Subsequences of given string consisting of non-repeating characters
Given a string str of length N, the task is to print all possible distinct subsequences of the string str which consists of non-repeating characters only.
Examples:
Input: str = “abac”
Output: a ab abc ac b ba bac bc c
Explanation:
All possible distinct subsequences of the strings are { a, aa, aac, ab, aba, abac, abc, ac, b, ba, bac, bc, c }
Therefore, the subsequences consisting non-repeating characters only are { a, ab, abc, ac, b, ba, bac, bc, c }Input: str = “aaa”
Output: a
Approach: The problem can be solved using Backtracing technique using the following recurrence relation:
FindSub(str, res, i) = { FindSub(str, res, i + 1), FindSub(str, res + str[i], i + 1) }
res = subsequence of the string
i = index of a character in str
Follow the steps below to solve the problem:
- Initialize a Set, say sub, to store all possible subsequences consisting of non-repeating characters.
- Initialize another Set, say ch, to check if a character is present in the subsequence or not.
- Traverse the string and print all possible subsequences consisting of non-repeating characters only using the above recurrence relation.
Below is the implementation of the above approach:
C++
// C++ program to implement// the above approach#include <bits/stdc++.h>using namespace std;// Function to find all the subsequences of// the string with non-repeating charactersvoid FindSub(set<string>& sub, set<char>& ch, string str, string res, int i){ // Base case if (i == str.length()) { // Insert current subsequence sub.insert(res); return; } // If str[i] is not present // in the current subsequence if (!ch.count(str[i])) { // Insert str[i] into the set ch.insert(str[i]); // Insert str[i] into the // current subsequence res.push_back(str[i]); FindSub(sub, ch, str, res, i + 1); // Remove str[i] from // current subsequence res.pop_back(); // Remove str[i] from the set ch.erase(str[i]); } // Not including str[i] from // the current subsequence FindSub(sub, ch, str, res, i + 1);}// Utility function to print all subsequences// of string with non-repeating charactersvoid printSubwithUniqueChar(string str, int N){ // Stores all possible subsequences // with non-repeating characters set<string> sub; // Stores subsequence with // non-repeating characters set<char> ch; FindSub(sub, ch, str, "", 0); // Traverse all possible subsequences // containing non-repeating characters for (auto subString : sub) { // Print subsequence cout << subString << " "; }}// Driver Codeint main(){ string str = "abac"; int N = str.length(); printSubwithUniqueChar(str, N); return 0;} |
Java
// Javs program to implement// the above approachimport java.util.*;class GFG { // Function to find all the subsequences of // the string with non-repeating characters public static void FindSub(HashSet<String> sub, HashSet<Character> ch, String str, String res, int i) { // Base case if (i == str.length()) { // Insert current subsequence sub.add(res); return; } // If str[i] is not present // in the current subsequence if (!ch.contains(str.charAt(i))) { // Insert str[i] into the set ch.add(str.charAt(i)); // Insert str[i] into the // current subsequence FindSub(sub, ch, str, res + str.charAt(i), i + 1); // Remove str[i] from the set ch.remove(str.charAt(i)); } // Not including str[i] from // the current subsequence FindSub(sub, ch, str, res, i + 1); } // Utility function to print all subsequences // of string with non-repeating characters public static void printSubwithUniqueChar(String str, int N) { // Stores all possible subsequences // with non-repeating characters HashSet<String> sub = new HashSet<>(); // Stores subsequence with // non-repeating characters HashSet<Character> ch = new HashSet<>(); FindSub(sub, ch, str, "", 0); // Traverse all possible subsequences // containing non-repeating characters for (String subString : sub) { // Print subsequence System.out.print(subString + " "); } } // Driver Code public static void main(String args[]) { String str = "abac"; int N = str.length(); printSubwithUniqueChar(str, N); }} |
Python3
