A contiguous subsequence of a list S is a subsequence made up of consecutive elements of S. For instance, if S is
5, 15, −30, 10, −5, 40, 10,
then 15, −30,10 is a contiguous subsequence but 5,15, 40 is not. Give a linear-time algorithm for the following task:
Input: A list of numbers, a1, a2,...,an.
Output: The contiguous subsequence of maximum sum (a subsequence of length zero has sum zero).
For the preceding example, the answer would be 10, −5,40,10, with a sum of 55.
(Hint: For each j ∈ {1, 2,..., n}, consider contiguous subsequences ending exactly at position j.)
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