Equations
Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6927 Accepted Submission(s): 2810
Problem Description
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.
Input
The 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.
End of file.
Output
For 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
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <cmath>
using namespace std;
int a,b,c,d;
int s[];
int search(int mid,int k)
{
return c*s[k]+d*s[mid];
}
void init()
{
for(int i=;i<=;i++) s[i]=i*i;
}
int main()
{
int i,j,k,ans,y;
freopen("in.txt","r",stdin);
init();
while(cin>>a>>b>>c>>d)
{
ans=;
if(a>&&b>&&c>&&d>||a<&&b<&&c<&&d<){
printf("0\n");
continue;
}
for(i=;i<=;i++)
{
for(j=;j<=;j++)
{
int sum=a*s[i]+b*s[j];
if(sum>&&c>&&d>||sum<&&c<&&d<) continue;
for(k=;k<=;k++)
{
int p=-sum-c*s[k];
if(p%d==)
{
p=p/d;
if(binary_search(s+,s+,p)) ans++;
}
}
}
}
cout<<ans*<<endl;
}
}