Question 5. In the previous question, suppose different books might have different heights and we have the freedom to adjust the height of each shelf to that of the tallest book on the shelf. Redefine the cost of a book placement plan to be the sum of the heights of the tallest book on each shelf. Give a dynamic programming algorithm for finding a book placement plan that minimizes the new cost. The algorithm should compute not only the cost of the optimal book placement plan, but also the plan itself. Analyze the time complexity of the algorithm. (25') Question 5. In the previous question, suppose different books might have different heights and we have the freedom to adjust the height of each shelf to that of the tallest book on the shelf. Redefine the cost of a book placement plan to be the sum of the heights of the tallest book on each shelf. Give a dynamic programming algorithm for finding a book placement plan that minimizes the new cost. The algorithm should compute not only the cost of the optimal book placement plan, but also the plan itself. Analyze the time complexity of the algorithm. (25')