Lexicographically smallest string of maximum length made up of first K alphabets that does not contain any repeating substring
Given a positive integer K, the task is to find lexicographically the smallest string that can be generated by using the first K lowercase alphabets such that no substring of length at least 2 is repeated in the generated string.
Examples:
Input: K = 3
Output: aabacbbcca
Explanation:
In the string “aabacbbcca”, all possible substrings of length at least 2 is repeated more than once.Input: K = 4
Output: aabacadbbcbdccdda
Approach: The given problem can be solved based on the following observations:
- If all substrings of length 2 are unique, then all substrings of length greater than 2 will also be unique.
- Hence, the maximum length string should contain all unique substrings of length 2 arrange in lexicographic order such that no 3 consecutive characters in the string are the same.
Follow the steps below to solve the problem:
- Initialize a string, say S as the empty string that stores the resultant string.
- Iterate over all the first K characters of the lowercase alphabet using the variable, say i and perform the following steps:
- Append the current character i to the string S.
- Iterate from the (i + 1)th character to the Kth character, and append the character i followed by character j to the string S.
- Add the character ‘a’ to the string S so that substring consisting of the last and the first alphabet is also present in the resultant string.
- After completing the above steps, print the string S as the resultant string.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the lexicographically// smallest string of the first K lower// case alphabets having unique substringsvoid generateString(int K){ // Stores the resultant string string s = ""; // Iterate through all the characters for (int i = 97; i < 97 + K; i++) { s = s + char(i); // Inner Loop for making pairs // and adding them into string for (int j = i + 1; j < 97 + K; j++) { s += char(i); s += char(j); } } // Adding first character so that // substring consisting of the last // the first alphabet is present s += char(97); // Print the resultant string cout << s;}// Driver Codeint main(){ int K = 4; generateString(K); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{ // Function to find the lexicographically// smallest string of the first K lower// case alphabets having unique substringsstatic void generateString(int K){ // Stores the resultant string String s = ""; // Iterate through all the characters for(int i = 97; i < 97 + K; i++) { s = s + (char)(i); // Inner Loop for making pairs // and adding them into string for(int j = i + 1; j < 97 + K; j++) { s += (char)(i); s += (char)(j); } } // Adding first character so that // substring consisting of the last // the first alphabet is present s += (char)(97); // Print the resultant string System.out.println(s);}// Driver codepublic static void main(String []args){ int K = 4; generateString(K);}}// This code is contributed by sanjoy_62 |
C#
// C# program for the above approachusing System;class GFG{ // Function to find the lexicographically// smallest string of the first K lower// case alphabets having unique substringsstatic void generateString(int K){ // Stores the resultant string string s = ""; // Iterate through all the characters for(int i = 97; i < 97 + K; i++) { s = s + (char)(i); // Inner Loop for making pairs // and adding them into string for(int j = i + 1; j < 97 + K; j++) { s += (char)(i); s += (char)(j); } } // Adding first character so that // substring consisting of the last // the first alphabet is present s += (char)(97); // Print the resultant string Console.Write(s);}// Driver Codepublic static void Main(){ int K = 4; generateString(K);}}// This code is contributed by ukasp |
Python3
# python 3 program for the above approach# Function to find the lexicographically# smallest string of the first K lower# case alphabets having unique substringsdef generateString(K): # Stores the resultant string s = "" # Iterate through all the characters for i in range(97,97 + K,1): s = s + chr(i); # Inner Loop for making pairs # and adding them into string for j in range(i + 1,97 + K,1): s += chr(i) s += chr(j) # Adding first character so that # substring consisting of the last # the first alphabet is present s += chr(97) # Print the resultant string print(s)# Driver Codeif __name__ == '__main__': K = 4 generateString(K) # This code is contributed by SURENDRA_GANGWAR. |
Javascript
<script>// JavaScript program for the above approach // Function to find the lexicographically// smallest string of the first K lower// case alphabets having unique substringsfunction generateString(K){ // Stores the resultant string var s = ""; // Iterate through all the characters for(var i = 97; i < 97 + K; i++) { s = s + String.fromCharCode(i); // Inner Loop for making pairs // and adding them into string for(var j = i + 1; j < 97 + K; j++) { s += String.fromCharCode(i); s += String.fromCharCode(j); } } // Adding first character so that // substring consisting of the last // the first alphabet is present s += String.fromCharCode(97); // Print the resultant string document.write(s);}// Driver codevar K = 4;generateString(K);// This code is contributed by 29AjayKumar</script> |
Output:
aabacadbbcbdccdda
Time Complexity: O(K2)
Auxiliary Space: O(K2)
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