# Python 3 program to implement# the above approach1# Function to find all the subsequences of# the str1ing with non-repeating ch1aractersdef FindSub(sub, ch1, str1, res, i): # Base case if (i == len(str1)): # Insert current subsequence sub.add(res) return # If str1[i] is not present # in the current subsequence if (str1[i] not in ch1): # Insert str1[i] into the set ch1.add(str1[i]) # Insert str1[i] into the # current subsequence FindSub(sub, ch1, str1, res+str1[i], i + 1) res += str1[i] # Remove str1[i] from # current subsequence res = res[0:len(res) - 1] # Remove str1[i] from the set ch1.remove(str1[i]) # Not including str1[i] from # the current subsequence FindSub(sub, ch1, str1, res, i + 1)# Utility function to print all subsequences# of str1ing with non-repeating ch1aractersdef printSubwithUniquech1ar(str1, N): # Stores all possible subsequences # with non-repeating ch1aracters sub = set() # Stores subsequence with # non-repeating ch1aracters ch1 = set() FindSub(sub, ch1, str1, "", 0) # Traverse all possible subsequences # containing non-repeating ch1aracters temp = [] for substr1ing in sub: temp.append(substr1ing) temp.sort(reverse = False) for x in temp: # Print subsequence print(x, end = " ")# Driver Codeif __name__ == '__main__': str2 = "abac" N = len(str2) printSubwithUniquech1ar(str2, N) # This code is contributed by bgangwar59. |
C#
// C# program to implement// the above approachusing System;using System.Collections.Generic;public class GFG{ // Function to find all the subsequences of // the string with non-repeating characters public static void FindSub(HashSet<String> sub, HashSet<char> ch, String str, String res, int i) { // Base case if (i == str.Length) { // Insert current subsequence sub.Add(res); return; } // If str[i] is not present // in the current subsequence if (!ch.Contains(str[i])) { // Insert str[i] into the set ch.Add(str[i]); // Insert str[i] into the // current subsequence FindSub(sub, ch, str, res + str[i], i + 1); // Remove str[i] from the set ch.Remove(str[i]); } // Not including str[i] from // the current subsequence FindSub(sub, ch, str, res, i + 1); } // Utility function to print all subsequences // of string with non-repeating characters public static void printSubwithUniqueChar(String str, int N) { // Stores all possible subsequences // with non-repeating characters HashSet<String> sub = new HashSet<String>(); // Stores subsequence with // non-repeating characters HashSet<char> ch = new HashSet<char>(); FindSub(sub, ch, str, "", 0); // Traverse all possible subsequences // containing non-repeating characters foreach (String subString in sub) { // Print subsequence Console.Write(subString + " "); } } // Driver Code public static void Main(String []args) { String str = "abac"; int N = str.Length; printSubwithUniqueChar(str, N); }}// This code contributed by shikhasingrajput |
Javascript
<script>// JavaScript program to implement// the above approach// Stores all possible subsequences// with non-repeating charactersvar sub = new Set();// Stores subsequence with// non-repeating charactersvar ch = new Set();// Function to find all the subsequences of// the string with non-repeating charactersfunction FindSub(str, res, i){ // Base case if (i == str.length) { // Insert current subsequence sub.add(res.join("")); return; } // If str[i] is not present // in the current subsequence if (!ch.has(str[i])) { // Insert str[i] into the set ch.add(str[i]); // Insert str[i] into the // current subsequence res.push(str[i]); FindSub(str, res, i + 1); res.pop() // Remove str[i] from the set ch.delete(str[i]); } // Not including str[i] from // the current subsequence FindSub(str, res, i + 1);}// Utility function to print all subsequences// of string with non-repeating charactersfunction printSubwithUniqueChar(str, N){ FindSub(str, [], 0); var tmp = [...sub].sort(); // Traverse all possible subsequences // containing non-repeating characters tmp.forEach(subString => { // Print subsequence document.write( subString + " "); });}// Driver Codevar str = "abac";var N = str.length;printSubwithUniqueChar(str, N);</script> |
Output:
a ab abc ac b ba bac bc c
Time complexity: O(N * log(N) * 2N)
Auxiliary Space O(N * 2N)
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