Problem
1. Use the dynamic programming approach to write an algorithm to find the maximum sum in any contiguous sub list of a given list of n real values. Analyze your algorithm, and show the results using order notation.
2. Let us consider two sequences of characters S1 and S2. For example, we could have S1 = A$CMA*MN and S2 = AXMC4ANB. Assuming that a subsequence of a sequence can be constructed by deleting any number of characters from any positions, use the dynamic programming approach to create an algorithm that finds the longest common subsequence of S1 and S2. This algorithm returns the maximum-length common subsequence of each sequence.