Given a set represented as a string, write a recursive code to print all subsets of it. The subsets can be printed in any order.
Examples:
Input : set = “abc”
Output : { “”, “a”, “b”, “c”, “ab”, “ac”, “bc”, “abc”}Input : set = “abcd”
Output : { “”, “a” ,”ab” ,”abc” ,”abcd”, “abd” ,”ac” ,”acd”, “ad” ,”b”, “bc” ,”bcd” ,”bd” ,”c” ,”cd” ,”d” }
Recursive program to generate power set using Backtracking:
The idea is to fix a prefix, and generate all subsets beginning with the current prefix. After all subsets with a prefix are generated, replace the last character with one of the remaining characters.
Follow the approach to implement the above idea:
- The base condition of the recursive approach is when the current index reaches the size of the given string (i.e, index == n), then return
- First, print the current subset
- Iterate over the given string from the current index (i.e, index) to less than the size of the string
- Appending the remaining characters to the current subset
- Make the recursive call for the next index.
- Once all subsets beginning with the initial “curr” are printed, remove the last character to consider a different prefix of subsets.
Follow the steps below to implement the above approach:
C++
// CPP program to generate power set#include <bits/stdc++.h>using namespace std;// str : Stores input string// curr : Stores current subset// index : Index in current subset, currvoid powerSet(string str, int index = -1, string curr = ""){ int n = str.length(); // base case if (index == n) return; // First print current subset cout << curr << "\n"; // Try appending remaining characters // to current subset for (int i = index + 1; i < n; i++) { curr += str[i]; powerSet(str, i, curr); // Once all subsets beginning with // initial "curr" are printed, remove // last character to consider a different // prefix of subsets. curr.erase(curr.size() - 1); } return;}// Driver codeint main(){ string str = "abc"; powerSet(str); return 0;} |
Java
// Java program to generate power setimport java.util.*;class GFG { // str : Stores input string // curr : Stores current subset // index : Index in current subset, curr static void powerSet(String str, int index, String curr) { int n = str.length(); // base case if (index == n) { return; } // First print current subset System.out.println(curr); // Try appending remaining characters // to current subset for (int i = index + 1; i < n; i++) { curr += str.charAt(i); powerSet(str, i, curr); // Once all subsets beginning with // initial "curr" are printed, remove // last character to consider a different // prefix of subsets. curr = curr.substring(0, curr.length() - 1); } } // Driver code public static void main(String[] args) { String str = "abc"; int index = -1; String curr = ""; powerSet(str, index, curr); }}// This code is contributed by PrinciRaj1992 |
Python3
# Python3 program to generate power set# str : Stores input string# curr : Stores current subset# index : Index in current subset, currdef powerSet(str1, index, curr): n = len(str1) # base case if (index == n): return # First print current subset print(curr) # Try appending remaining characters # to current subset for i in range(index + 1, n): curr += str1[i] powerSet(str1, i, curr) # Once all subsets beginning with # initial "curr" are printed, remove # last character to consider a different # prefix of subsets. curr = curr.replace(curr[len(curr) - 1], "") return# Driver codeif __name__ == '__main__': str = "abc" powerSet(str, -1, "")# This code is contributed by# Surendra_Gangwar |
C#
// C# program to generate power setusing System;class GFG { // str : Stores input string // curr : Stores current subset // index : Index in current subset, curr static void powerSet(string str, int index, string curr) { int n = str.Length; // base case if (index == n) { return; } // First print current subset Console.WriteLine(curr); // Try appending remaining characters // to current subset for (int i = index + 1; i < n; i++) { curr += str[i]; powerSet(str, i, curr); // Once all subsets beginning with // initial "curr" are printed, remove // last character to consider a different // prefix of subsets. curr = curr.Substring(0, curr.Length - 1); } } // Driver code public static void Main() { string str = "abc"; int index = -1; string curr = ""; powerSet(str, index, curr); }}// This code is contributed by Ita_c. |
Javascript
<script>// Javascript program to generate power set // str : Stores input string // curr : Stores current subset // index : Index in current subset, curr function powerSet(str,index,curr) { let n = str.length; // base case if (index == n) { return; } // First print current subset document.write(curr+"<br>"); // Try appending remaining characters // to current subset for (let i = index + 1; i < n; i++) { curr += str[i]; powerSet(str, i, curr); // Once all subsets beginning with // initial "curr" are printed, remove // last character to consider a different // prefix of subsets. curr = curr.substring(0, curr.length - 1); } } // Driver code let str = "abc"; let index = -1; let curr = ""; powerSet(str, index, curr); // This code is contributed by rag2127</script> |
Output
a ab abc ac b bc c
Time Complexity: O(2n)
Auxiliary Space: O(n), For recursive call stack
Recursive program to generate power set using Recursion:
The idea is to consider two cases for every character.
