Sequence alignment. When a new gene is discovered, a standard approach to understanding its function is to look through a database of known genes and find close matches. The closeness of two genes is measured by the extent to which they are aligned. To formalize this, think of a gene as being a long string over an alphabet sigma = {A, C, G, T}. Consider two genes (strings) x = ATGCC and y = TACGCA. An alignment of x and y is a way of matching up these two strings by writing them in columns, for instance: - A T - G C C T A - C G C A Here the "-" indicates a "gap." The characters of each string must appear in order, and each column must contain a character from at least one of the strings. The score of an alignment is specified by a scoring matrix delta of size (|sigma| + 1) times (|sigma| + 1), where the extra row and column are to accommodate gaps. For instance, the preceding alignment has the following score: delta (-, T) + delta (A, A) + delta (T, -) + delta (-, C) + delta (G, G) + delta (C, C) + delta (C, A). Give a dynamic programming algorithm that takes as input two strings x [1 ... n] and y [1 ... m] and a scoring matrix delta, and returns the highest-scoring alignment. The running time should be O (mn).

This question involves a class named textfile that represents a text file. public class textfile { private string filename; private string filename; private arraylist words; // constructors not shown // postcondition: returns the number of bytes in this file public int filesize() { } // precondition: 0 < = index < words.size() // postcondition: removes numwords words from the words arraylist beginning at // index. public void deletewords(int index, int numwords) { } // precondition: 0 < = index < = words.size() // postcondition: adds elements from newwords array to words arraylist beginning // at index. pub lic voidaddwords(int index, string[] newwords) { } // other methods not shown } complete the filesize() method. the filesize() is computed in bytes. in a text file, each character in each word counts as one byte. in addition, there is a space in between each word in the words arraylist, and each of those spaces also counts as one byte. for example, suppose the words arraylist stores the following words: { mary had a little lamb; its fleece was white as snow. } the filesize() method would compute 4 + 3 + 1 + 6 + 5 + 4 + 6 + 3 + 5 + 2 + 5 as the sum of the lengths of each string in the arraylist. the value returned would be this sum plus 10, because there would also be 10 spaces in between the 11 words. complete the filesize() method below: // postcondition: returns the number of bytes in this file public int filesize() { }

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In a heat transfer course, we can derive the equation for the temperature distribution in a flat rectangular plate. in this example, we will look at a plate at steadystate with three sides being held at t1, and one side held at t2. the temperature for any location on the plate, t(x,y), can be calculated by where create a function (prob3_5) that will take inputs of vectors x and y in feet, scalar n, scalars l and w in feet and scalars t1 and t2 in degrees fahrenheit. it will output a matrix t which is the temperature of each x and y locations. t will have the number of columns equal to the number of elements in x and rows equal to the number of elements in y. though this can be done without loops (perhaps more efficiently), your program must use a nested loop.