Homework Assignment: Dynamic Programming Task: Review the article Dynamic Programming Patterns and complete three problems from the lists mentioned in the article. For each problem, provide both a recursive formulation of the problem and a non-recursive memoized version using dynamic programming loops. Submission: Please submit your homework in the following format: a. [20 points each problem] Recursive Formulation: Describe the recursive function, including the base case and recursive case. Include any relevant pseudocode or code snippets. b. [13.33 points each problem] Non-Recursive Memoized Version (Dynamic Programming Looped Version): Problem 1: Merging Intervals Pattern Review the Merging Intervals pattern from the article. Choose a problem from this pattern on LeetCode, solve it, and provide the recursive and dynamic programming versions. Problem 2: Decision Making Pattern Review the Decision-Making pattern from the article. Choose a problem from this pattern on LeetCode, solve it, and provide the recursive and dynamic programming versions. Problem 3: DP on Strings Provide the dynamic programming solution using loops. Include code and explain the algorithm and data structures used. Review the DP on Strings pattern from the article. Choose a problem from this pattern on LeetCode, solve it, and provide the recursive and dynamic programming versions. Grading: Your homework will be evaluated based on the correctness of your solutions, the clarity of your explanations, and the quality of your code. https://leetcode.com/discuss/general-discussion/458695/Dynamic-Programming-Patterns