Let A = {a1, a2, ..., an} and be a set of n positive integer and let T be another integer. Design a dynamic programming algorithm that determines whether there exists a subset of A whose total sum is exactly T. Analyze the time complexity of your solution. For instance, if A = 4, 5, 17, 23, 11, 2 and T = 35 the algorithm should return True because the subset 5, 17, 11, 2 sums to 35. For the same set of numbers if we choose T = 31 the problem has no solution, and the algorithm will return False. When designing the dynamic programming algorithm, please describe the size and dimensionality of the dynamic programming table, and explicitly formulate the recurrence relationship.

Let A = {a1, a2, ..., an} and be a set of n positive integer and let T be another integer. Design a dynamic programming algorithm that determines whether there exists a subset of A whose total sum is exactly T. Analyze the time complexity of your solution. For instance, if A = 4, 5, 17, 23, 11, 2 and T = 35 the algorithm should return True because the subset 5, 17, 11, 2 sums to 35. For the same set of numbers if we choose T = 31 the problem has no solution, and the algorithm will return False. When designing the dynamic programming algorithm, please describe the size and dimensionality of the dynamic programming table, and explicitly formulate the recurrence relationship.