Simple calculations

纯公式推导。。。，不谢。。

Simple calculations

The Problem

There is a sequence of n+2 elements a₀, a₁,…, a_n+1 (n <= 3000; -1000 <=  a_i 1000). It is known that a_i = (a_i–1 + a_i+1)/2 – c_i   for each i=1, 2, ..., n. You are given a₀, a_n+1, c₁, ... , c_n. Write a program which calculates a₁.

The Input

The first line is the number of test cases, followed by a blank line.

For each test case, the first line of an input file contains an integer n. The next two lines consist of numbers a₀ and a_n+1 each having two digits after decimal point, and the next n lines contain numbers c_i (also with two digits after decimal point), one number per line.

Each test case will be separated by a single line.

The Output

For each test case, the output file should contain a₁ in the same format as a₀ and a_n+1.

Print a blank line between the outputs for two consecutive test cases.

Sample Input

1150.5025.5010.15

Sample Output

27.85

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#include <stdio.h>
#include <string.h>
int main()
{
    int t, n, i, j, k;
    double a, b, s[3004], x, y;
    scanf("%d",&t);
    for(i = 0; i < t; i++)
    {
        x = 0;
        memset(s,0,sizeof(s));
        scanf("%d%lf%lf", &n, &a, &b);
        for(j = 1; j <= n; j++)
        {
            scanf("%lf", &s[j]);
            y = 0;
            for(k = 1; k <= j; k++)
            {
                y = y + s[k];
            }
            x = x + y;
        }
        printf("%.2lf\n", (n*a+b-2*x)/(n+1));
        if(i != t-1)
            printf("\n");
    }
    return 0;
}