poj 2601 Simple calculations - c++编程基础

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 6559		Accepted: 3291

Description

There is a sequence of n+2 elements a ₀, a ₁, ..., 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 a ₀, a _n+1, c ₁, ... , c _n. Write a program which calculates a ₁.

Input

The first line of an input contains an integer n. The next two lines consist of numbers a ₀ 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

The output file should contain a ₁ in the same format as a ₀ and a _n+1.

Sample Input

Sample Output

27.85

解题思路：

大概过程：
a[0]+a[2]-2a[1]-2c[1]=0
a[1]+a[3]-2a[2]-2c[2]=0
……
a[n-1] + a[n+1] - 2a[n] - 2c[n] = 0
累加可得：
a[0]+a[n+1]-a[1]-a[n]-2c[1]-2c[2]-...-2c[n]=0
根据a[n-1]+a[n+1]-2a[n]-2c[n]=0  => a[n+1]-2c[n]-a[n]=a[n]+2c[n]-a[n-1]
化简：a[0]+a[n]-a[1]-a[n-1]-2c[1]-2c[2]-...-2c[n-1]=0
同理：a[0]+a[n-1]-a[1]-a[n-2]-2c[1]-2c[2]-...-2c[n-2]=0
      ……
      a[0]+a[2]-a[1]-a[1]-2c[1]=0
相加上面各式可得n*a[0]+a[n+1]-(n+1)*a[1]-2*n*c[1]-2*(n-1)*c[2]-...-2*c[n]=0
即a[1]=(n*a[0]+a[n+1]-2*n*c[1]-2*(n-1)*c[2]-...-2*c[n])/(n+1)

#include 
  
   
#include 
   
     using namespace std; #define MAX 3005 int main(){ int n; double a0,an; double c[MAX]; while (cin>>n){ cin>>a0>>an; double ans=0; for (int i=0;i
    
     >c[i]; ans+=2*(n-i)*c[i]; } ans=(n*a0+an-ans)/(n+1); cout<