C++ Program for Generating Lyndon words of length n Last Updated : 18 Aug, 2023 Comments Improve Suggest changes Like Article Like Report Given an integer n and an array of characters S, the task is to generate Lyndon words of length n having characters from S. A Lyndon word is a string which is strictly less than all of its rotations in lexicographic order. For example, the string "012" is a Lyndon word as it is less than its rotations "120" and "201", but "102" is not a Lyndon word as it is greater than its rotation "021". Note: "000" is not considered to be a Lyndon word as it is equal to the string obtained by rotating it. Examples: Input: n = 2, S = {0, 1, 2} Output: 01 02 12 Other possible strings of length 2 are "00", "11", "20", "21", and "22". All of these are either greater than or equal to one of their rotations. Input: n = 1, S = {0, 1, 2} Output: 0 1 2 Approach: There exists an efficient approach to generate Lyndon words which was given by Jean-Pierre Duval, which can be used to generate all the Lyndon words upto length n in time proportional to the number of such words. (Please refer to the paper "Average cost of Duval’s algorithm for generating Lyndon words" by Berstel et al. for the proof) The algorithm generates the Lyndon words in a lexicographic order. If w is a Lyndon word, the next word is obtained by the following steps: Repeat w to form a string v of length n, such that v[i] = w[i mod |w|]. While the last character of v is the last one in the sorted ordering of S, remove it. Replace the last character of v by its successor in the sorted ordering of S. For example, if n = 5, S = {a, b, c, d}, and w = "add" then we get v = "addad". Since 'd' is the last character in the sorted ordering of S, we remove it to get "adda" and then replace the last 'a' by its successor 'b' to get the Lyndon word "addb". Below is the implementation of the above approach: C++ // C++ implementation of // the above approach #include<bits/stdc++.h> using namespace std; int main() { int n = 2; char S[] = {'0', '1', '2' }; int k = 3; sort(S, S + 3); // To store the indices // of the characters vector<int> w; w.push_back(-1); // Loop till w is not empty while(w.size() > 0) { // Incrementing the last character w[w.size()-1]++; int m = w.size(); if(m == n) { string str; for(int i = 0; i < w.size(); i++) { str += S[w[i]]; } cout << str << endl; } // Repeating w to get a // n-length string while(w.size() < n) { w.push_back(w[w.size() - m]); } // Removing the last character // as long it is equal to // the largest character in S while(w.size() > 0 && w[w.size() - 1] == k - 1) { w.pop_back(); } } return 0; } // This code is contributed by AdeshSingh1 Output: 01 02 12 Please refer complete article on Generating Lyndon words of length n for more details! Comment More infoAdvertise with us Next Article C++ Program for Generating Lyndon words of length n K kartik Follow Improve Article Tags : Strings Combinatorial Technical Scripter C++ Programs C++ DSA Technical Scripter 2018 rotation +4 More Practice Tags : CPPCombinatorialStrings Similar Reads C++ Program to Print the First Letter of Each Word of a String String str is given which contains lowercase English letters and spaces. It may contain multiple spaces. Get the first letter of every word and return the result as a string. The result should not contain any space. Examples: Input: str = "geeks for geeks" Output: gfg Input: str = "happy coding" Out 4 min read C++ Program To Print Continuous Character Pattern Here we will build a C++ Program To Print Continuous Character patterns using 2 different methods i.e: Using for loopsUsing while loopsInput: rows = 5Output: A B C D E F G H I J K L M N O 1. Using for loopApproach 1: Assign any character to one variable for the printing pattern. The first for loop i 5 min read Program to generate random alphabets Prerequisite : rand() and srand() Given all alphabets in a character array, print a string of random characters of given size.We will use rand() function to print random characters. It returns random integer values. This number is generated by an algorithm that returns a sequence of apparently non-r 4 min read Iterative program to generate distinct Permutations of a String Given a string str, the task is to generate all the distinct permutations of the given string iteratively. Examples: Input: str = "bba" Output: abb bab bba Input: str = "abc" Output: abc acb bac bca cab cba Approach: The number of permutations for a string of length n are n!. The following algorithm 15+ min read Program to print reverse character bridge pattern For a given value N, denoting the number of Charters starting from the A, print reverse character bridge pattern.Examples : Input : n = 5 Output : ABCDEDCBA ABCD DCBA ABC CBA AB BA A A Input : n = 8 Output : ABCDEFGHGFEDCBA ABCDEFG GFEDCBA ABCDEF FEDCBA ABCDE EDCBA ABCD DCBA ABC CBA AB BA A A Recomm 5 min read Like