c# – 用于查找数字总和等于数字显示中的段数的时间的聪明算法

Find the number of distinct times of
the day (using 24-hour display and
assuming that morning hours are
presented as 8:15 as opposed to 08:15)
where the number of segments are equal
to the sum of the digits. Eg. 8:15 has
7+2+5=14 segments in electronic format
and the sum of the digits is 8+1+5=14,
so it qualifies as a case.

所以我在C#3.0中提出了以下简单(但是迟钝的暴力)解决方案：

// Number of segments in each digit
var digitMap = 
    new Dictionary<char,int>
    {
        {'0',6},{'1',2},{'2',5},{'3',{'4',4},{'5',{'6',{'7',3},{'8',7},{'9',5}
    };

var numMatches = (
            from h in Enumerable.Range(0,24)
            from m in Enumerable.Range(0,60)
            select h.ToString() + m.ToString().PadLeft(2,'0') into t 
            let chars = t.ToCharArray()
            where chars.Sum(c => int.Parse(c.ToString())) == chars.Sum(c => digitMap[c])
            select t).Count();

但是,他补充说：

Brute force approach is not allowed.

我已经考虑了一段时间了,我正在努力想出一个更聪明的算法.我正在沿着预先过滤不可能性的路线(例如,数字总和小于6的时间,因为那是最小的段总和) – 但最后我想这只会导致更小的解空间,然后是暴力强迫.

无论如何,我认为把它扔出去是一个有趣的问题,看看是否有人能想出一个更聪明的方法.