各位数字全不同的下一天（MM/DD/YYYY）

Distinct Date I

专题: Algorithmic Programming / 算法编程
难度: L4
来源: QuantQuestion

题目详情

找“下一天”的日期，使得按 $MM/DD/YYYY$ 表示时出现的所有数字都互不相同。

例如 $01/23/4567$ 是合法的。用 $MMDDYYYY$ 的形式给出答案。

Find the next date where all of the digits, when expressed in the form $MM/DD/YYYY$ are distinct. For example, $01/23/4567$ would be a valid date. Express your answer in the form $MMDDYYYY$ .

解析

为了尽量早，优先最小化年份，并分析月日中必须包含的 0/1/2 的位置。

综合约束后可得到最早满足条件的日期为 $06/17/2345$ ，因此答案是

06172345.

Original Explanation

We want to minimize the year, as that will be the biggest influence on how soon it is. Note that the first $M$ is either $0$ or $1$ . If the first $M$ is $0$ , then the first day must be $1$ or $2$ OR the day is $31$ ( $30$ doesn't work since we already have a $0$ ). If the first $M$ is $1$ , then either the second $M$ is a $0$ OR the second $M$ is a $2$ and the day contains a $0$ somewhere. Therefore, these both imply that the $0$ and either the $1$ or $2$ must be used in the $MMDD$ portion. Since we ideally don't want to skip $1000$ years, we should put the $2$ in the year portion, so thus far, we have that our date is in the form $0M/1D/2YYY$ . After this, it's just an objective to minimize the rest of the digits. Namely, $YYY = 345$ , as that is the smallest number that can be made with the remaining digits. Then, we want to minimize the month, so $M = 6$ . Then, lastly, $D = 7$ , as that is the smallest remaining number. Our answer is therefore $06/17/2345$ .