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 32.2, Problem 2E
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To explain how to extend the Robin-Karp method to the problem of searching a text string for an occurrence of any one of a given set of k patterns.
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We 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?
Write an algorithm for addressing the subset-superset problem in string matching. That is, search a text with several strings, some of which are factors of others. do not return any strings that are factors of other test strings found in text (b) Repeat with text consisting of 100 appended copies of and the test items
Suppose you have a string with length 1000 and you want to find all occurrences of a certain substring using the Knuth-Morris-Pratt algorithm. What is the time complexity of this operation?
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- Develop and implement an ADT for preprocessing a string to support efficiently answering queries of the form How many times does a given k-gram appear ? Each query should take time proportional to k log N in the worst case, where N is the length of the string.arrow_forwardHow would you modify the Rabin-Karp algorithm to determine whether any ofa subset of k patterns (say, all of the same length) is in the text?arrow_forwardGiven an input string (s) and a pattern (p), implement wildcard pattern matching with support for '?' and '*' where: '?' Matches any single character. '*' Matches any sequence of characters (including the empty sequence). The matching should cover the entire input string (not partial). Example 1: Input: s = "aa", p = "a" Output: false Explanation: "a" does not match the entire string "aa". Example 2: Input: s = "aa", p = "*" Output: true Explanation: '*' matches any sequence. Example 3: Input: s = "cb", p = "?a" Output: false Explanation: '?' matches 'c', but the second letter is 'a', which does not match 'b'. Constraints: 0 <= s.length, p.length <= 2000 s contains only lowercase English letters. p contains only lowercase English letters, '?' or '*'. In c# pleasearrow_forward
- If Σ is an alphabet, how many strings are there over Σ? How many string of at most lengthk are there over Σ?arrow_forwardDo any implementations of the Boyer-Moore string search method already exist? Give details on what will be done to make the concept a reality.arrow_forwardGiven 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_forward
- If the sequence number space is large enough to include k bits of information, you should carefully consider employing both the selective-repeat technique and the Go-Back-N strategy while searching for a solution. What is the biggest size that the sender window that we are allowed to use may be in total?arrow_forwardWhen trying to find a solution, you should give serious attention to employing both the selective-repeat technique and the Go-Back-N strategy if the sequence number space is wide enough to incorporate k bits of information. If the sequence number space is not big enough, you should not even bother trying to find a solution. In its whole, what is the maximum size that the sender window that we are allowed to use is authorised to be allowed to be?arrow_forwardDesign a method to find the frequency of occurrences of any given word in abook. What if we were running this algorithm multiple times?arrow_forward
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