蓝桥杯：特殊时间（C++）

禁止转载，该文章内容并非教学，仅为个人笔记。

问题描述

2022 年 2 月 22 日 22:20 是一个很有意义的时间，
年份为 2022，由 3 个 2 和 1 个 0 组成，
如果将月和日写成 4 位，为 0222，也是由 3 个 2 和 1 个 0 组成，
如果将时间中的时和分写成 4 位，还是由 3 个 2 和 1 个 0 组成。

小蓝对这样的时间很感兴趣，他还找到了其它类似的例子，比如 111 年 10 月 11 日 01:11，2202 年 2 月 22 日 22:02 等等。

请问，总共有多少个时间是这种年份写成 4 位、月日写成 4 位、时间写成4 位后由 3 个一种数字和 1 个另一种数字组成。注意 1111 年 11 月 11 日11:11不算，因为它里面没有两种数字。

解题思路

数据中要特别注意的是日月组合，因为一个月有几天取决于月份。
看下图，在可能的最大组合值中，有且仅有日月组合为 11 月 31 日是无效的，排除日月组合中所有日大于等于31即可。
2月的最大组合是 02 月 22 日，所以不用考虑闰年问题。

代码实现

#include<iostream>
using namespace std;
void IsOk(int&, int&, int&);
int Numbers[4], Count;
int main()
{for (int j = 0; j < 10; ++j){for (int k = 0; k < 10; ++k)  // j,k 为种子数据，接下来生成的年月日时分都由种子数据组成{if(j == k) continue;int y = 0, m = 0, hs = 0;      // y,m,hs 为由当前种子组成下可以分别满足条件的年，月日，时分总数for (int i = 0; i < 4; ++i){Numbers[i] = j;Numbers[(i + 1) % 4] = Numbers[(i + 2) % 4] = Numbers[(i + 3) % 4] = k;IsOk(y, m, hs);}cout << "count: " << y * m * hs << endl;Count += y * m * hs;            // 组合}}cout << Count;return 0;
}void IsOk(int &y, int &m, int &hs)
{int year = Numbers[0] * 1000 + Numbers[1] * 100 + Numbers[2] * 10 + Numbers[3];int month = Numbers[0] * 10 + Numbers[1];int day = Numbers[2] * 10 + Numbers[3];int hour = month;int minute = day;if (year > 0){++y;cout << "Year:" << year << ",";}if (month > 0 && month < 13 && day > 0 && day < 31){++m;cout << "MonthDay:" << month << "-" << day << ",";}if (hour > 0 && hour < 25 && minute >= 0 && minute < 60){++hs;cout << "HourMinute:" << hour << ":" << minute;}cout << endl;
}

运行结果

共 212 种组合
0111-01-11 01:11
0111-01-11 10:11
0111-01-11 11:01
0111-01-11 11:10
0111-10-11 01:11
0111-10-11 10:11
…

Year:111,MonthDay:1-11,HourMinute:1:11
Year:1011,MonthDay:10-11,HourMinute:10:11
Year:1101,MonthDay:11-1,HourMinute:11:1
Year:1110,MonthDay:11-10,HourMinute:11:10
count: 64
Year:222,MonthDay:2-22,HourMinute:2:22
Year:2022,HourMinute:20:22
Year:2202,HourMinute:22:2
Year:2220,HourMinute:22:20
count: 16
...
Year:1222,MonthDay:12-22,HourMinute:12:22
Year:2122,HourMinute:21:22
Year:2212,HourMinute:22:12
Year:2221,HourMinute:22:21
count: 16
...
Year:2111,HourMinute:21:11
Year:1211,MonthDay:12-11,HourMinute:12:11
Year:1121,MonthDay:11-21,HourMinute:11:21
Year:1112,MonthDay:11-12,HourMinute:11:12
count: 48
...
Year:3111,
Year:1311,HourMinute:13:11
Year:1131,HourMinute:11:31
Year:1113,MonthDay:11-13,HourMinute:11:13
count: 12
...
Year:4111,
Year:1411,HourMinute:14:11
Year:1141,HourMinute:11:41
Year:1114,MonthDay:11-14,HourMinute:11:14
count: 12
...
Year:5111,
Year:1511,HourMinute:15:11
Year:1151,HourMinute:11:51
Year:1115,MonthDay:11-15,HourMinute:11:15
count: 12
...
Year:6111,
Year:1611,HourMinute:16:11
Year:1161,
Year:1116,MonthDay:11-16,HourMinute:11:16
count: 8
...
Year:7111,
Year:1711,HourMinute:17:11
Year:1171,
Year:1117,MonthDay:11-17,HourMinute:11:17
count: 8
...
Year:8111,
Year:1811,HourMinute:18:11
Year:1181,
Year:1118,MonthDay:11-18,HourMinute:11:18
count: 8
...
Year:9111,
Year:1911,HourMinute:19:11
Year:1191,
Year:1119,MonthDay:11-19,HourMinute:11:19
count: 8
...
212