Problem 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.
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
***************************************************************************************************************************
hash表的应用
***************************************************************************************************************************
1 #include<iostream> 2 #include<string> 3 #include<cstring> 4 #include<cmath> 5 #include<cstdio> 6 using namespace std; 7 const int maxn=20000000;//防止出现负; 8 char hash[40000000];//此处用char节省内存 9 int a1,a2,a3,a4,a5; 10 int i,j,k; 11 int main() 12 { 13 int sum; 14 while(scanf("%d%d%d%d%d",&a1,&a2,&a3,&a4,&a5)!=EOF) 15 { 16 sum=0; 17 memset(hash,0,sizeof(hash)); 18 //前两个 19 for(i=-50;i<=50;i++) 20 for(j=-50;j<=50;j++) 21 if(i!=0&&j!=0) 22 hash[i*i*i*a1+j*j*j*a2+maxn]++;//hash表存储 23 //后三个 24 for(i=-50;i<=50;i++) 25 for(j=-50;j<=50;j++) 26 for(k=-50;k<=50;k++) 27 if(i!=0&&j!=0&&k!=0) 28 sum+=hash[i*i*i*a3+j*j*j*a4+k*k*k*a5+maxn];//由结果的对称性,可得 29 printf("%d ",sum); 30 } 31 }