Some positive integers are arranged in a triangle with $$ numbers in its base like the one shown in the figure below for $=4.$ The problem is to find the smallest sum in a descent from the triangle apex to its base through a sequence of adjacent numbers $($shown in the figure by the circles$).$ Design a dynamic programming algorithm for this problem and indicate its time efficiency. Your solution should be general and not just for this example. It should be applicable to any triangle of any size.