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.
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
0
1 #include <cstdio> 2 #include <cstring> 3 #include <algorithm> 4 #include <iostream> 5 #include <cmath> 6 using namespace std; 7 int a,b,c,d; 8 int s[101]; 9 int search(int mid,int k) 10 { 11 return c*s[k]+d*s[mid]; 12 } 13 void init() 14 { 15 for(int i=1;i<=100;i++) s[i]=i*i; 16 } 17 int main() 18 { 19 int i,j,k,ans,y; 20 freopen("in.txt","r",stdin); 21 init(); 22 while(cin>>a>>b>>c>>d) 23 { 24 ans=0; 25 if(a>0&&b>0&&c>0&&d>0||a<0&&b<0&&c<0&&d<0){ 26 printf("0 "); 27 continue; 28 } 29 for(i=1;i<=100;i++) 30 { 31 for(j=1;j<=100;j++) 32 { 33 int sum=a*s[i]+b*s[j]; 34 if(sum>0&&c>0&&d>0||sum<0&&c<0&&d<0) continue; 35 for(k=1;k<=100;k++) 36 { 37 int p=0-sum-c*s[k]; 38 if(p%d==0) 39 { 40 p=p/d; 41 if(binary_search(s+1,s+101,p)) ans++; 42 } 43 } 44 } 45 } 46 cout<<ans*16<<endl; 47 } 48 }