Program to find list of all possible combinations of letters of a given string s in Python

Sometimes we need to find all possible combinations of letters from a given string. This problem involves generating all non-empty subsequences of characters while maintaining lexicographical order when duplicates exist.

So, if the input is like s = "pqr", then the output will be ['r', 'qr', 'q', 'pr', 'pqr', 'pq', 'p']

Algorithm Approach

To solve this, we will follow these steps ?

• Create an empty result list
• Iterate through the string from right to left
• For each character, combine it with all existing combinations
• Add the character itself as a new combination

Implementation

Let us see the following implementation to get better understanding ?

def solve(s):
    st_arr = []
    
    for i in range(len(s) - 1, -1, -1):
        # Create combinations with current character and existing combinations
        for j in range(len(st_arr)):
            st_arr.append(s[i] + st_arr[j])
        # Add the current character as a single combination
        st_arr.append(s[i])
    
    return st_arr

s = "pqr"
print(solve(s))

The output of the above code is ?

['r', 'qr', 'q', 'pr', 'pqr', 'pq', 'p']

How It Works

The algorithm processes the string from right to left. For each character:

• Step 1: Start with character 'r' ? result: ['r']
• Step 2: Process 'q' ? combine with 'r' to get 'qr', add 'q' ? result: ['r', 'qr', 'q']
• Step 3: Process 'p' ? combine with existing combinations ? result: ['r', 'qr', 'q', 'pr', 'pqr', 'pq', 'p']

Alternative Approach Using itertools

Python's itertools module provides a more concise solution ?

from itertools import combinations

def solve_itertools(s):
    result = []
    # Generate combinations of all possible lengths
    for length in range(1, len(s) + 1):
        for combo in combinations(s, length):
            result.append(''.join(combo))
    return result

s = "pqr"
print(solve_itertools(s))

The output of the above code is ?

['p', 'q', 'r', 'pq', 'pr', 'qr', 'pqr']

Comparison

Conclusion

The manual approach builds combinations incrementally from right to left, while itertools provides a cleaner solution with lexicographical ordering. Choose based on your specific ordering requirements.