Given a string s, print all possible subsequences of the given string in an iterative manner. We have already discussed Recursive method to print all subsequences of a string.
Examples:
Input : abc Output : a, b, c, ab, ac, bc, abc Input : aab Output : a, b, aa, ab, aab
Approach 1 :
Here, we discuss much easier and simpler iterative approach which is similar to Power Set. We use bit pattern from binary representation of 1 to 2^length(s) – 1.
input = “abc”
Binary representation to consider 1 to (2^3-1), i.e 1 to 7.
Start from left (MSB) to right (LSB) of binary representation and append characters from input string which corresponds to bit value 1 in binary representation to Final subsequence string sub.
Example:
001 => abc . Only c corresponds to bit 1. So, subsequence = c. 101 => abc . a and c corresponds to bit 1. So, subsequence = ac. binary_representation (1) = 001 => c binary_representation (2) = 010 => b binary_representation (3) = 011 => bc binary_representation (4) = 100 => a binary_representation (5) = 101 => ac binary_representation (6) = 110 => ab binary_representation (7) = 111 => abc
Below is the implementation of above approach:
// C++ program to print all Subsequences // of a string in iterative manner #include <bits/stdc++.h> using namespace std;
// function to find subsequence string subsequence(string s, int binary, int len)
{ string sub = "" ;
for ( int j = 0; j < len; j++)
// check if jth bit in binary is 1
if (binary & (1 << j))
// if jth bit is 1, include it
// in subsequence
sub += s[j];
return sub;
} // function to print all subsequences void possibleSubsequences(string s){
// map to store subsequence
// lexicographically by length
map< int , set<string> > sorted_subsequence;
int len = s.size();
// Total number of non-empty subsequence
// in string is 2^len-1
int limit = pow (2, len);
// i=0, corresponds to empty subsequence
for ( int i = 1; i <= limit - 1; i++) {
// subsequence for binary pattern i
string sub = subsequence(s, i, len);
// storing sub in map
sorted_subsequence[sub.length()].insert(sub);
}
for ( auto it : sorted_subsequence) {
// it.first is length of Subsequence
// it.second is set<string>
cout << "Subsequences of length = "
<< it.first << " are:" << endl;
for ( auto ii : it.second)
// ii is iterator of type set<string>
cout << ii << " " ;
cout << endl;
}
} // driver function int main()
{ string s = "aabc" ;
possibleSubsequences(s);
return 0;
} |
// Java program to print all Subsequences // of a String in iterative manner import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.SortedMap;
import java.util.TreeMap;
class Graph{
// Function to find subsequence static String subsequence(String s,
int binary,
int len)
{ String sub = "" ;
for ( int j = 0 ; j < len; j++)
// Check if jth bit in binary is 1
if ((binary & ( 1 << j)) != 0 )
// If jth bit is 1, include it
// in subsequence
sub += s.charAt(j);
return sub;
} // Function to print all subsequences static void possibleSubsequences(String s)
{ // Map to store subsequence
// lexicographically by length
SortedMap<Integer,
HashSet<String>> sorted_subsequence = new TreeMap<Integer,
HashSet<String>>();
int len = s.length();
// Total number of non-empty subsequence
// in String is 2^len-1
int limit = ( int ) Math.pow( 2 , len);
// i=0, corresponds to empty subsequence
for ( int i = 1 ; i <= limit - 1 ; i++)
{
// Subsequence for binary pattern i
String sub = subsequence(s, i, len);
// Storing sub in map
if (!sorted_subsequence.containsKey(sub.length()))
sorted_subsequence.put(
sub.length(), new HashSet<>());
sorted_subsequence.get(
sub.length()).add(sub);
}
for (Map.Entry<Integer,
HashSet<String>> it : sorted_subsequence.entrySet())
{
// it.first is length of Subsequence
// it.second is set<String>
System.out.println( "Subsequences of length = " +
it.getKey() + " are:" );
for (String ii : it.getValue())
// ii is iterator of type set<String>
System.out.print(ii + " " );
System.out.println();
}
} // Driver code public static void main(String[] args)
{ String s = "aabc" ;
possibleSubsequences(s);
} } // This code is contributed by sanjeev2552 |
# Python3 program to print all Subsequences # of a string in iterative manner # function to find subsequence def subsequence(s, binary, length):
sub = ""
for j in range (length):
# check if jth bit in binary is 1
if (binary & ( 1 << j)):
# if jth bit is 1, include it
# in subsequence
sub + = s[j]
return sub
# function to print all subsequences def possibleSubsequences(s):
# map to store subsequence
# lexicographically by length
sorted_subsequence = {}
length = len (s)
# Total number of non-empty subsequence
# in string is 2^len-1
limit = 2 * * length
