SRM145 DIV2 500
枚举题，原题重新表述为：
求 \(\{\frac{100x}{time} \ | \ x \in (0,time)\}\) 集合内整数的个数
\(time\) 的范围不算大，直接枚举即可
优化
\(整数个数=gcd(time,100)-1\)
证明如下：
\(\frac{100x}{time}\) 是整数当且仅当 \(x=k \times \frac{time}{gcd(time,100)}, k \in Z \)，则：
\(\begin{equation}\begin{split}x &\in (0, time) \\ k \times \frac{time}{gcd(time,100)} &\in (0, time) \\ k &\in (0, gcd(time, 100)) \end{split}\end{equation}\)
\(k\) 的个数即为整数的个数
1 class ExerciseMachine: 2 def getPercentages(self, time): 3 h = int(time[0:2]) 4 m = int(time[3:5]) 5 s = int(time[6:8]) 6 tot = h * 3600 + m * 60 + s 7 8 counter = 0 9 for time in range(1, tot): 10 if 100 * time % tot == 0: 11 counter += 1 12 13 return counter 14 15 16 # test 17 o = ExerciseMachine() 18 19 # test case 20 assert(o.getPercentages("00:30:00") == 99) 21 assert(o.getPercentages("00:28:00") == 19)
