## Shortest substring problem

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Code Review Stack Exchange is a question and answer site for peer programmer code reviews. It only takes a minute to sign up. I'm working on a problem to find wholly repeated shortest substring of a given string, and if no match, return length of the string. My major idea is using a Trie tree to build substrings from length 1 to half length of the whole string, then traverse the Trie tree to find if there is a wholly repetitive match or not since when I build Trie tree, I record the depth of leaf node and also how many times the leaf node has been reached.

You don't need a trie? Just keep the 'shortest repeating current substring' Which would end up being O n. The idea is simple: for each chararcter try to match it to the current shorterst string. You will need a pointer to the current character, and one to the current character in the shortest string. Both start at the first character.

The shortest string will be that character. Each time you move to the next character in the main string, try also to move the in current shortest string. If the shortest string is exhausted, i. While the characters match, keep going.

If the characters do not match, we had a wrong shortest substring and re-initialize it to be the all the characters that we have visited in the main string. Then, reset the pointer in the current shortest string to it's begin and continue.

I'm not from algorithmic background. Thanks for introducing the trie graph with this question. Below are my comments:. This is a variation perhaps improvement of my earlier answer. Here, we can construct the tree and then obtain relevant tree information via its various methods.

The output from running it is shown at the end. Sign up to join this community. The best answers are voted up and rise to the top.Given a set of n strings arr[], find the smallest string that contains each string in the given set as substring.

We may assume that no string in arr[] is substring of another string. A solution that always finds shortest superstring takes exponential time. Below is an Approximate Greedy algorithm. Two strings are overlapping if prefix of one string is same suffix of other string or vice verse. The maximum overlap mean length of the matching prefix and suffix is maximum.

Below is the implementation of above algorithm.

Performance of above algorithm: The above Greedy Algorithm is proved to be 4 approximate i. This algorithm is conjectured to 2 approximate nobody has found case where it generates more than twice the worst. There exist better approximate algorithms for this problem.

Please use ide. Let arr[] be given set of strings. Copy contents of arr[] to temp[] 2 While temp[] contains more than one strings a Find the most overlapping string pair in temp[]. Let this pair be 'a' and 'b'. Working of above Algorithm:. Improved By : sanjeev Load Comments. We use cookies to ensure you have the best browsing experience on our website.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I try to write I program that given a string comprised of lowercase lettes in the range ascii[a-z] and determine the length of the smallest substring that contains all of the letters present on the string. We first traverse the string to find out how many distinct characters are in it.

After this, we initialize two pointers denoting the left and right index of the substring to 0. We also keep an array counting the number of each character currently present in the substring. If not all characters are contained, we increase the right pointer in order to get another character. If all characters are contained, we increase the left pointer in order to possibly get a smaller substring.

Since either the left or right pointer increase at each step, this algorithm should run in O n time. For inspiration for this algorithm, see Kadane's algorithm for the maximum subarray problem.

Unfortunately, I do not know C. However, I have written a Java solution which hopefully has similar syntax. I haven't stress tested this rigorously so it's possible I missed an edge case. This is not ideal; however, we can do several things to avoid testing sub-strings that cannot be valid candidates. I suggest to return the sub-string itself, instead of its length.

This helps to validate the result. We begin by counting the occurrence of each character in the range ['a'. We can subtract 'a' from a character to get its zero-based index. To count the number of distinct characters in the sub-string, we need the following Boolean array:. Now, let's test sub-strings starting at different positions.

The maximum start position must allow sub-strings at least as long as the totalDistinctCharCount the shortest possible sub-string. Inside this loop we have another loop counting the distinct characters of the sub-string. Note that we work directly on the input string to avoid creating a lot of new strings. We only need to test sub-strings that are shorter than any shortest one found before. Therefore the inner loop uses Math. Min input. Length - 1 as limit. Content of loop in place of theIn computer sciencethe longest common substring problem is to find the longest string or strings that is a substring or are substrings of two or more strings.

