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Questions tagged [strings]

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Questions about sequences of symbols, sets thereof and their properties as well as uses.

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33 views

How can I prove that the empty string is the identity element with regards to the operation of concatenation?

Let $w$ be a string over an alphabet $\Sigma$. It is obvious that $w \circ \epsilon = \epsilon \circ w = w$. However I'm having a hard time coming up with a proof for that (which I assume should be ...
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1answer
30 views

Sum of squares of length of longest common prefix for all pairs in given strings

Given a list of unique strings, how can I find the sum of squares of longest common prefixes length for all pairs? I think a trie will be useful but I'm not sure how to calculate the final result. For ...
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1answer
37 views

please help me understand the algorithm for building the KMP failure function

I am struggling to grasp the algorithm for building the KMP failure function. The bulk of what is making my understanding incomplete concerns the line ...
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1answer
71 views

What is the optimal solution for the following “Largest lexicographical string with <= K consecutive elements” problem? Why is my answer wrong?

This is a simple question I ran into in a remote interview: Given a collection of letters, permute them (or one of its subset) into a string such that: each letter can only be repeated for <= 11 ...
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1answer
33 views

Z-function and the minimum string period

Let $s$ be a string of length $n$. One of the classical solutions to the problem of finding the smallest period $p$ of $s$ (that is, smallest $p$ such that $s$ can be obtained as a concatenation of ...
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question about common prefix of Strings

we are given n Strings of total Length K and also we have m queries about these strings. each query, contains 2 index ( for example a , b ) and then we should calculate the length of longest common ...
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76 views

Remove a subsequence from a string and append it at the end

Consider the following operation on strings: pick a (not necessarily contiguous) subsequence, remove it and then append all the characters in the same order at the end. This operation preserves the ...
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1answer
23 views

List the lengths of all the prefix-suffixes in $O(n^{1+\epsilon})$ time

A proper prefix of a string $s$ that is also equal to a suffix of $s$ is called a PS (prefix-suffix). Given a string $s$ of length $n$ is there an algorithm listing the lengths of all the PSs in $O(n^{...
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1answer
41 views

Number of subsequence with k distinct characters

"A string is a subsequence of a given string, that is generated by deleting some(possibly zero) character of a given string without changing its order." Suppose we have string s="aabca&...
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1answer
24 views

Proving $S=SL\implies S=\emptyset$

Let $L\subseteq \Sigma^*$ such that $\{\epsilon\}\not\in L$. Then for any $S\subseteq \Sigma^*, S=SL\implies S=\emptyset$. So we suppose $S=SL$ and $S\ne\emptyset$. Then $\exists w\in S$ such that $...
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20 views

How to find the LCP of string pairs in a set

I have a set of $k$ strings of $n$ length each. I need an algorithmic strategy that finds the LCP (Longest Common Prefix) of each set's string pair. In addition, I need time complexity $O(k*n+a)$, ...
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1answer
19 views

Finding which strings in a set of strings have a certain prefix - can it be smaller than O(number of strings*length of prefix)

If I have a set of words and need to return which of them start with a certain prefix, can that complexity be less than O(n*d), where n is the number of words and d is the prefix. I'm asking because ...
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0answers
47 views

Longest palindrome after swapping operation

I know that Manacher's algorithm can be used to find the longest palindromic substring of a string in linear time. But I want to find the longest palindromic substring after swapping any two indices ...
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106 views

Can a Turing machine start on a blank?

Couldn't find a definitive answer anywhere so asking here. I have a Turing machine and the start state can go straight to the end state without passing through any of the other five states via Blank -...
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1answer
174 views

calculating the string similarity of an optimal alignment

description of the algorithms behavior I have two strings s1 and s2, with $len\_s1 <= len\_s2$. I would like to find the ...
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1answer
124 views

Number of substrings possible with even characters

Consider a string 'ABBAA' Possible substrings with even number of characters are $4$ 'ABBA' : Count of 'A' is even and 'B' is even 'AA' : Count of 'A' is even and 'B' is even - ($0$) Similarly 'BB' ...
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1answer
67 views

