acm--math--hdoj 2086--a1 =?

Hdoj Title Address: Portal

A1 =?Time limit:5000/1000 MS (java/others) Memory limit:32768/32768 K (java/others) Total Submission (s): 6965 Accepted Submission (s): 4330

Problem description has the following equation: Ai = (Ai-1 + ai+1)/2-ci (i = 1, 2, 3, ...).
If given A0, an+1, and C1, C2, ..... Cn.
Please program calculate A1 =?
Input inputs include multiple test instances.
For each instance, the first is a positive integer n, (n <= 3000); Then there are 2 numbers a0, an+1. The next n rows have a number ci (i = 1, .... n) per line; the input ends with a file terminator.

Output for each test instance, the A1 (Reserved 2 decimal places) is evaluated in one line.
Sample Input

150.0025.0010.00250.0025.0010.0020.00

Sample Output

27.5015.00

because: ai= (ai-1+ai+1)/2-ci,

2. a1= (A0 +a2)/2-c1;
4. a2= (A1 + A3)/2-c2, ...
6. = = A1+A2 = (A0+A2+A1+A3)/2-(C1+C2)
8. 2[(A1+A2) + (C1+C2)] = A0+A2+A1+A3;
10. A1+A2 = A0+a3-2 (C1+C2);
12. = = A1+A2 = A0+a3-2 (C1+C2)
14. In the same vein, you get:
16. A1+A1 = a0+a2-2 (C1)
18. A1+A2 = A0+a3-2 (C1+C2)
20. A1+A3 = A0+a4-2 (C1+C2+C3)
22. A1+A4 = a0+a5-2 (C1+C2+C3+C4)
24. ...
26. A1+an = A0+an+1-2 (C1+C2+...+CN)
28. Sum-----------------------------------------------------left and right
30. (n+1) a1+ (A2+a3+...+an) = nA0 + (A2+a3+...+an) + an+1-2 (nc1+ (n-1) C2+...+2CN-1+CN)
34. = = (n+1) A1 = nA0 + an+1-2 (nc1+ (n-1) C2+...+2CN-1+CN)
38. = = A1 = [nA0 + an+1-2 (nc1+ (n-1) C2+...+2CN-1+CN)]/(n+1)
    

#include <iostream> #include <cstdio>using namespace Std;int main () {      int i,j,n;      Double sum;      while (scanf ("%d", &n)!=eof) {         sum=0;         Double a[3500],c[3500],d;         scanf ("%lf%lf", &a[0],&a[n+1]);         for (I=1; i<=n; i++)             scanf ("%lf", &c[i]);         A[1]=N*A[0]+A[N+1];         for (i = n, j = 1; I >=1&&j <= n; j++,i--)             sum + = i*c[j];         A[1] = (a[1]-2*sum)/(n+1);         printf ("%.2lf\n", a[1]);     }     return 0; }

acm--math--hdoj 2086--a1 =?