# i=0, corresponds to empty subsequence
for i in range ( 1 , limit):
# subsequence for binary pattern i
sub = subsequence(s, i, length)
# storing sub in map
if len (sub) in sorted_subsequence.keys():
sorted_subsequence[ len (sub)] = \
tuple ( list (sorted_subsequence[ len (sub)]) + [sub])
else :
sorted_subsequence[ len (sub)] = [sub]
for it in sorted_subsequence:
# it.first is length of Subsequence
# it.second is set<string>
print ( "Subsequences of length =" , it, "are:" )
for ii in sorted ( set (sorted_subsequence[it])):
# ii is iterator of type set<string>
print (ii, end = ' ' )
print ()
# Driver Code s = "aabc"
possibleSubsequences(s) # This code is contributed by ankush_953 |
// C# program to print all Subsequences // of a String in iterative manner using System;
using System.Collections.Generic;
class Graph {
// Function to find subsequence
static string subsequence( string s, int binary, int len)
{
string sub = "" ;
for ( int j = 0; j < len; j++)
// Check if jth bit in binary is 1
if ((binary & (1 << j)) != 0)
// If jth bit is 1, include it
// in subsequence
sub += s[j];
return sub;
}
// Function to print all subsequences
static void possibleSubsequences( string s)
{
// Map to store subsequence
// lexicographically by length
SortedDictionary< int , HashSet< string > >
sorted_subsequence
= new SortedDictionary< int , HashSet< string > >();
int len = s.Length;
// Total number of non-empty subsequence
// in String is 2^len-1
int limit = ( int )Math.Pow(2, len);
// i=0, corresponds to empty subsequence
for ( int i = 1; i <= limit - 1; i++) {
// Subsequence for binary pattern i
string sub = subsequence(s, i, len);
// Storing sub in map
if (!sorted_subsequence.ContainsKey(sub.Length))
sorted_subsequence[sub.Length]
= new HashSet< string >();
sorted_subsequence[sub.Length].Add(sub);
}
foreach ( var it in sorted_subsequence)
{
// it.first is length of Subsequence
// it.second is set<String>
Console.WriteLine( "Subsequences of length = "
+ it.Key + " are:" );
foreach (String ii in it.Value)
// ii is iterator of type set<String>
Console.Write(ii + " " );
Console.WriteLine();
}
}
// Driver code
public static void Main( string [] args)
{
string s = "aabc" ;
possibleSubsequences(s);
}
} // This code is contributed by phasing17 |
<script> // Javascript program to print all Subsequences // of a string in iterative manner // function to find subsequence function subsequence(s, binary, len)
{ let sub = "" ;
for (let j = 0; j < len; j++)
// Check if jth bit in binary is 1
if (binary & (1 << j))
// If jth bit is 1, include it
// in subsequence
sub += s[j];
return sub;
} // Function to print all subsequences function possibleSubsequences(s)
{ // map to store subsequence
// lexicographically by length
let sorted_subsequence = new Map();
let len = s.length;
// Total number of non-empty subsequence
// in string is 2^len-1
let limit = Math.pow(2, len);
// i=0, corresponds to empty subsequence
for (let i = 1; i <= limit - 1; i++)
{
// Subsequence for binary pattern i
let sub = subsequence(s, i, len);
// Storing sub in map
if (!sorted_subsequence.has(sub.length))
sorted_subsequence.set(sub.length, new Set());
sorted_subsequence.get(sub.length).add(sub);
}
for (let it of sorted_subsequence)
{
// it.first is length of Subsequence
// it.second is set<string>
document.write( "Subsequences of length = " +
it[0] + " are:" + "<br>" );
for (let ii of it[1])
// ii is iterator of type set<string>
document.write(ii + " " );
document.write( "<br>" );
}
} // Driver code let s = "aabc" ;
possibleSubsequences(s); // This code is contributed by gfgking </script> |
Output
Subsequences of length = 1 are: a b c Subsequences of length = 2 are: aa ab ac bc Subsequences of length = 3 are: aab aac abc Subsequences of length = 4 are: aabc
Time Complexity : O(2^n), where n is length of string to find subsequences and n is length of binary string.
Space Complexity: O(1)
Approach 2 :
Approach is to get the position of rightmost set bit and reset that bit after appending corresponding character from given string to the subsequence and will repeat the same thing till corresponding binary pattern has no set bits.
If input is s = “abc” Binary representation to consider 1 to (2^3-1), i.e 1 to 7. 001 => abc . Only c corresponds to bit 1. So, subsequence = c 101 => abc . a and c corresponds to bit 1. So, subsequence = ac. Let us use Binary representation of 5, i.e 101. Rightmost bit is at position 1, append character at beginning of sub = c ,reset position 1 => 100 Rightmost bit is at position 3, append character at beginning of sub = ac ,reset position 3 => 000 As now we have no set bit left, we stop computing subsequence.
