Weakness and Poorness

题意翻译

给定一个长度为n的数组ai，求一个实数x，使得序列a1-x,a2-x,...,an-x的不美好程度最小。 不美好程度定义为，一个序列的所有连续子序列的糟糕程度的最大值。 糟糕程度定义为，一个序列的所有位置的和的绝对值。 输入 第一行n。 第二行n个数，表示ai。 输出 一个实数，精确到6位小数，表示最小不美好程度值。

题目描述

You are given a sequence of n integers $ a_{1},a_{2},...,a_{n} $ . Determine a real number $ x $ such that the weakness of the sequence $ a_{1}-x,a_{2}-x,...,a_{n}-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.

输入输出格式

输入格式

The first line contains one integer $ n $ ( $ 1<=n<=200000 $ ), the length of a sequence. The second line contains $ n $ integers $ a_{1},a_{2},...,a_{n} $ ( $ |a_{i}|<=10000 $ ).

输出格式

Output a real number denoting the minimum possible weakness of $ a_{1}-x,a_{2}-x,...,a_{n}-x $ . Your answer will be considered correct if its relative or absolute error doesn't exceed $ 10^{-6} $ .

输入输出样例

输入样例 #1

3
1 2 3

输出样例 #1

1.000000000000000

输入样例 #2

4
1 2 3 4

输出样例 #2

2.000000000000000

输入样例 #3

10
1 10 2 9 3 8 4 7 5 6

输出样例 #3

4.500000000000000

说明

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.