【POJ】【2601】Simple calculations

推公式/二分法

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　　好题！

　　题解：http://blog.csdn.net/zck921031/article/details/7690288

　　这题明显是一个方程组……可以推公式推出来……

　　然而这太繁琐了！发现a[i]是满足单调性的话，我们就可以二分a[1]，递推出a[n+1]，进行验证……

　　思维复杂度比推公式低到不知哪里去了，真是一种优秀的算法（然而我想不到，并没有什么*用……）

Source Code
Problem: 2601        User: sdfzyhy
Memory: 736K        Time: 16MS
Language: G++        Result: Accepted

    Source Code

    //PKUSC 2013 B
    //POJ 2601
    #include<vector>
    #include<cstdio>
    #include<cstring>
    #include<cstdlib>
    #include<iostream>
    #include<algorithm>
    #define rep(i,n) for(int i=0;i<n;++i)
    #define F(i,j,n) for(int i=j;i<=n;++i)
    #define D(i,j,n) for(int i=j;i>=n;--i)
    using namespace std;
    typedef long long LL;
    inline int getint(){
        int r=1,v=0; char ch=getchar();
        for(;!isdigit(ch);ch=getchar()) if (ch=='-') r=-1;
        for(; isdigit(ch);ch=getchar()) v=v*10-'0'+ch;
        return r*v;
    }
    const int N=3010;
    const double eps=1e-4;
    /*******************template********************/

    int n;
    double a[N],c[N],ed;
    inline double check(double x){
        a[1]=x;
        F(i,2,n+1) a[i]=2*(a[i-1]+c[i-1])-a[i-2];
        return a[n+1];
    }
    int main(){
    #ifndef ONLINE_JUDGE
        freopen("B.in","r",stdin);
        freopen("B.out","w",stdout);
    #endif 
        scanf("%d%lf%lf",&n,&a[0],&ed);
        F(i,1,n) scanf("%lf",&c[i]);
        double l=-1000,r=1000,mid;
        while(r-l>eps){
            mid=(l+r)/2;
            if (check(mid)>ed) r=mid;
            else l=mid;
        }
        printf("%.2f
",l);
        return 0;
    }

Simple calculations

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 6646		Accepted: 3322

Description

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.

Input

The first line of an input 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

The output file should contain a₁ in the same format as a₀ and a_n+1.

Sample Input

1
50.50
25.50
10.15

Sample Output

27.85

Source

Ural State University collegiate programming contest 2000

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