Job 2412 divide the finger

Question: divide a number no more than 16 digits into M portions and obtain the maximum product. Example: Split 12345 into two parts: 1234 | 5, 123 | 45...... But the maximum value is 1234*5 = 6170

Idea: Dynamic Planning. f (I, j, T) indicates the maximum I-to-J digits and splits them into the T-part. Equation: f (I, j, t) = max {f (I, k, 1) * F (k + 1, J, t-1)}, K = I .. (J-t + 1 );

That is, the maximum product of T, is equal to the maximum value of 1 to the left and the maximum of the remaining t-1. ----- Principle of optimization. Decision K divides the problem into two subproblems

Code:

Code

  # Include  <  Cstdio  >  
# Include  <  Cstring  >  
  Using     Namespace  STD;

 Int  N, m;
  Char  Num [  20  ];
  Long     Long  DP [  20  ] [  20  ] [  20  ];

  Long    Long  Str_int (  Int  I,  Int  J ){  //  I <= J  
    Long     Long  B, S;
B  =     1 ;
S  =     0  ;
  For  (  Int  K  =  J; k  > =  I;  --  K ){
S  + =  (Num [k]  -    '  0  '  )  *  B;
B  * =     10  ;
}
  Return  S;
}


  Void  Process (){
  Int  I, j, T, K;
 Long     Long  Max, TMP;
  For  (I  =  1  ; I  <=  N;  ++  I)
  For  (J  =  I; j  <= N;  ++  J)
DP [I] [J] [  1  ]  =  Str_int (I, j );
  For  (T  =  2  ; T  <=  M;  ++  T)  // Into TB  
    For  (I  =  1  ; I  <=  N;  ++  I)
  For  (J  =  I  +  T -  1  ; J  <=  N;  ++  J ){
Max  =     0  ;
  For  (K  =  I; j  -  K  + 1     > =  T;  ++  K ){
TMP  =  DP [I] [k] [  1  ]  *  DP [K  +  1  ] [J] [t  -  1 ];
  If  (TMP  >  Max)
Max  =  TMP;
}
DP [I] [J] [T]  =  Max;
}
}

  Int  Main (){
  //  Freopen ("in", "r", stdin );  
  
 While  (Scanf (  "  % S % d  "  ,  &  Num [  1  ],  &  M)  ! =  EOF ){
N  =  Strlen (  & Num [  1  ]);

Process ();

Printf (  "  % LLD \ n  "  , DP [  1  ] [N] [m]);
}
}