Longest subsequence where each character occurs at least k times

Last Updated : 20 Mar, 2025

Given a string ‘s’ and an integer k, find other string ‘t’ such that ‘t’ is the largest subsequence of given string ‘s’ and each character of ‘t’ must occur at least k times in string s.

Examples :

Input s = “geeksforgeeks” k = 2
Output geeksgeeks
Explanation ‘g’, ‘e’, ‘k’, and ‘s’ appear twice or more, so the output is "geeksgeeks"

Input s = “baaabaacba” k = 3
Output baaabaaba
Explanation Characters ‘b’ and ‘a’ appear at least 3 times, so the result is "baaabaaba".

[Naive Approach] Generate All Subsequences – Exponential time

We can solve the problem by generating all subsequences of the string. For each subsequence, we check if every character appears at least k times. Among all valid subsequences, we keep track of the longest one.

[Efficient Approach] Using Frequency Counting – O(n) time and O(1) space

We use a counter array to store the frequency of each character in the string.
Then, iterate through the string, and for each character, check if its count is greater than or equal to k. If it is, include that character in the result.

C++

#include <iostream> using namespace std;  #define MAX_CHAR 26  // Function to find the subsequence string findSubsequence(string &str, int k) {     int count[MAX_CHAR] = { 0 };      // Counting occurrences of all characters     for (char c : str)          count[c - 'a']++;      // Storing characters with count >= k     string res;     for (char c : str)          if (count[c - 'a'] >= k)             res += c;          return res; }  int main() {     string str = "geeksforgeeks";     int k = 2;     cout << findSubsequence(str, k);     return 0; }

Java

// Importing necessary libraries import java.util.HashMap; import java.util.Map;  public class Main {          // Function to find the subsequence     public static String findSubsequence(String str, int k) {         int[] count = new int[26];          // Counting occurrences of all characters         for (char c : str.toCharArray())             count[c - 'a']++;          // Storing characters with count >= k         StringBuilder res = new StringBuilder();         for (char c : str.toCharArray())             if (count[c - 'a'] >= k)                 res.append(c);          return res.toString();     }      public static void main(String[] args) {         String str = "geeksforgeeks";         int k = 2;         System.out.println(findSubsequence(str, k));     } }

Python

# Function to find the subsequence def find_subsequence(s, k):     count = [0] * 26      # Counting occurrences of all characters     for c in s:         count[ord(c) - ord('a')] += 1      # Storing characters with count >= k     res = ''     for c in s:         if count[ord(c) - ord('a')] >= k:             res += c      return res  # Main function if __name__ == '__main__':     str = 'geeksforgeeks'     k = 2     print(find_subsequence(str, k))

// Function to find the subsequence using System; using System.Collections.Generic;  class Program {     public static string FindSubsequence(string str, int k) {         int[] count = new int[26];          // Counting occurrences of all characters         foreach (char c in str)             count[c - 'a']++;          // Storing characters with count >= k         string res = "";         foreach (char c in str)             if (count[c - 'a'] >= k)                 res += c;          return res;     }      static void Main() {         string str = "geeksforgeeks";         int k = 2;         Console.WriteLine(FindSubsequence(str, k));     } }

JavaScript

// Function to find the subsequence function findSubsequence(str, k) {     const count = new Array(26).fill(0);      // Counting occurrences of all characters     for (let c of str)          count[c.charCodeAt(0) - 'a'.charCodeAt(0)]++;      // Storing characters with count >= k     let res = '';     for (let c of str)          if (count[c.charCodeAt(0) - 'a'.charCodeAt(0)] >= k)             res += c;      return res; }  // Main function const str = 'geeksforgeeks'; const k = 2; console.log(findSubsequence(str, k));