One important application of the Longest Common Subsequences problem is to compare DNA sequences. consider the following two small DNA sequences: X = TAGTC and Y = AGACT. we use Dynamic programming to find the LCS of X and y.
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One important application of the Longest Common Subsequences problem is to compare DNA sequences. consider the following two small DNA sequences: X = TAGTC and Y = AGACT. we use Dynamic
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- Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) ?[?, ?] = ( ?[? − 1, ?] ?? ?[?, ? − ?? ]) b) ?[?, ?] = ( ?[? − 1, ?] ??? ?[?, ? − ?? ]) c) ?[?, ?] = ( ?[? − 1, ?] ?? ?[? − 1, ? − ?? ]) d) ?[?, ?] = ( ?[? − 1, ?] ??? ?[? − 1, ? − ?? ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) ?[1, ? + 1] b) ?[?, ?] c) ?[?, 0] d) ?[?, ? + 1]Consider a open bucket hash table and closed bucket hash table in which the keys are student identifiers (strings of 6 digits). Assume the following number of buckets and hash function: m = 100; hash(id) = first two digits of id #. Starting with an empty hash table, show the effect of successively adding the following student identifiers: 000014, 990021, 990019, 970036, 000015, 970012, 970023. Use following function as second hash function hash(id) = last digit of id # Show the effect of deleting 000014 from the hash table. (Java Programming DSA)The code of a sequential search function is shown on textbook page 60. In fact, if the list is already sorted, the search can halt when the target is less than a given element in the list. For example, given my_list = [2, 5, 7, 9, 14, 27], if the search target is 6, the search can halt when it reaches 7 because it is impossible for 6 to exist after 7. Define a function linearSearchSorted, which is used to search a sorted list. This function displays the position of the target item if found, or ‘Target not found’ otherwise. It also displays the elements it has visited. To test your function, search for these targets in the list [2, 5, 7, 9, 14, 27]: 2, 6, 14, 27 and 28.
- Consider the LCS problem discussed in class. Suppose we only want to compute the length of the LCS of x[1..m] and y[1..n] (i.e. we do not care about the actual subsequence itself). This means we do not need to “traceback” to find the LCS. In this setting, show how the algorithm can be altered so that it only needs min(m,n) + O(1) space rather than m · n space (note that it must be min(m,n) and not O(min(m, n))).We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) 1) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Doing the corresponding numerical simulations show what happens with the increase of the difference between the frequencies of the two waves and vice versa.a. Propose a data structure that supports the stack push and pop operations and a third operation FindMin, which returns the smallest element in the data structure, all in O(1) worst case time. b. Prove that if we add the fourth operation DeleteMin which finds and removes the smallest element, then at least one of the operations must take Ω(log n) time.
- Note: Your solution should have O(n) time complexity, where n is the number of elements in l, and O(1) additional space complexity, since this is what you would be asked to accomplish in an interview. Given a linked list l, reverse its nodes k at a time and return the modified list. k is a positive integer that is less than or equal to the length of l. If the number of nodes in the linked list is not a multiple of k, then the nodes that are left out at the end should remain as-is. You may not alter the values in the nodes - only the nodes themselves can be changed.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.Professor JAson uses the following algorithm for merging k sorted lists, each having n/k elements. He takes the first list and merges it with the second list using a linear-time algorithm for merging two sorted lists, such as the merging algorithm used in mergesort. Then, he merges the resulting list of 2n/k elements with the third list, merges the list of 3n/k elements that results with the fourth list, and so forth, until he ends up with a single sorted list of all n elements. Analyze the worst-case running time of the professor’s algorithm in terms of n and k.
- The Virtual Weight (VW) of an integer number (which consists of more than 1 digit) is the sumof the individual digits that are composing the number. For example, consider the followingtwo numbers; 5638 and 1145, then the VW of each is calculated as following:VW(5638) = 5+6+3+8 = 22VW(1145) = 1+1+4+5 = 11Then, the VW can be classified as L (mean Low) or H (means High) using a specific cut-offvalue. For example, if the cut-off value is 15, then the VW of the number 5638 is H (High),and the VW of the number 1145 is L because 22 > 15 and 11 ≤ 15 respectivelyWrite a C++ program that: reads a positive integer n (where 5≤n≤20) from the user. If the user enters invalidnumber, then the program should continue prompting until he/she enters a valid numberwithin the specified range. Then, the program should generate n random numbers using the built-in rand()function. Every time a random number is generated, the program will classify that number as Lor H using the above method. Use a…You are given a string X of length n and another string Y of length m ≤n. Say,the indexes p1, p2, p3, p4 and q1, q2, q3, q4 form two sub-sequences, i.e., 0 ≤ p1 < p2 < p3 < p4 < nand 0 ≤q1 < q2 < q3 < q4 < n; then, they are non-overlapping if p4 < q1.The task is to count the maximum number of non-overlapping sub-sequences of X that are thesame as Y . Thus, if X = GAXTYAWBGTAUGBTABGRGTAXB and Y = GTAB, then the answer is3 as shown by the red fonts. We cannot select the underlined GTAB as it overlaps with a red GTAB(i.e., among overlapping sub-sequences, you can select only one of them).Describe an O(m + n) time algorithm to obtain the count. Write a pseudo-code.I'm trying to create a Python program that given a data set, I need to determine parameters r, s so f(a) = r exp(sa) fits the given data set in a least squares sense. A sample data set would look something like a = 1,2,3,4,5 and b = 2,4,6,8,10.