Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 15.4, Problem 2E
Program Plan Intro

To writes the pseudo-code of reconstructing an LCS from the completed c table for the original sequence X and Y .

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Make a MATLAB code and than use an for-end loop to produce a vector that stores values for y(x) using the equation :  y(x) = -3( - 0.1x2 + 5x + 4) Use these for-loop structure: x = 1.8 : 0.3 : 4.5 ; for n = 1 : length(x) y(n) = ... (Hint: Express the polynomial in terms of x(n)) ... end   Then plot the resulting curve as (x,y).
Two DNA strands of length 100 (number of bases in the sequence) are given in DNA1.txt and DNA2.txt file.  Solve the LCS problem using dynamic programming top-down (memorization) approach. Submit your code to solve the problem. How much time (in seconds or milliseconds) is required by your computer to run the algorithm.
Let us define a sequence parity function as a function that takes in a sequence of binary inputs and returns a sequence indicating the number of 1’s in the input so far; specifically, if at time t the 1’s in the input so far is even it returns 1, and 0 if it is odd. For example, given input sequence [0, 1, 0, 1, 1, 0], the parity sequence is [0, 0, 0, 1, 0, 0]. Implement the minimal vanilla recurrent neural network to learn the parity function. Explain your rationale using a state transition diagram and parameters of the network.
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