C. Weakness and Poorness
ternary search
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.
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 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.
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.