A generalization is the k-common substring problem. The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The nodes representing "A", "B", "AB" and "BA" all have descendant leaves from all of the strings, numbered 0, 1 and 2. The following pseudocode finds the set of longest common substrings between two strings with dynamic programming:.

The variable z is used to hold the length of the longest common substring found so far. The set ret is used to hold the set of strings which are of length z. Thus all the longest common substrings would be, for each i in retS[ ret[i]-z. From Wikipedia, the free encyclopedia. Aho—Corasick Commentz-Walter algorithm. Comparison of regular-expression engines Regular grammar Thompson's construction Nondeterministic finite automaton. Hirschberg's algorithm Needleman—Wunsch algorithm Smith—Waterman algorithm.

Parsing Pattern matching Compressed pattern matching Longest common subsequence Longest common substring Sequential pattern mining Sorting. Categories : Problems on strings Dynamic programming.

1092. Shortest Common Supersequence (Leetcode Hard)

Hidden categories: Articles with example pseudocode. Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. The Wikibook Algorithm implementation has a page on the topic of: Longest common substring.You are given a string and a set of characters. Your task is to return any shortest substring that contains all the characters in the set.

The only possible answer is as illustrated in the following diagram. The input consists of one or more cases. Each case consists of two strings, each one on a separate line. The first string is the string where you will search for a shortest substring. The second string indicates the characters in the set.

The input is terminated by EOF. The following is a sample input file.

For each input case, print on a single line a shortest substring or the empty string. The following is the output file that corresponds to the sample input file. Given an input pair of set and string, the structure of the string consists of solutions, candidate solutions, and pre-candidate solutions.

A pre-candidate solution is a substring that contains all characters in the set.

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For a given prefix of the input string, a candidate solution is the suffix that is a pre-candidate and shortest. There may not be a candidate solution for a given prefix. For example. A solution is a shortest candidate solution in the string.

## Find the smallest window in a string containing all characters of another string

When there are no candidate solutions, the solution is the empty string. Our approach to the problem consists in finding the leftmost candidate solution if any and transforming each candidate solution into the next from left to right if any. The process involves expanding and contracting a window.

Finding the leftmost candidate consists in finding the leftmost pre-candidate and refining it until we have the leftmost candidate.

Finding the leftmost candidate consists in expanding the window to the right until we cover all characters in the input set. When we do not find all characters in the set, we know that there is no solution and we return the empty string. Refining the leftmost pre-candidate into the leftmost candidate consists in contracting the window to the right until we cannot drop a character. We cannot drop a character when the character is in the input set and there are no more copies of the character in the window.

We transform a candidate solution into the next by a sequence of expansions and contractions of the window.Given two strings string1 and string2, the task is to find the smallest substring in string1 containing all characters of string2 efficiently.

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Diagram to explain the above algorithm:. This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.

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How to swap two numbers without using a temporary variable? If yes then no such window can exist. Python3 program to find the smallest window.

Function to find smallest window. If string's char matches with. Try to minimize the window i. If no window found. Return substring starting from.

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This code is contributed by Rituraj Jain. WriteLine "No such window exists". If yes. Load Comments. We use cookies to ensure you have the best browsing experience on our website.Lilah has a string,of lowercase English letters that she repeated infinitely many times.

Given an integer,find and print the number of letter a 's in the first letters of Lilah's infinite string. For example, if the string andthe substring we consider isthe first characters of her infinite string. There are occurrences of a in the substring.

Complete the repeatedString function in the editor below. It should return an integer representing the number of occurrences of a in the prefix of length in the infinitely repeating string. The first line contains a single string.

The second line contains an integer. Print a single integer denoting the number of letter a 's in the first letters of the infinite string created by repeating infinitely many times. Explanation 0 The first letters of the infinite string are abaabaabaa.

Because there are a 's, we print on a new line. Explanation 1 Because all of the first letters of the infinite string are awe print on a new line. We use cookies to ensure you have the best browsing experience on our website.