HDU 2086 a1 =?

Question link: http://acm.hdu.edu.cn/showproblem.php? PID = 1, 2086

I think it's good to know that mathematics is not good on the Internet ....

1. Because: AI = (Ai-1 + AI + 1)/2-ci,

   1. A1 = (A0 + A2)/2-C1;
   2. A2 = (A1 + A3)/2-C2 ,...
   3. => A1 + A2 = (A0 + A2 + A1 + A3)/2-(C1 + C2)
   4. 2 [(A1 + A2) + (C1 + C2)] = A0 + A2 + A1 + A3;
   5. A1 + A2 = A0 + A3-2 (C1 + C2 );
   6. => A1 + A2 = A0 + A3-2 (C1 + C2)
   7. Likewise:
   8. A1 + A1 = A0 + A2-2 (C1)
   9. A1 + A2 = A0 + A3-2 (C1 + C2)
   10. A1 + A3 = A0 + A4-2 (C1 + C2 + C3)
   11. A1 + A4 = A0 + A5-2 (C1 + C2 + C3 + C4)
   12. ...
   13. A1 + an = A0 + An + 1-2 (C1 + C2 +... + CN)
   14. ----------------------------------------------------- Sum of left and right
   15. (N + 1) A1 + (A2 + A3 +... + an) = na0 + (A2 + A3 +... + an) + An + 1-2 (NC1 + (n-1) C2 +... + 2cn-1 + CN)
   17. => (N + 1) a1 = na0 + An + 1-2 (NC1 + (n-1) C2 +... + 2cn-1 + CN)
   19. => A1 = [na0 + An + 1-2 (NC1 + (n-1) C2 +... + 2cn-1 + CN)]/(n + 1)

    

 

 

 

 

Code Attached

 1 #include <iostream> 2 #include <cstdio> 3  4 using namespace std; 5 int main () 6 { 7     int i,j,n; 8     double sum; 9     while (~scanf("%d",&n))10     {11         sum=0;12         double a[3500],c[3500],d;13         scanf("%lf%lf",&a[0],&a[n+1]);14         for (i=1; i<=n; i++)15             scanf("%lf",&c[i]);16         a[1]=n*a[0]+a[n+1];17         for (i = n, j = 1; i >=1&&j <= n; j++,i--)18             sum += i*c[j];19         a[1] = (a[1] - 2*sum)/(n+1);20         //sum+=c[i];21         //cout<<a[1]<<endl;22         printf ("%.2lf\n",a[1]);23     }24     return 0;25 }