Please help me quickly ExerciseThe longest palindromic subsequence problem is a classic variation of the Longest CommonSubsequence (LCS) problem. The idea is to find LCS of the given string with its reverse, i.e., call LCS(X,reverse(X)) and the longest common subsequence will be the longest palindromic subsequence.1- We consider the sequence X = ABBDCACB. Apply the appropriate dynamic programmingalgorithm to compute the longest palindrome sequence and it is length. You must show all thecomputing steps.Exercise 2Find an optimal solution for the knapsack instance n (number of objects) -7 and W (total weight) -15, insuch a way that the total weight is less than or equal to a given limit and the total profit value is aslarge as possible. Profits and weights of each object are as follows(p1, p2p7)(10, 5, 15, 7, 6, 18, 3)(w1, w2.........w7) = (2,3,5,7,6,4,1)

Exercise:To solve the Longest Palindromic Subsequence (LPS) problem for the given sequence X =…

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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Given two strings A[1...n] and B[1..m], such that n >= m, propose an al- gorithm to find the number of distinct subsequences that can be formed from A such that they are identical to B. = caaat and B = cat, then the answer is 3, since the For example, let A subsequences ca.t, c_a_t, and cat are identical to B.
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Show that the problem L (M) contains any string that contains at least 3 consecutive a’s is undecidable.
Let M be the language of all binary strings that contain the substring 11 and whose number of 0’s is even. (For example, 0101100 is in M.) (a) Give a largest possible set of strings that are pairwise distinguishable with respect to M. (b) Give a largest possible set of strings that are pairwise indistinguishable with respect to M.
4. Show that it is undecidable if every string in the langauge of a TM has even length.
Construct a recurrence and appropriate initial conditions for the number of strings of English letters of length n, n ≥ 0, which follow the rule that whenever ‘a’ is in the string, the letter ‘b’ follows immediately. Briefly explain your recurrence.
Consider the set of strings on {0, 1} defined by the requirements below. For each, construct an accepting dfa. (1) Every substring of four symbols has, at most, two 0’s. For example, 001110 and 011001 are in the language, but 10010 is not because one of its substrings, 0010, contains three zeros. no hand written
Please do question 6 (it is in the photo) with python coding.
A cyclic permutation of a string takes the string and shifts each letter forward by a constant amount k, with letters that shift off the end of the string coming back in at the front. For instance, the cyclic permutations of the string ABCDEF are FABCDE, EFABCD, DEFABC, CDEFAB, BCDEFA, and ABCDEF itself. A reverse cyclic permutation is the reverse of a cyclic permutation; for instance ABCDEF has the reverse cyclic permutation DCBAFE amongst others. Given two strings S and S", provide a linear time algorithm to decide whether S is a reverse cyclic permutation of S'.
Let E = {0,1} and La be the language of all strings that represent binary numbers that are not divisible by 4. L, be the language of all strings that end with 0. d) We know that La and L, are both regular. But what about their complements, La and L,? Justify your answer. e) Show that (L. n L,), the intersection between La and Lp, is also a regular language.
A substring of a string is a contiguous sequence of characters from the string. For example, BC is a substringof ABCD which starts from the second character of ABCD. Another example, ABC is a substring of ABCD whichstarts from the first character of ABCD. Note that ABCD itself is also a substring of ABCD.In this problem, we define a special substring as a non-empty substring that contains only the same character.For example, B and CC are special substrings of ABBCCC, while ABBC and BC are not special substrings.You are given a string S of length N and an integer K. Your task is to determine the minimum number ofcharacters of S that need to be changed such that there exists a special substring of length K in S.For example, let N = 6, K = 4, and S = ABBCCC. In this example, we only need to change the third characterof S to C (i.e. ABBCCC → ABCCCC) so that we have a special substring CCCC of length 4.InputInput begins with a line containing two integers: N K (1 ≤ K ≤ N ≤ 100 000)…
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