Example:
binary_representation (1) = 001 => c binary_representation (2) = 010 => b binary_representation (3) = 011 => bc binary_representation (4) = 100 => a binary_representation (5) = 101 => ac binary_representation (6) = 110 => ab binary_representation (7) = 111 => abc
Below is the implementation of above approach :
// C++ code all Subsequences of a // string in iterative manner #include <bits/stdc++.h> using namespace std;
// function to find subsequence string subsequence(string s, int binary)
{ string sub = "" ;
int pos;
// loop while binary is greater than 0
while (binary>0)
{
// get the position of rightmost set bit
pos=log2(binary&-binary)+1;
// append at beginning as we are
// going from LSB to MSB
sub=s[pos-1]+sub;
// resets bit at pos in binary
binary= (binary & ~(1 << (pos-1)));
}
reverse(sub.begin(),sub.end());
return sub;
} // function to print all subsequences void possibleSubsequences(string s){
// map to store subsequence
// lexicographically by length
map< int , set<string> > sorted_subsequence;
int len = s.size();
// Total number of non-empty subsequence
// in string is 2^len-1
int limit = pow (2, len);
// i=0, corresponds to empty subsequence
for ( int i = 1; i <= limit - 1; i++) {
// subsequence for binary pattern i
string sub = subsequence(s, i);
// storing sub in map
sorted_subsequence[sub.length()].insert(sub);
}
for ( auto it : sorted_subsequence) {
// it.first is length of Subsequence
// it.second is set<string>
cout << "Subsequences of length = "
<< it.first << " are:" << endl;
for ( auto ii : it.second)
// ii is iterator of type set<string>
cout << ii << " " ;
cout << endl;
}
} // driver function int main()
{ string s = "aabc" ;
possibleSubsequences(s);
return 0;
} |
import java.util.*;
public class GFG {
// function to find subsequence
public static String subsequence(String s, int binary) {
String sub = "" ;
int pos;
// loop while binary is greater than 0
while (binary > 0 ) {
// get the position of rightmost set bit
pos = ( int ) (Math.log(binary & -binary) / Math.log( 2 )) + 1 ;
// append at beginning as we are
// going from LSB to MSB
sub = s.charAt(pos - 1 ) + sub;
// resets bit at pos in binary
binary = (binary & ~( 1 << (pos - 1 )));
}
sub = new StringBuilder(sub).reverse().toString();
return sub;
}
// function to print all subsequences
public static void possibleSubsequences(String s) {
// map to store subsequence
// lexicographically by length
Map<Integer, Set<String>> sortedSubsequence = new HashMap<>();
int len = s.length();
// Total number of non-empty subsequence
// in string is 2^len-1
int limit = ( int ) Math.pow( 2 , len);
// i=0, corresponds to empty subsequence
for ( int i = 1 ; i <= limit - 1 ; i++) {
// subsequence for binary pattern i
String sub = subsequence(s, i);
// storing sub in map
sortedSubsequence.computeIfAbsent(sub.length(), k -> new TreeSet<>()).add(sub);
}
for (Map.Entry<Integer, Set<String>> it : sortedSubsequence.entrySet()) {
// it.getKey() is length of Subsequence
// it.getValue() is Set<String>
System.out.println( "Subsequences of length = " + it.getKey() + " are:" );
for (String ii : it.getValue())
// ii is element of Set<String>
System.out.print(ii + " " );
System.out.println();
}
}
// driver function
public static void main(String[] args) {
String s = "aabc" ;
possibleSubsequences(s);
}
} |
# Python3 program to print all Subsequences # of a string in an iterative manner from math import log2, floor
# function to find subsequence def subsequence(s, binary):
sub = ""
# loop while binary is greater than
while (binary > 0 ):
# get the position of rightmost set bit
pos = floor(log2(binary& - binary) + 1 )
# append at beginning as we are
# going from LSB to MSB
sub = s[pos - 1 ] + sub
# resets bit at pos in binary
binary = (binary & ~( 1 << (pos - 1 )))
sub = sub[:: - 1 ]
return sub
# function to print all subsequences def possibleSubsequences(s):
# map to store subsequence
# lexicographically by length
sorted_subsequence = {}
length = len (s)
# Total number of non-empty subsequence
# in string is 2^len-1
limit = 2 * * length
# i=0, corresponds to empty subsequence
for i in range ( 1 , limit):
# subsequence for binary pattern i
sub = subsequence(s, i)
# storing sub in map
if len (sub) in sorted_subsequence.keys():
