Eqs

题目链接：http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=15029

题意：

给出系数a1,a2,a3,a4,a5,求出方程a1x1 ³+ a2x2 ³+ a3x3 ³+ a4x4 ³+ a5x5 ³=0 有多少个解。

样例：

Sample Input

37 29 41 43 47

Sample Output

654


分析：
   如果直接用5个for循环是会超时的，所以把方程a1x1x1x1+a2x2x2x2+a3x3x3x3+a4x4x4x4+a5x5x5x5=0
转变成-（a1x1x1x1+a2x2x2x2）=a3x3x3x3+a4x4x4x4+a5x5x5x5这样就将5层循环减少到3层循环。

 1 #include<iostream>
 2 #include<cstring>
 3 #include<cmath>
 4 using namespace std;
 5 const int maxn=25000000;
 6 int i,a[10],count=0,sum=0;
 7 short b[maxn];
 8 int x1,x2,x3,x4,x5;
 9 int main()
10 {
11     memset(b,0,sizeof(b));
12 for(i=0;i<5;i++)
13    cin>>a[i];
14 for(x1=-50;x1<=50;x1++)
15 {   if(x1==0)  continue;
16       for(x2=-50;x2<=50;x2++)
17     {     
18         if(x2==0)  continue;
19         sum=-1*(a[0]*x1*x1*x1+a[1]*x2*x2*x2);
20         if(sum<0)
21             b[maxn+sum]++;
22         else b[sum]++;
23       }
24 }
25 for(x3=-50;x3<=50;x3++)
26 {    
27    if(x3==0)  continue; 
28       for(x4=-50;x4<=50;x4++)
29       {
30         if(x4==0)  continue;  
31           for(x5=-50;x5<=50;x5++)
32         {     
33             if(x5==0)  continue;
34          sum=a[2]*x3*x3*x3+a[3]*x4*x4*x4+a[4]*x5*x5*x5;
35              if(sum<0)
36                 sum=maxn+sum;
37               count=count+b[sum];
38                 }
39 
40     }
41     }
42 cout<<count<<endl;
43 return 0;
44 }