Consider equations having the following form:
a*x1^2+b*x2^2+c*x3^2+d*x4^2=0
a, b, c, d are integers from the interval [-50,50] and any of them cannot be 0.
It is consider a solution a system ( x1,x2,x3,x4 ) that verifies the equation, xi is an integer from [-100,100] and xi != 0, any i ∈{1,2,3,4}.
Determine how many solutions satisfy the given equation.
a*x1^2+b*x2^2+c*x3^2+d*x4^2=0
a, b, c, d are integers from the interval [-50,50] and any of them cannot be 0.
It is consider a solution a system ( x1,x2,x3,x4 ) that verifies the equation, xi is an integer from [-100,100] and xi != 0, any i ∈{1,2,3,4}.
Determine how many solutions satisfy the given equation.
InputThe input consists of several test cases. Each test case consists of a single line containing the 4 coefficients a, b, c, d, separated by one or more blanks.
End of file.OutputFor each test case, output a single line containing the number of the solutions.
Sample Input
1 2 3 -4
1 1 1 1
Sample Output
39088 0
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include<cstdio> #include<cstdlib> #include<iostream> #include<algorithm> #include<memory> #include<map> #include<cstring> using namespace std; int a,b,c,d; int q[4000000]; int main() { int i,j,k,ans; while(cin>>a>>b>>c>>d){ ans=0; if(a>0&&b>0&&c>0&&d>0){ printf("0 "); continue; } if(a<0&&b<0&&c<0&&d<0){ printf("0 "); continue; } memset(q,0,sizeof(q)); for(i=1;i<=100;i++) for(j=1;j<=100;j++) q[i*i*a+j*j*b+1000000]++; for(i=1;i<=100;i++) for(j=1;j<=100;j++) ans+=q[1000000-i*i*c-j*j*d]; printf("%d ",ans*16); } return 0; }
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include<cstdio> #include<cstdlib> #include<iostream> #include<algorithm> #include<memory> #include<map> using namespace std; int a,b,c,d; map<int,int>q; int main() { int i,j,k,ans; while(cin>>a>>b>>c>>d){ ans=0; if(a>0&&b>0&&c>0&&d>0||a<0&&b<0&&c<0&&d<0) //因为x那项永远是正数,如果系数都为正或者为负的时候明显不等于0 { printf("0 "); continue; } q.clear(); for(i=1;i<=100;i++) for(j=1;j<=100;j++) q[i*i*a+j*j*b]++; for(i=1;i<=100;i++) for(j=1;j<=100;j++) ans+=q[-i*i*c-j*j*d]; printf("%d ",ans*16); } return 0; }