DAT600: Dynamic Programming - Largest Common Subsequence - Engineering Assignment Help

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Dynamic Programming Engineering Assignment Help

Assignment Task: Task-1: Matrix Multiplication The table given below shows the dimensions of five matrices: Matrix Dimension A1 30 x 35 A2 35 x 15 A3 15 x 5 A4 5 x 10 A5 10 x 25 This problem is to find the most expensive way of multiplying the matrices A1 to A5.

• Parenthesize the product A15 such that the total number of scalar multiplications is maximized
• Verify whether your answer for a) is correct by modifying the MATLAB code for “matrix chain multiplication”.

Task-2: Extended Fibonacci Series (Exam Q5, May 2014)A series of number F(n) is generated by the following formula: n=0: F(0) = 0 n=1: F(1) = 1 n=2: F(2) = 2 n>2: F(n) = (F(n-1) * F(n-2)) + (n-3) * F(n-3)

• Propose a divide-and-conquer (DaQ) based recursive algorithm to find F(n).
• Show the “subproblem graph” for the DaQ solution, and determine the time taken in terms of big-O notation.
• Propose a dynamic programming based solution.
• Show the “subproblem graph” for the dynamic programming based solution; determine the time taken in terms of big-O notation.

Task-3: LCS (Exam Q2, Feb 2012)This problem is about finding the Largest-Common-Subsequence (LCS) between two sequences of alphabets (you may take subsequences as text substrings).

• For finding LCS, explain why dynamic programming is efficient.
• Explain the steps involved in developing an algorithm based on dynamic programming.
• Using the sequences “CACAQ” and “CADACA” show how the dynamic programming based algorithm for LCS works (it is suffice to show the tables).

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