POJ 1840, Eqs

Time Limit: 5000MS  Memory Limit: 65536K
Total Submissions: 3409  Accepted: 1514

Description
Consider equations having the following form:
a1x13+ a2x23+ a3x33+ a4x43+ a5x53=0
The coefficients are given integers from the interval [-50,50].
It is consider a solution a system (x1, x2, x3, x4, x5) that verifies the equation, xi∈[-50,50], xi != 0, any i∈{1,2,3,4,5}.

Determine how many solutions satisfy the given equation.

 

Input
The only line of input contains the 5 coefficients a1, a2, a3, a4, a5, separated by blanks.

 

Output
The output will contain on the first line the number of the solutions for the given equation.

 

Sample Input
37 29 41 43 47

 

Sample Output
654

 

Source
Romania OI 2002

---

//  POJ1840.cpp : Defines the entry point for the console application.
//

#include  < iostream >
using   namespace  std;

struct  Node
{
    Node():count( 0 ), num( 0 ), next(NULL){}
     int  num;
     int  count;
    Node *  next;
};

int  main( int  argc,  char *  argv[])
{
     int  a[ 5 ];
    cin  >>  a[ 0 ]  >>  a[ 1 ]  >>  a[ 2 ]  >>  a[ 3 ]  >>  a[ 4 ];

     const   int  SIZE  =   33119 ;
    Node hash[SIZE];

     // create lookup table
     int  X[ 51 ];
     for  ( int  i  =   0 ; i  <= 50 ;  ++ i) X[i]  =  i  *  i  *  i;

     // init hash table
     for  ( int  i  =   - 50 ; i  <= 50 ;  ++ i)
         for  ( int  j  =   - 50 ; j  <=   50 ;  ++ j)
             if  (i  !=   0   &&  j  !=   0 )
            {
                 int  num  =  a[ 0 ]  *  (i  <   0   ?   - X[ - i]:X[i])  +  a[ 1 ]  *  (j  <   0   ?   - X[ - j]:X[j]);
                 int  key  =  num  %  SIZE;
                 if  (key  <   0 ) key  +=  SIZE;
                Node *  pt  =   & hash[key];
                 bool  found  =   false ;
                 while  (pt -> next  !=  NULL)
                {
                    pt  =  pt -> next;
                     if  (pt -> num  ==  num)
                    {
                         ++ (pt -> count);
                        found  =   true ;
                         break ;
                    }
                }
                 if  (found  ==   false )
                {
                    Node *  pc  =   new  Node;
                    pc -> count  =   1 ;
                    pc -> num  =  num;
                    pt -> next  =  pc;        
                };
            };

     // search hash table and find match
     int  cnt  =   0 ;
     for  ( int  i  =   - 50 ; i  <= 50 ;  ++ i)
         for  ( int  j  =   - 50 ; j  <=   50 ;  ++ j)
             for  ( int  k  =   - 50 ; k  <=   50 ;  ++ k)
                 if  (i  !=   0   &&  j  !=   0   &&  k  !=   0 )
                {
                     int  num  =   - (a[ 2 ]  *  (i  <   0   ?   - X[ - i]:X[i])  +
　　　　　　　　　　 a[ 3 ]  *  (j  <   0   ?   - X[ - j]:X[j])  +  a[ 4 ]  *  (k  <   0   ?   - X[ - k]:X[k]));
                     int  key  =  num  %  SIZE;
                     if  (key  <   0 ) key  +=  SIZE;

                    Node *  pt  =   & hash[key];
                     while  (pt -> next  !=  NULL)
                    {
                        pt  =  pt -> next;
                         if  (pt -> num  ==  num)
                        {
                            cnt  +=  pt -> count;
                             break ;
                        }
                    }
                };

    cout  <<  cnt  << endl;
     return   0 ;
}