Freshman race 1011 Singles Day gift of the world

Topic:

Now, 11.11 in college life is a special day, many schools have it as a boy's day, as a sister, LPT also want to give the younger brother, but so much, how to send? So she thought of an idea,
Can out a math problem exam, the first three AC this problem of the younger brother can get small gifts!
There is a set of sequences, it has n+2 elements, a[0],a[1], ..., a[n+1] (n <=, -10000 <= a[i]<=10000), for i = 1,2,3,...,n satisfies a[i]-c[i]= (a[i-1]+a [I+1]) /2-b[i],
If given a[0],a[n+1] and the values of all elements of set B, C (i.e. given b[1],b[2]...b[n] and c[1],c[2],..., c[n],-100≤b[i], c[i]≤100), are reserved for the two digits after the decimal point, the Smart
Can you figure out a[1]?

Ideas:

      first, constant items can be combined, ci=  (ai+1"/2 −  with - ci bashi sub-formation:   < Span class= ">aaa

variants: a -  -  =   -         

      Then, i  1 start, to i   n

a  " a1 2   

A3 - a2 - 2d2 = a2 - A 1

···

An+1 - an - 2dn = an - an-1

Add the n to get

 a0 -< Span class= "> a1 + n+1n * $ \sum_{i=1}^{n}d_i$< Span class= ">= 0        (

by formula (1) available

An+1 - an - 2dN= an - an-1

2                      

a0 - 1nn-12 * $ \sum_{i=1}^{n-1}d_i$ =     (

Repeat , get:

A0 - a1 + a2 - a1 - 2 d1 = 0 (n+1)

The formula (2) is added to the formula (n+1)to:

A1=(n*A0+AN+1-2* * 1  -2 *     2dn

Code:

1#include <cstdio>2 intMain ()3 {4     //freopen ("Data_in.txt", "R", stdin);5     //freopen ("Data_out.txt", "w", stdout);6     intN, I, T;7     DoubleA1, X, Y, b[3010], c[3010], d[3010], sum=0.0;8scanf"%d", &T);9      while(t--)Ten     { Onescanf"%d", &n); Ascanf"%LF%LF", &x, &y); -          for(i =1; I <= N; i++) -         { thescanf"%LF", &b[i]); -         } -          for(i =1; I <= N; i++) -         { +scanf"%LF", &c[i]); -D[i] = b[i]-C[i]; +         } A          for(i =1; I <= N; i++) at         { -Sum + =2* (N-i +1) *D[i]; -         } -A1 = (n * x-sum + y)/(n +1); -printf"%.2lf\n", A1); -     } in  -     return 0; to}

AC Code

Freshman race 1011 Singles Day gift of the world