Las Vegas algorithm for finding 00000 in bit string

Problem 1: Consider the following problem: given a binary string $w=a_1a_2\cdots a_n \in\{0,1\}^*$, decide whether $w$ contains 00000 as a substring (i.e., where $w$ contains five consecutive 0's). ...
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1answer
57 views

Let $\Sigma = \{a, b\}$ and $L = \{aa, bb\}$. Use set notation to describe $\overline L$

Let $\Sigma = \{a, b\}$ and $L = \{aa, bb\}$. Use set notation to describe $\overline L$. This is exercise 6 (page 28) from "An Introduction to Formal Languages and Automata" by Peter Linz. ...
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1answer
56 views

Prove that $(uv)^R = v^Ru^R$

The reverse of a string, introduced informally above, can be defined more precisely by the recursive rules $$a^R=a,$$ $$(wa)^R=aw^R,$$ for all $a \in \Sigma$, $w \in \Sigma^*$. Use this to prove that $...
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2answers
41 views

Find the maximum number of contiguous occurrences of smaller string s in a larger string l

Say we have two strings s and l, and they only have characters 'a' through 'z' (lowercase English alphabet characters). The task is to find the maximum number of consecutive occurrences of s in l. Ex. ...
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1answer
35 views

Families of sets indexed by another set

I am reading Automata and Computability by Dexter C. Kozen and I am in the first chapter entitled Strings and Sets. If we have a set $A=\{ab,b\}$ do we get to assume that the null string $\epsilon$ is ...
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1answer
16 views

Sorting in computing longest increasing subsequence

I am currently reading the paper On computing the length of longest increasing subsequences by Michael L. Fredman. I'm struggling to understand parts of the proof of Theorem 3.5, especially this bit: ...
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1answer
59 views

Can't wrap my head around on building a suffix table for Boyer Moore

My resources were the following video, as well as this video. Basically, in one of the videos they state that the good suffix table for the pattern "ABCBAB" is the following: k suffix d2 1 ...
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1answer
19 views

Replacement of a substring with another substring in a string

I apologize if this is not the right stackexchange for this question. I was playing around with the Python programming language, when I discovered something strange. It concerns replacing a substring ...
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2answers
128 views

What is the simplest algorithm to compress a string?

I need to compress a string in my application but I am very limited in the operations I can perform. In particular, I cannot store data in any file and I cannot query any database. Also, I cannot call ...
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2answers
103 views

Time complexity of comparing $N$ strings

I would like to double check myself. As I understand time complexity of comparing two strings in the worst case is $O(n)$, where $n$ is the length of the strings (let's say they are equal length). In ...
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1answer
56 views

Is string spliting formally defined when the string delimiter is an empty string?

Depending on the API/language you use, splitting the string "ABCD" using "" as a delimiter gets you: ...
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Find optimal alignment between 2 strings with gap cost function

I have a homework question that I trying to solve for many hours without success, maybe someone can guide me to the right way of thinking about it. The problem: Given two strings S1 and S2, find the ...
2
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1answer
173 views

Find optimal local alignment of two strings with restrictions

I have a homework question that I trying to solve for many hours without success, maybe someone can guide me to the right way of thinking about it. The problem: We want to find an optimal local ...
2
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1answer
48 views

What is the SetHorspool string searching algorithm and how is it implemented?

What is the SetHorspool string searching algorithm with pseudo-code so it can be easily implemented in a language of choice? This has been implemented in 2 libraries I have come across: https://app-...
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0answers
85 views

Boyer-Moore jump table

I have a pattern $P$ of length $m$, i.e. $P = p_0, p_1, \ldots, p_{m-1}$ which I want to build a simple jump table for (not considering special optimizing cases for now). I only want to build a jump ...
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0answers
22 views

How many strings of length |w| are unrelated?

For sufficiently large |w|, how many of the 2^|w| strings of length |w| are entirely unrelated? A way to define this: two strings are unrelated if their joint Kolomogorov complexity is practically ...
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1answer
59 views

Why is KMP preprocessing O(N)?

