How, did you discover this expression?



>                                      n
>               (A[n+1] - A[0] - 2 * Sigma(k * c[n - k + 1]))
>                                     k=1
> A[1] = A[0] + ----------------------------------------------
>                                   n + 1

Your algoritmh not correct again. It very long. This problem solve with other algoritmh.
Used that a[0] = 2*a[1] + 2*c[1] - a[2] = 3*a[2] - 2*a[3] + 2*c[1] + 4*c[2], etc.

3
0
4
0
0
0

answer=1
-----
The sequence is: 0 1 2 3 4

> program a1047;
> var
> c:array[1..3000]of longint;
> n,i:longint;
> a0,an1,a1,s:real;
> begin
>     read(n);
>     read(a0);
>     read(an1);
>     for i:=1 to n do read(c[i]);
>     s:=0;
>     for i:=1 to n do
>         s:=s+i*c[n-i+1];

This string must look like that:
                s:=s+c[i]*(n-1+1);






>     a1:=a0+(an1-a0-2*s)/(n+1);

      ..and this one like that a1:=(an1+n*a0-2*s)/(n+1);




>     writeln(a1:0:2);
> end.

> I think that this problem could be solved also by an approximation
> method. (In adition to discovering the exact expression for a[1])
>
> The method that I offer in simplifaction look as follows:
>
> for (i=1; i<=elemNum; i++)
>   a[i] = 0;
>
> for (j=0; j<elemNum*N; j++) {
>   for (i=1; i<=elemNum; i++)
>     a[i] = (a[i-1] + a[i+1]) / 2 - c[i];
>
>   printf("%.2f", a[1]);
>
> I think that after enough number of iterations it should reach the
> exact answer.
>
> Though, some tests that I ran with this method gave the right
result,
> but it gave a Wrong Answer when I submitted.
> May be I need to make some tunnings to my method.
>
> What do you think?

Well, it does not work always :)) I do not know why, but the truth is
that on different PCs these do not work identically....... a BIG BUG

But I had even a bigger problem. I submitted a solution of problem
1176 (in fact, I submitted four different solutions over 30
times ;) ), but I always got TL exceeded. I always used cin/cout. I
changed cin to scanf() and cout to printf() and all was OK -> my
solution got AC, having in mind that
1. When using CIN/COUT it worked over the time limit i.e. more than 2
secs
2. When I changed them to scanf/printf i got AC and my program worked
0.9 secs............

So-> I advice you -> always use printf, scanf and all the C stuff :))
C++ input/output has lots of bugs, and as it seems, it si quite
slow.............

> which is the TIP of the of the {a0, an+1, c1, ... , cn}
> because my formula is correct but I still get Wrong Answer

Maybe your formula is wrong. It happend to me too the first
time. Here is the code which solves the problem. It was
accepted.

for (int k=n;k>=1;k--)
    {
        a[k]=a[0];
        for (i=k;i>=1;i--)
            a[k]-=i*2*c[i];
        a[k]+=k*a[k+1];
        a[k]/=k+1;
    };

> which is the TIP of the of the {a0, an+1, c1, ... , cn}
> because my formula is correct but I still get Wrong Answer

Here you are the program I have sent one more time and it
was accepted.

#include<stdio.h>
#include<string.h>
#include<stdlib.h>


void main()
{
//    FILE *f=fopen("input.txt","rt");
#define f stdin
    int n,i;
    float a[3003],c[3003];

    fscanf(f,"%d",&n);
    memset(a,0,sizeof(a));
    memset(c,0,sizeof(c));
    fscanf(f,"%f %f",&a[0],&a[n+1]);
    for (i=1;i<=n;i++)
        fscanf(f,"%f",&c[i]);
    fclose(f);
    for (int k=n;k>=1;k--)
    {
        a[k]=a[0];
        for (i=k;i>=1;i--)
            a[k]-=i*2*c[i];
        a[k]+=k*a[k+1];
        a[k]/=k+1;
    };
    printf("%0.2f",a[1]);
}