HDU 4282 a very hard mathematic problem

Question:

IfCodeError. Please note
X ^ Z + y ^ Z + XYZ = K
K (0 <k <2 ^ 31), (x <y, z> 1)

Analysis:

Note that the maximum value of Z is 30 (x <y so y> = 2)
When K = 2, it can be determined by using the full square formula, which can be changed to (x + y) ^ 2 = K.
When K> 2, the values of Z, X, and y can be enumerated directly (when z> 2, the maximum value of X is About 1290)

6726850

2012-09-09 17:12:22

Accepted

4282

281 Ms

472 K

1151 B

G ++

View code

 1 # Include <iostream> 2 # Include <cstdio>3 # Include <cmath> 4   5   Using   Namespace  STD;  6   7   Long   Long Pow ( Long   Long X, Int  Z ){  8       Long  Long Temp = X;  9       For ( Int I = 2 ; I <= z; I ++ )  10 X * = Temp;  11       Return  X;  12   }  13   14  Int  Main (){  15 Freopen ( "  Sum. In  " , "  R  "  , Stdin );  16       Int  N;  17       While (CIN> N, N ){  18          Int Ans = 0  ;  19           Int Temp = SQRT (N );  20           If (Temp * temp = N)  21 Ans + = (temp- 1 )> 1  ;  22   23           For ( Int Z = 3 ; Z < 31 ; Z ++ ){  24               For ( Long   Long X = 1 ; X ++ ){  25                   Long   Long U = Pow (x, z );  26                  If (U> = N/ 2  )  27                       Break  ;  28                   For ( Long   Long Y = x + 1 ; Y ++ ){  29                       Long   Long V = Pow (Y, Z ); 30                       If (U + V + z * x * Y> N)  31                           Break  ;  32                       Else   If (U + V + z * x * Y = N ){  33 Ans ++ ;  34                           Break  ;  35  }  36   }  37   }  38   }  39 Cout <ans < Endl;  40   }  41       Return   0  ;  42 }