Program to find smallest value of K for K-Similar Strings in Python

Given two anagram strings s and t, we need to find the minimum number of swaps required to transform s into t. Two strings are K-similar if we can swap exactly K pairs of characters in s to make it equal to t.

For example, if s = "abc" and t = "bac", we need only 1 swap to transform "abc" to "bac" by swapping characters at positions 1 and 2.

Algorithm

We use BFS (Breadth-First Search) to find the minimum number of swaps ?

• neighbors() function: Generates all possible strings after one valid swap

• Main BFS logic: Explores all possible transformations level by level

• Early termination: Stops when we find the target string

Implementation

from collections import deque

def k_similar_strings(s, t):
    def neighbors(string_data):
        # Find first position where characters don't match
        for i, char in enumerate(string_data):
            if char != t[i]:
                break
        
        # Try swapping with all valid positions
        for j in range(i + 1, len(string_data)):
            if string_data[j] == t[i]:
                # Perform swap
                string_data[i], string_data[j] = string_data[j], string_data[i]
                yield "".join(string_data)
                # Undo swap for next iteration
                string_data[i], string_data[j] = string_data[j], string_data[i]
    
    # BFS to find minimum swaps
    queue = deque([(s, 0)])
    visited = {s}
    
    while queue:
        current_string, swap_count = queue.popleft()
        
        # Check if we reached target
        if current_string == t:
            return swap_count
        
        # Generate all possible next states
        for neighbor in neighbors(list(current_string)):
            if neighbor not in visited:
                visited.add(neighbor)
                queue.append((neighbor, swap_count + 1))
    
    return 0

# Example usage
s = "abc"
t = "bac"
result = k_similar_strings(s, t)
print(f"Minimum swaps needed: {result}")

Minimum swaps needed: 1

How It Works

The algorithm works by exploring all possible single-character swaps in a breadth-first manner ?

1. Find mismatch: Locate the first position where s[i] != t[i]

2. Generate swaps: Try swapping s[i] with all valid positions where s[j] == t[i]

3. BFS exploration: Use a queue to explore all possibilities level by level

4. Track visited: Avoid revisiting the same string configuration

Example with More Complex Input

# Test with a more complex example
s1 = "abcd"
t1 = "dcba"
result1 = k_similar_strings(s1, t1)
print(f"'{s1}' to '{t1}' requires: {result1} swaps")

s2 = "abcdef"
t2 = "fedcba"
result2 = k_similar_strings(s2, t2)
print(f"'{s2}' to '{t2}' requires: {result2} swaps")

'abcd' to 'dcba' requires: 2 swaps
'abcdef' to 'fedcba' requires: 3 swaps

Time and Space Complexity

• Time Complexity: O(N! × N) in worst case, where N is string length

• Space Complexity: O(N!) for storing visited states

Conclusion

This BFS approach guarantees finding the minimum number of swaps needed to transform one anagram into another. The algorithm efficiently explores all possible swap combinations while avoiding redundant computations through visited state tracking.