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Ural 1047 Simple calculations

1047. Simple calculations

Time Limit: 1.0 second
Memory Limit: 16 MB

There is a sequence of N + 2 elements a₀, a₁, …, a_N+1 (1 ≤ N ≤ 3000, −2000 ≤ a_i ≤ 2000). 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.

Input

The first line 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.

Output

Output a₁ in the same format as a₀ and a_N+1.

Sample

input	output
1 50.50 25.50 10.15	27.85

Problem Author: Dmitry Filimonenkov
Problem Source: Ural State University collegiate programming contest (25.03.2000)

用數學方法推出公式即可：

//ural1047
//a1=( aN_1 +N*a0 -2*( (c1+……cN)+ (c1+……cN-1 ) +……(c1+c2)+(c1) ))/(N+1)
#include<iostream>
using namespace std;
double ci[3010]={0};  //ci[i]=c1+c2+……ci
int main()
{
   int N,i;
   double a0,aN_1,temp,sum=0;
   cin>>N>>a0>>aN_1;
   for(i=1; i<=N; i++)
   {
       cin>>temp;
       ci[i]=ci[i-1]+temp;
       sum+=ci[i];
   }

   sum*=2;

   cout.precision(2);
   cout<<fixed<<( aN_1+ N*a0 -sum)/(N+1)<<endl;

   system("pause");
    return 0;
}

posted on 2010-06-24 23:09 田兵閱讀(353) 評論(0) 編輯收藏引用所屬分類: URAL

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