Exercise 3. DYNAMIC PROGRAMMING. Consider two arrays of nonnegative integers, A = {a¡ :1<i< n} and B = {b₁ : 1≤ i ≤m}. We call a sequence ( from A special if ie+1 ≥ ie + 2 for all between 1 and k-1. Let a = (aia) and b = (bj₁) bj) be special sequences from A and B, respectively. Define the inner product Design a dynamic programming algorithm that returns the maximal inner product between all possible pairs of special sequences of equal length, where the length is not specified. For your algorithm, also report the RAM model time complexity. An example: if A = [3, 5, 2, 2, 7, 4] and B = [3,4,1,6], then the maximal inner product is 62, obtained by using the special sequences (5, 7) and (4, 6).

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