sorted_subsequence[ len (sub)] = \
tuple ( list (sorted_subsequence[ len (sub)]) + [sub])
else :
sorted_subsequence[ len (sub)] = [sub]
for it in sorted_subsequence:
# it.first is length of Subsequence
# it.second is set<string>
print ( "Subsequences of length =" , it, "are:" )
for ii in sorted ( set (sorted_subsequence[it])):
# ii is iterator of type set<string>
print (ii, end = ' ' )
print ()
# Driver Code s = "aabc"
possibleSubsequences(s) # This code is contributed by ankush_953 |
// C# program to print all Subsequences // of a string in an iterative manner using System;
using System.Collections.Generic;
using System.Linq;
class GFG
{ // function to find subsequence
static string subsequence( string s, int binary)
{
string sub = "" ;
// loop while binary is greater than
while (binary > 0) {
// get the position of rightmost set bit
var pos = ( int )Math.Floor(
Math.Log(binary & (-binary))
/ Math.Log(2))
+ 1;
// append at beginning as we are
// going from LSB to MSB
sub = s[pos - 1] + sub;
// resets bit at pos in binary
binary = (binary & ~(1 << (pos - 1)));
}
char [] charArray = sub.ToCharArray();
Array.Reverse(charArray);
return new string (charArray);
}
// function to print all subsequences
static void possibleSubsequences( string s)
{
// map to store subsequence
// lexicographically by length
Dictionary< int , HashSet< string > > sorted_subsequence
= new Dictionary< int , HashSet< string > >();
int length = s.Length;
// Total number of non-empty subsequence
// in string is 2^len-1
int limit = ( int )Math.Pow(2, length);
// i=0, corresponds to empty subsequence
for ( int i = 1; i < limit; i++) {
// subsequence for binary pattern i
string sub = subsequence(s, i);
// storing sub in map
if (sorted_subsequence.ContainsKey(
sub.Length)) {
sorted_subsequence[sub.Length].Add(sub);
}
else {
sorted_subsequence[sub.Length]
= new HashSet< string >();
sorted_subsequence[sub.Length].Add(sub);
}
}
foreach ( var it in sorted_subsequence)
{
// it.first is length of Subsequence
// it.second is set<string>
Console.WriteLine( "Subsequences of length = "
+ it.Key + " are:" );
var arr = (it.Value).ToArray();
Array.Sort(arr);
for ( int i = 0; i < arr.Length; i++) {
Console.Write(arr[i] + " " );
}
Console.WriteLine();
}
}
// Driver Code
public static void Main( string [] args)
{
string s = "aabc" ;
possibleSubsequences(s);
}
} // This code is contributed by phasing17 |
// JavaScript program to print all Subsequences // of a string in an iterative manner // function to find subsequence function subsequence(s, binary)
{ var sub = "" ;
// loop while binary is greater than
while (binary > 0)
{
// get the position of rightmost set bit
var pos= Math.floor(Math.log2(binary&-binary) + 1);
// append at beginning as we are
// going from LSB to MSB
sub = s[pos - 1] + sub;
// resets bit at pos in binary
binary= (binary & ~(1 << (pos - 1)));
}
sub = sub.split( "" );
sub = sub.reverse();
return sub.join( "" );
} // function to print all subsequences function possibleSubsequences(s)
{ // map to store subsequence
// lexicographically by length
var sorted_subsequence = {};
var length = s.length;
// Total number of non-empty subsequence
// in string is 2^len-1
var limit = 2 ** length;
// i=0, corresponds to empty subsequence
for ( var i = 1; i < limit; i++)
{
// subsequence for binary pattern i
var sub = subsequence(s, i);
// storing sub in map
if (sorted_subsequence.hasOwnProperty(sub.length))
{
//var list = sorted_subsequence[sub.length];
//list.push(sub);
sorted_subsequence[sub.length].push(sub);
}
else
sorted_subsequence[sub.length] = [sub];
}
for (const it in sorted_subsequence)
{
// it.first is length of Subsequence
// it.second is set<string>
console.log( "Subsequences of length =" , it, "are:" );
var arr = sorted_subsequence[it];
arr.sort();
var set = new Set(arr);
for (const ii of set)
// ii is iterator of type set<string>
process.stdout.write(ii + " " );
console.log()
}
} // Driver Code var s = "aabc" ;
possibleSubsequences(s); // This code is contributed by phasing17 |
Output
Subsequences of length = 1 are: a b c Subsequences of length = 2 are: aa ab ac bc Subsequences of length = 3 are: aab aac abc Subsequences of length = 4 are: aabc
Time Complexity:
Auxiliary Space: O(n)