Given a set S = {a1, a2, ..., an} of positive integers (denoting asset values), Set partitioning requires to partition S into two subsets S1 and S2 that minimizes the difference in the total (asset) values of S1 and S2. Identify a dynamic programming (DP) algorithm for the Set partition problem. Clarify all relevant details, justifying the DP formulation, and analyze your time-complexity. Illustrate the working of your DP algorithm, partitioning this example set S = {10, 6, 4, 4, 4, 3}

The use of phrases, fragments, and punctuation can influence the mood of a passage; keeping this in mind, how would you describe the mood of the followingpassage? "fog on the essex marshes, fog on the kentish heights, fog creeping into the cabooses of collier-brigs; fog lying out on the yards, and hovering in the riggingof great ships; fog drooping on the gunwales of barges and small boats. fog in the eyes and throats of ancient greenwich pensioners, wheezing by thefiresides of their wards; fog in the stem and bowl of the afternoon pipe of the wrathful skipper; fog cruelly pinching the toes and fingers of his shivering little'prentice boy on deck." (5 points)