Given an array P[1..n] where Pi represents the price of a stock on day i, find the length of the longest rising trend. A rising trend is a subsequence of days, beginning on day 1 and not necessarily contiguous, where the price of the stock strictly increases. 1. (7 marks) Given P, define a recurrence relation for L; which denotes the longest rising trend that begins on day j. 2. Using this recurrence, implement and test a dynamic programming algorithm that: (a) (10 marks) Finds the longest rising trend. (b) (5 marks) Describes the optimal solution. 3. (3 marks) State the order of complexity of your algorithm