codeforces578C. Weakness and Poorness

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a sequence of n integers a1, a2, ..., an.

Determine a real number x such that the weakness of the sequence a1 - x, a2 - x, ..., an - x is
as small as possible.

The weakness of a sequence is defined as the maximum value of the poorness over all segments (contiguous subsequences) of a sequence.

The poorness of a segment is defined as the absolute value of sum of the elements of segment.

Input

The first line contains one integer n (1 ≤ n ≤ 200 000),
the length of a sequence.

The second line contains n integers a1, a2, ..., an (|ai| ≤ 10 000).

Output

Output a real number denoting the minimum possible weakness of a1 - x, a2 - x, ..., an - x.
Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Sample test(s)

input

3
1 2 3

output

1.000000000000000

input

4
1 2 3 4

output

2.000000000000000

input

10
1 10 2 9 3 8 4 7 5 6

output

4.500000000000000

Note

For the first case, the optimal value of x is 2 so
the sequence becomes  - 1, 0, 1 and
the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to 1 in this case.

For the second sample the optimal value of x is 2.5 so
the sequence becomes  - 1.5,  - 0.5, 0.5, 1.5 and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer)
equals to 2 in this case.

这题可以用三分，但是在三分判断条件的时候要注意，用循环限定次数比较好，因为double精度不够高。

#include<iostream>
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<string>
#include<algorithm>
using namespace std;
#define ll long long
#define inf 99999999
#define maxn 200060
#define eps 1e-10
int n;
double a[maxn],b[maxn],sum1[maxn],sum2[maxn],c[maxn];  

double cal(double x)
{
    int i,j,f;
    double maxnum=0;
    sum1[0]=sum2[0]=0;
    for(i=1;i<=n;i++){
        b[i]=a[i]-x;
        sum1[i]=max(b[i],sum1[i-1]+b[i]);maxnum=max(maxnum,sum1[i]);
        c[i]=x-a[i];
        sum2[i]=max(c[i],sum2[i-1]+c[i]);maxnum=max(maxnum,sum2[i]);
    }
    return maxnum;  

}  

int main()
{
    int m,i,j;
    double l,r,m1,m2,minx,maxx;
    while(scanf("%d",&n)!=EOF)
    {
        for(i=1;i<=n;i++){
            scanf("%lf",&a[i]);
        }
        l=-10005;r=10005;
        for(i=0;i<100;i++){
            double d=(l+r)/2.0;
            m1=d;
            m2=(d+r)/2.0;
            if(cal(m2)-cal(m1)>=0){
                r=m2;
            }
            else l=m1;
        }
        printf("%.9f\n",cal(l));
    }
    return 0;
}