Maximum Consecutive Subsequence

You are given an array of integer of size N (A[0],A[1],A[2],...A,[N-1])
containing both negative and non-negative integers. Design an efficient
algorithm to find the sub sequence A[i],A[i+1],A[i+2]...,A[j] having the
maximum summation (A[i]+A[i+1]+A[i+2] + ...+A[j] have the highest sum). What
is the complexity of your algorithm?

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