(3 points) suppose that we have a sequence a1, a2, . . , an that we wish to memorize. we memorize it by computing partial sums of the forms ai + . . + aj . let us say that the cost of memorizing a particular integer a is |a|. the goal is to use the minimum cost to remember the partial sums so that we can reconstruct the original sequence. for example, if (a1, a2, a3, a4) = (1, −3, 2, 4), one of the possible solution is to memorize: • a1 = 1 • a2 + a3 = −1 • a2 + a3 + a4 = 3 • a3 = 2 the total cost is |1| + | − 1| + |3| + |2| = 7, and a1, a2, a3, a4 can be reconstructed by using gaussian elimination from the information memorized. note that the minimum cost to memorize the sequence above is 6. give an algorithm that computes the minimum cost to memorize a sequence a1, a2, . . , an. the running time of the algorithm should be polynomial in n. (hint: