Print all subsequences of a string in Python

Last Updated : 25 Nov, 2024

Given a string s of size n (1 ≤ n ≤ 20), the task is to print all subsequences of string. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Examples:

Input: s = “abc”
Output: [“”, “a”, “b”, “c”, “ab”, “ac”, “bc”, “abc”]
Explanation: All possible combinations of the characters in the string are returned, including the empty string.

Input: S = “ab”
Output: [“”, “a”, “b”, “ab”]
Explanation: All subsequences of the string ab are returned in any order.

Table of Content

Using Recursion

The recursive approach works by considering two options for each character:

Include the character in the current subsequence.
Exclude the character from the current subsequence.

By recursively generating subsequences for all characters, we can obtain the complete set of subsequences.

Python

# Recursive function to generate subsequences. def subseq_rec(idx, curr, s, res):        # Base case: If we've processed all characters,     # add current subsequence     if idx == len(s):         res.append(curr)         return            # Include current character in subsequence     subseq_rec(idx + 1, curr + s[idx], s, res)          # Exclude current character from subsequence     subseq_rec(idx + 1, curr, s, res)   # Wrapper function to generate all subsequences recursively. def all_subseq_rec(s):         # List to store results     res = []            # Start recursion from index 0     subseq_rec(0, "", s, res)       return res  s = "abc" print(all_subseq_rec(s))

Output

['abc', 'ab', 'ac', 'a', 'bc', 'b', 'c', '']

Time Complexity: O(n * 2^n), where n is length of the string. At each step we make two recursive calls resulting in 2^n subsequences.
Auxiliary Space: O(2^n) for storing all subsequences and O(n) recursion stack.

Using Iterative Bit Masking

The iterative approach uses bit masking to generate all subsequences. Each bit in a number represents whether a character is included in the subsequence.

How it Works:

For a string of length n there are 2^n subsets.
Each number from 0 to 2^n – 1 represents a subset, where binary representation of number determines which characters are included in the subsequence.
If the j-th bit is 1 then include the j-th character of string in subsequence.

Python

# Generate subsequences using bit masking. def all_subseq(s):      n = len(s)            # List to store results     res = []            # Loop over all possible masks from 0 to 2^n - 1     for mask in range(1 << n):       	         # Current subsequence being formed         curr = ""                    # Check each bit in mask         for i in range(n):                        # If i-th bit is set, include s[i]             if mask & (1 << i):                   curr += s[i]                          # Add current subsequence to result list         res.append(curr)     return res  s = "abc" print(all_subseq(s))

Output

['', 'a', 'b', 'ab', 'c', 'ac', 'bc', 'abc']

Time Complexity: O(n * 2^n), where 2^n is the number of subsequences and n is the maximum length of each subsequence.
Auxiliary Space: O(2^n), as all subsequences are stored in a list.

Using Python’s Built-in Libraries (Combinations)

Using itertools.combinations library we can generate all subsequences of lengths 0 to n.

Python

from itertools import combinations  # Generate subsequences using combinations from itertools. def all_subseq(s): 	     # Start with the empty subsequence     res = [""]            # Generate combinations of lengths 1 to n     for r in range(1, len(s) + 1):                # Add all combinations of length r to result         res.extend([''.join(comb) for comb in combinations(s, r)])     return res  s = "abc" print(all_subseq(s))

Output

['', 'a', 'b', 'c', 'ab', 'ac', 'bc', 'abc']

Time Complexity: O(n * 2^n), as it generates all subsets.
Auxiliary Space: O(2^n), as all subsequences are stored.

Print all subsequences of a string | Iterative Method

kartik

Improve

Article Tags :

Practice Tags :

python

Print all subsequences of a string in Python

Using Recursion

Using Iterative Bit Masking

Using Python’s Built-in Libraries (Combinations)

Similar Reads