My intuition tells me that there is <=1 increase in lps for each increase in the index. Can someone make a better argument why this is O(N)? My confusion arises from ...
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0answers
19 views

Given start strings, find simplest DAG that constructs target strings by concatenation

Say we have a number of start strings (green) and a number of target strings (red). Two strings can always be concatenated to a new string which can then be arbitrarily often reused (two arrows in, (1,...
2
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1answer
47 views

Algorithm for cyclic $n$-string Hamming distance with constant sized language $\Sigma$

Suppose we are given a language $\Sigma$ where, suppose, $|\Sigma| = O(1)$. Consider two fixed strings $A, B \in \Sigma^n$. Define the Hamming metric between these strings as $$d_{H}(A,B) = \sum_{i=1}^...
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0answers
41 views

String membership in hash set time complexity

Given a string s and a hashset of strings words, what is the time complexity of the operation: ...
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0answers
12 views

What is the currently know fastest algorithms to convert each individual Java primitive and Number types to a Char Array/String

What is the currently know fastest algorithms to convert each individual Java primitive and Number types to a Char Array/String number representation while ...
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0answers
26 views

Filtering Messages

I saw this question posted and can't seem to find it for some reason, so I'm posting it again. There's a leetcode problem that's asking for the number of possible strings that are alphabetically ...
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1answer
78 views

$\omega$-string avoiding a set of substrings

Given a set of strings $S$ over $\{a,b\}$. How to determine whether there is an infinite sequence consisting of ${a, b}$ (i.e., a $\omega$-string), which doesn't have any string in $S$ as a substring? ...
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1answer
20 views

which neural network is good for predecting the value of strings

I have a dataset that contains some strings. A numeric value is assigned to each string. I want to develop a machine learning (deep learning) model to get a string and predict its value. What neural ...
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1answer
22 views

In a set of sentences, how could I determine the fewest sentences that contains all characters?

So, for the sake of simplicity, I am going to use English characters for this example. Let's say I have a set of strings of characters in English ranked by difficulty: Easy, Intermediate, Advanced. So ...
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2answers
23 views

string concatenation vs language concatenation

What exactly is the difference between $$ C = \{a^*\}\{b\}\{a^*\}\{b\}\{a^*\}\{b\} $$ and $$ D = \{a^nba^nba^nb | n \geq 0 \} $$ It is known that D is non-regular and C is regular, but I am not sure ...
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2answers
46 views

A silly doubt on Computer Science Objects: Arrays, Lists, Strings, and Vectors, are they the same concept?

First of all I'm a Physics Student and I've been arguing with my brother concerning the usage and the fundamental meaning of a vector on Computer Science (CS). I) Vectors A vector have a axiomatic ...
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1answer
26 views

How do you prove these string/number radix encoding/decoding algorithms work?

A while back I learned of these great algorithms: ...
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0answers
43 views

Finding first occurence of all possible matches?

Say you have multiple strings that you're trying to match in a text. And it's possible all these strings have a match in the text. Is there a good way to return out of all the matching strings the ...
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1answer
89 views

Binary string satisfying several constraints

I'm trying to solve this problem, but without success. Problem: You're given a binary string where some of the bits are replaced by ?. You're also given several ...
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1answer
89 views

Minimum number of given operations in order to group letters in a string

Description Suppose we have a string containing letters 'A', 'B', 'C', 'D', and the characters are placed in a stack. We also have an empty stack. Ultimately, we want all of the same letters to be ...
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2answers
98 views

If we want to map abbreviations of full-English words (e.g. map “Jan” to “January”), how can we identify abbreviations which map to multiple words?

Short Version: How can we construct a trie which maps abbreviations of names-of-the-month to full-month (we map the abbreviation "mar" to "march")? The set of all abbreviations is ...
2
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1answer
64 views

Is there a way to determine whether a list of integers can be a prefix function?

Say you had (0,0,0,1,2,3,4,5,6,7,8,9,10) or (0,1,0,1,0,1,2,3,0,1,0,0,1) Could you use, for example, the KMP algorithm to deduce the validity of the above lists as prefix functions? I know there is a ...

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