Equations（hdu 1496 二分查找+各种剪枝）

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.

 

 

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\n");
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 }