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 32.1, Problem 2E
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Show that the problem L (M) contains any string that contains at least 3 consecutive a’s is undecidable.
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Write a program that implements n-point Lagrange interpolation. Treat n as aninput parameter.
Find a regular expression for the set {a"bm: n > 3,m is even}.
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- Correct answer will be upvoted else downvoted. you can choose any substring of a containing exactly k characters 1 (and arbitrary number of characters 0) and reverse it. Formally, if a=a1a2…an, you can choose any integers l and r (1≤l≤r≤n) such that there are exactly k ones among characters al,al+1,…,ar, and set a to a1a2…al−1arar−1…alar+1ar+2…an. Find a way to make a equal to b using at most 4n reversals of the above kind, or determine that such a way doesn't exist. The number of reversals doesn't have to be minimized. Input Each test contains multiple test cases. The first line contains the number of test cases t (1≤t≤2000). Description of the test cases follows. Each test case consists of three lines. The first line of each test case contains two integers n and k (1≤n≤2000; 0≤k≤n). The second line contains string a of length n. The third line contains string b of the same length. Both strings consist of characters 0 and 1. It is guaranteed that the sum of n over all…arrow_forwardWe consider certain strings of length 6 over the alphabet S = {A,B,C}. We require that the string contains exactly two As, and exactly two B's, and exactly two C's. How many such strings are there? That is, how many strings of length 6 over the alphabet {A,B,C} contains exactly two A's, two B's and two C's?arrow_forwardA string is called "s-palindrome" if it is symmetric about the middle of the string. For example, the string "oHo" is "s-palindrome", but the string "aa" is not. The string "aa" is not "s-palindrome", because the second half of it is not a mirror reflection of the first half. Given a string, determine if it is s-palindrome or not. WRITE PYTHON AND SHOW OUTPUTarrow_forward
- Give a DFA over {a,b} that accepts all strings of length exactly 5 For each state in your automaton, give a brief description of the strings associated with that state.arrow_forwardLeetcide Given two strings A and B, find the minimum number of times A has to be repeated such that B is a substring of it. If no such solution, return -1.For example, with A = "abcd" and B = "cdabcdab".Return 3, because by repeating A three times (“abcdabcdabcd”), B is a substring of it; and B is not a substring of A repeated two times ("abcdabcd").Note:The length of A and B will be between 1 and 10000.Reference: https://leetcode.com/problems/repeated-string-match/description/"""def repeat_string(A, B): count = 1 tmp = A max_count = (len(B) / len(A)) + 1 while not(B in tmp): tmp = tmp + A if (count > max_count): count = -1 break.arrow_forwardLet E={0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 4 symbols, that is, the length of w is at least 4) and (the first symbol of w is different from the last symbol of w) and (interior(w) is vorpal according to the following two definitions)}. For any string y containing at least 4 symbols, let interior (y) be the substring of y obtained by removing the first two symbols and the last two symbols of y. A string x over Σ is called vorpal if x satisfies one or more of the following conditions: • x is made up of exactly k 0-symbols where k modulo 4 is 3 (and no 1-symbols) ● x is made up of at least two 1-symbols (and no 0-symbols) ● x contains 011arrow_forward
- Find all strings in L(ba + ab*a) of length less than four. Find a regular expression for the set { a" bm : n, m are even}.arrow_forwardA digraph, G, is strongly connected, if each cycle in G has even length. True or False?arrow_forwardProve the following argument is valid: Væ [p(x) → (q(x) V r(x)] Væ (r(x) → q(x)] -3x q(x) 3x p(x) ..arrow_forward
- Let E= {0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 2 symbols, that is, the length of w is at least 2) and (the first symbol of w is different from the last symbol of w) and (centre (w) is mimsy according to the following two definitions)}. For any string y containing at least 2 symbols, let centre (y) be the substring of y obtained by removing the first symbol and the last symbol of y. A string x over Σ is called mimsy if x is made up of either • at least two 0-symbols (and no 1-symbols), or • an even number of 1-symbols (and no 0-symbols).arrow_forwardLet E={〈M〉| M is a TM and every string in L(M) has even length}. Argue that the property described in E is not trivial – i.e., that Rice’s theorem applies to E.arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Computer science. inquiry is depicted by a couple of integers li, ri (1≤li<ri≤n). For each question, he needs to decide if there exists a decent aftereffect in s that is equivalent to the substring s[li… ri]. A substring s[i… j] of a string s is the string shaped by characters sisi+1… sj. String an is supposed to be an aftereffect of string b if a can be gotten from b by erasing a few characters without changing the request for the excess characters. An aftereffect is supposed to be acceptable in case it isn't coterminous and has length ≥2. For instance, in the event that s is "1100110", the aftereffects s1s2s4 ("1100110") and s1s5s7 ("1100110") are acceptable, while s1s2s3 ("1100110") isn't acceptable. Would you be able to help Hr0d1y answer each question? Input The primary line of the input contains a solitary integer t (1≤t≤100) — the number of experiments. The portrayal of each experiment is as per the…arrow_forward
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