knuth-morris-pratt

Find the smallest period of input string in O(n)?

由 大兔子大兔子 提交于 2019-12-18 12:36:10
问题 Given the following problem : Definition : Let S be a string over alphabet Σ . S' is the smallest period of S if S' is the smallest string such that : S = (S')^k (S'') , where S'' is a prefix of S . If no such S' exists , then S is not periodic . Example : S = abcabcabcabca . Then abcabc is a period since S = abcabc abcabc a , but the smallest period is abc since S = abc abc abc abc a . Give an algorithm to find the smallest period of input string S or declare that S is not periodic. Hint :

What is the performance of KMP if the prefix table is all zero?

由 走远了吗. 提交于 2019-12-11 04:18:06
问题 If my pattern is "Brudasca", then the KMP prefix table will be all zeroed out. In that case, is there any performance difference between KMP and the trivial solution? And would not this be worst case of O(n*m)? 回答1: This is the best case for KMP algorithm. Let's look at the failure/prefix function of KMP (KMP-search has similar logics): int curLen = 0; for (int i = 1; i < len; ++i) { while (curLen > 0 && s[curLen] != s[i]) curLen = prefixFunc[curLen - 1]; if (s[curLen] == s[i]) ++curLen;

Understanding the Knuth Morris Pratt(KMP) Failure Function

由 浪尽此生 提交于 2019-12-09 23:37:13
问题 I've been reading the Wikipedia article about the Knuth-Morris-Pratt algorithm and I'm confused about how the values are found in the jump/partial match table. i | 0 1 2 3 4 5 6 W[i] | A B C D A B D T[i] | -1 0 0 0 0 1 2 If someone can more clearly explain the shortcut rule because the sentence "let us say that we discovered a proper suffix which is a proper prefix and ending at W[2] with length 2 (the maximum possible)" is confusing. If the proper suffix ends at W[2] wouldn't it be size of 3

What's the worst case complexity for KMP when the goal is to find all occurrences of a certain string?

由 假装没事ソ 提交于 2019-12-09 18:03:17
问题 I would also like to know which algorithm has the worst case complexity of all for finding all occurrences of a string in another. Seems like Boyer–Moore's algorithm has a linear time complexity. 回答1: The KMP algorithm has linear complexity for finding all occurrences of a pattern in a string, like the Boyer-Moore algorithm¹. If you try to find a pattern like "aaaaaa" in a string like "aaaaaaaaa", once you have the first complete match, aaaaaaaaa aaaaaa aaaaaa ^ the border table contains the

“Partial match” table (aka “failure function”) in KMP (on wikipedia)

由 倾然丶 夕夏残阳落幕 提交于 2019-12-06 12:11:33
I'm reading the KMP algorithm on wikipedia. There is one line of code in the "Description of pseudocode for the table-building algorithm" section that confuses me: let cnd ← T[cnd] It has a comment: (second case: it doesn't, but we can fall back) , I know we can fall back, but why T[cnd], is there a reason? Because it really confuses me. Here is the complete pseudocode fot the table-building algorithm: algorithm kmp_table: input: an array of characters, W (the word to be analyzed) an array of integers, T (the table to be filled) output: nothing (but during operation, it populates the table)

How does the Failure function used in KMP algorithm work?

由 人盡茶涼 提交于 2019-12-05 10:33:01
I've tried my best reading most of the literature on this, and still haven't understood anything about how the failure function used in KMP algorithm is constructed. I've been referring mostly to http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=stringSearching tutorial which most of the people consider excellent. However, I still have not understood it. I'd be thankful if you could take the pain of giving me a simpler and easy to understand explanation on it. Dominik Gleich The failure function actually tells us this: if you matched X characters of a string, what is the longest

Knuth-Morris-Pratt Fail table

由 人走茶凉 提交于 2019-12-05 08:10:43
问题 I am studying for an exam I have and I am looking over the Knuth-Morris-Pratt algorithm. What is going to be on the exam is the Fail table and DFA construction. I understand DFA construction, but I don't really understand how to make the fail table. If I have an example of a pattern "abababc" how do I build a fail table from this? The solution is: Fail table: 0 1 2 3 4 5 6 7 0 0 0 1 2 3 4 0 but how do I get that? No code just an explanation of how to get that is necessary. 回答1: The value of

When to use Rabin-Karp or KMP algorithms?

由 …衆ロ難τιáo~ 提交于 2019-12-04 08:19:27
问题 I have generated an string using the following alphabet. {A,C,G,T} . And my string contains more than 10000 characters. I'm searching the following patterns in it. ATGGA TGGAC CCGT I have asked to use a string matching algorithm which has O(m+n) running time. m = pattern length n = text length Both KMP and Rabin-Karp algorithms have this running time. What is the most suitable algorithm (between Rabin-Carp and KMP) in this situation? 回答1: When you want to search for multiple patterns,

Knuth-Morris-Pratt algorithm in Haskell

由 笑着哭i 提交于 2019-12-04 01:43:08
I have a trouble with understanding this implementation of the Knuth-Morris-Pratt algorithm in Haskell. http://twanvl.nl/blog/haskell/Knuth-Morris-Pratt-in-Haskell In particular I don't understand the construction of the automaton. I know that it uses the "Tying the Knot" method to construct it, but it isn't clear to me and I also don't know why it should have the right complexity. Another thing I would like to know is whether you think that this implementation could be easily generalized to implement the Aho-Corasick algorithm. Thanks for your answers! So here's the algorithm: makeTable :: Eq

Knuth-Morris-Pratt Fail table

由 懵懂的女人 提交于 2019-12-03 21:14:02
I am studying for an exam I have and I am looking over the Knuth-Morris-Pratt algorithm. What is going to be on the exam is the Fail table and DFA construction. I understand DFA construction, but I don't really understand how to make the fail table. If I have an example of a pattern "abababc" how do I build a fail table from this? The solution is: Fail table: 0 1 2 3 4 5 6 7 0 0 0 1 2 3 4 0 but how do I get that? No code just an explanation of how to get that is necessary. The value of cell i in the fail table for string s is defined as follows: take the substring of s that ends at position i
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