(i) Consider current character as part of current subset
(ii) Do not consider current character as part of the current subset.
Follow the approach to implement the above idea:
- The base condition of the recursive approach is when the current index reaches the size of the given string (i.e, index == n). then print the current string say, curr.
- Make two recursive calls for the two cases for every character
- We consider the character as part of the current subset
- We do not consider current character as part of the current subset
Follow the steps below to implement the above approach:
C++
// CPP program to generate power set#include <bits/stdc++.h>using namespace std;// str : Stores input string// curr : Stores current subset// index : Index in current subset, currvoid powerSet(string str, int index = 0, string curr = ""){ int n = str.length(); // base case if (index == n) { cout << curr << endl; return; } // Two cases for every character // (i) We consider the character // as part of current subset // (ii) We do not consider current // character as part of current // subset powerSet(str, index + 1, curr + str[index]); powerSet(str, index + 1, curr);}// Driver codeint main(){ string str = "abc"; powerSet(str); return 0;} |
Java
// Java program to generate power setclass GFG { // str : Stores input string // curr : Stores current subset // index : Index in current subset, curr static void powerSet(String str, int index, String curr) { int n = str.length(); // base case if (index == n) { System.out.println(curr); return; } // Two cases for every character // (i) We consider the character // as part of current subset // (ii) We do not consider current // character as part of current // subset powerSet(str, index + 1, curr + str.charAt(index)); powerSet(str, index + 1, curr); } // Driver code public static void main(String[] args) { String str = "abc"; int index = 0; String curr = ""; powerSet(str, index, curr); }}// This code is contributed by 29AjayKumar |
Python3
# Python3 program to generate power setdef powerSet(string, index, curr): # string : Stores input string # curr : Stores current subset # index : Index in current subset, curr if index == len(string): print(curr) return powerSet(string, index + 1, curr + string[index]) powerSet(string, index + 1, curr)# Driver Codeif __name__ == "__main__": s1 = "abc" index = 0 curr = "" powerSet(s1, index, curr)# This code is contributed by Ekta Singh |
C#
// C# program to generate power setusing System;class GFG { // str : Stores input string // curr : Stores current subset // index : Index in current subset, curr static void powerSet(String str, int index, String curr) { int n = str.Length; // base case if (index == n) { Console.WriteLine(curr); return; } // Two cases for every character // (i) We consider the character // as part of current subset // (ii) We do not consider current // character as part of current // subset powerSet(str, index + 1, curr + str[index]); powerSet(str, index + 1, curr); } // Driver code public static void Main() { String str = "abc"; int index = 0; String curr = ""; powerSet(str, index, curr); }}// This code is contributed by Rajput-Ji |
Javascript
<script>// Javascript program to generate power set // str : Stores input string// curr : Stores current subset// index : Index in current subset, curr function powerSet(str,index,curr) { let n = str.length; // base case if (index == n) { document.write(curr+"<br>"); return; } // Two cases for every character // (i) We consider the character // as part of current subset // (ii) We do not consider current // character as part of current // subset powerSet(str, index + 1, curr + str[index]); powerSet(str, index + 1, curr); } // Driver code let str = "abc"; let index = 0; let curr=""; powerSet(str,index,curr); // This code is contributed by avanitrachhadiya2155</script> |
Output
abc ab ac a bc b c
Time Complexity: O(2n)
Auxiliary Space: O(n), For recursive call stack
Recursive program to generate power set using Backtracking using Bottom Up Approach:
The idea is to pick each element one by one from the input set, then generate a subset for the same, and we follow this process recursively.
Follow the steps below to implement the above idea:
- The base condition for the recursive call, when the current index becomes negative then add empty list into the allSubsets.
- Make recursive call for the current index – 1, then we’ll receive allSubsets list from 0 to index -1
- Create a list of list moreSubsets
- Iterate over all the subsets that are received from above recursive call
- Copy all the subset into newSubset
- Add the current item into newSubset
- Add newSubset into moreSubsets
- Add moreSubsets into allSubsets
- Finally, return allSubsets.
Follow the steps below to implement the above approach:
C++
// C++ Recursive code to print// all subsets of set using ArrayList#include <bits/stdc++.h>using namespace std;vector<vector<string> > getSubset(vector<string> set, int index){ vector<vector<string> > allSubsets; if (index < 0) { vector<string> v; allSubsets.push_back(v); } else { allSubsets = getSubset(set, index - 1); string item = set[index]; vector<vector<string> > moreSubsets; for (vector<string> subset : allSubsets) { vector<string> newSubset; for (auto it : subset) newSubset.push_back(it); newSubset.push_back(item); moreSubsets.push_back(newSubset); } for (auto it : moreSubsets) allSubsets.push_back(it); } return allSubsets;}int main(){ vector<string> set = { "a", "b", "c" }; int index = set.size() - 1; vector<vector<string> > result = getSubset(set, index); for (auto it : result) { cout << " [ "; for (auto itr : it) { cout << itr << ","; } cout << "],"; }}// This code is contributed by garg28harsh. |
Java
// Java Recursive code to print// all subsets of set using ArrayListimport java.util.ArrayList;public class PowerSet { public static void main(String[] args) { String[] set = { "a", "b", "c" }; int index = set.length - 1; ArrayList<ArrayList<String> > result = getSubset(set, index); System.out.println(result); } static ArrayList<ArrayList<String> > getSubset(String[] set, int index) { ArrayList<ArrayList<String> > allSubsets; if (index < 0) { allSubsets = new ArrayList<ArrayList<String> >(); allSubsets.add(new ArrayList<String>()); } else { allSubsets = getSubset(set, index - 1); String item = set[index]; ArrayList<ArrayList<String> > moreSubsets = new ArrayList<ArrayList<String> >(); for (ArrayList<String> subset : allSubsets) { ArrayList<String> newSubset = new ArrayList<String>(); newSubset.addAll(subset); newSubset.add(item); moreSubsets.add(newSubset); } allSubsets.addAll(moreSubsets); } return allSubsets; }} |
Python3
# Python recursive code to print# all subsets of set using ArrayListdef get_subset(s, index): all_subsets = [] if index < 0: all_subsets.append([]) else: all_subsets = get_subset(s, index-1) item = s[index] more_subsets = [] for subset in all_subsets: new_subset = [] for i in subset: new_subset.append(i) new_subset.append(item) more_subsets.append(new_subset) for i in more_subsets: all_subsets.append(i) return all_subsets# Driver Codeset = ["a", "b", "c"]index = len(set) - 1result = get_subset(set, index)for subset in result: print("[", end=" ") for item in subset: print(item, end=" ") print("],", end=" ") |
C#
// c# code for the above approachusing System;using System.Collections.Generic;namespace Subsets {public class GFG { static List<List<string> > GetSubsets(List<string> set, int index) { List<List<string> > allSubsets; if (index < 0) { List<string> emptyList = new List<string>(); allSubsets = new List<List<string> >{ emptyList }; } else { allSubsets = GetSubsets(set, index - 1); string item = set[index]; List<List<string> > moreSubsets = new List<List<string> >(); foreach(List<string> subset in allSubsets) { List<string> newSubset = new List<string>(); foreach(string it in subset) { newSubset.Add(it); } newSubset.Add(item); moreSubsets.Add(newSubset); } foreach(List<string> it in moreSubsets) { allSubsets.Add(it); } } return allSubsets; } static void Main(string[] args) { List<string> set = new List<string>{ "a", "b", "c" }; int index = set.Count - 1; List<List<string> > result = GetSubsets(set, index); foreach(List<string> it in result) { Console.Write("[ "); foreach(string itr in it) { Console.Write(itr + " "); } Console.Write("], "); } }}} |
Javascript
//javascript code for the above approachfunction getSubset(set, index) { let allSubsets = []; if (index < 0) { let v = []; allSubsets.push(v); } else { allSubsets = getSubset(set, index - 1); let item = set[index]; let moreSubsets = []; for (let subset of allSubsets) { let newSubset = []; for (let it of subset) newSubset.push(it); newSubset.push(item); moreSubsets.push(newSubset); } for (let it of moreSubsets) allSubsets.push(it); } return allSubsets;}let set = ["a", "b", "c"];let index = set.length - 1;let result = getSubset(set, index);for (let it of result) { console.log(" [ " + it.join(",") + " ],");} |
Output
[[], [a], [b], [a, b], , [a, c], [b, c], [a, b, c]]
Time Complexity: O(n*2n)
Auxiliary Space: O(n), For recursive call stack
Iterative program for the power set.
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