start interviewing candidates one after the other, they can all be ranked, so thisone is better than that, or that one is worse than another, etc. There are no ties. But the order in which they are interviewed is random. What is the best strategy for maximizing the probability of getting the best secretary?
解析
最优策略是“观察期 + 选择期”的停规则:
- 先面试前 人,一律不录用,只记住这 人中的最好水平;
- 从第 人开始,遇到第一个比之前所有人都优秀的候选人就立刻录用;
- 若一直没遇到,则录用最后一人。
当 很大时,最优 约为
此时录到全局最优者的最大概率约为