在 2015年6月11日星期四 UTC-7下午1:02:09,Jing Huang写道:
> I used the dynamic programming approach to solve the problem, but my program 
> failed at the following input for large data:
> 
> 7 36
> 
> The correct output is 16 while my output is 24.
> 
> This test case could be reduced to the input of
> 
> 7 12
> 
> where the correct output (by the programs from others) is 16 and my output is 
> still 24.
> 
> However, when I try to check the result by hand using the following 
> representation:
> 
> Block A2 (period = 1)
> 333333333333
> 333333333333
> 
> Block B3 (period = 4)
> 222122212221
> 212121212121
> 212221222122
> 
> Block C2 (period = 3)
> 221221221221
> 221221221221
> 
> Block D2 (period = 6)
> 211222211222
> 222211222211
> 
> Block E1 (period = 1)
> 222222222222
> 
> I get the following results:
> 
> Input 4 12
> Output 5 (Correct)
> 1: A2 + C2
> 2: A2 + D2
> 3: C2 + A2
> 4: D2 + A2
> 5: E1 + A2 + E1
> 
> Input 5 12
> Output 7 (Correct)
> 1: A2 + B3
> 2: A2 + E1 + A2
> 3: B3 + A2
> 4: C2 + A2 + E1
> 5: D2 + A2 + E1
> 6: E1 + A2 + C2
> 7: E1 + A2 + D2
> 
> Input 6 12
> Output 21 (Correct)
> 1: A2 + C2 + A2  (p3 +)  (Note: p3 means period = 3, + means ended with A2)
> 2: A2 + D2 + A2  (p6 +)
> 3: A2 + E1 + A2 + E1  (p1)
> 4: B3 + A2 + E1  (p4)
> 5,6,7: C2 + A2 + D2 (p6)
> 8,9,10: C2 + A2 + C2 (p3)
> 11,12,13: D2 + A2 + C2 (p6)
> 14,15,16,17,18,19: D2 + A2 + D2 (p6)
> 20: E1 + A2 + B3 (p4)
> 21: E1 + A2 + E1 + A2 (p1 +)
> 
> Input 7 12
> Output 24 (Incorrect)
> 1:                            A2 + B3 + A2 (p4 +)
> 2:                            A2 + C2 + A2 + E1 (p3)
> 3:                            A2 + D2 + A2 + E1 (p6)
> 4:                            A2 + E1 + A2 + C2 (p3)
> 5:                            A2 + E1 + A2 + D2 (p6)
> 6,7,8:                                B3 + A2 + C2 (p12)  (3 combinations)
> 9,10,11,12:                   B3 + A2 + D2 (p12)  (4 combinations)
> 13,14,15:                     C2 + A2 + B3 (p12)  (3 combinations)
> 16,17,18,19:          D2 + A2 + B3 (p12)  (4 combinations)
> 20:                           C2 + A2 + E1 + A2 (p3 +)
> 21:                           D2 + A2 + E1 + A2 (p6 +)
> 22:                           E1 + A2 + C2 + A2 (p3 +)
> 23:                           E1 + A2 + D2 + A2 (p6 +)
> 24:                           E1 + A2 + E1 + A2 + E1 (p1)
> 
> I still cannot figure out what cases among the 24 I listed are duplicated or 
> wrong. Could anybody point it out for me?
> 
> Thanks in advance!

I finally know where I was wrong thanks to Mikhail Goncharov's answer on 
Google+:

E.g. d2 + a2 + b3 gives you only 2 combinations = gcd(4, 6) not min(4, 6)

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