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.