Fun Algorithm

Detecting Single-Character Differences

Here’s an algorithm to check if the input array is a sequence of strings that differs by exactly one character.

Breaking Down the Algorithm:

bool HasExactlyOneCharacterDifference(string A, string B){
    var singleMismatch = false;

    for(int i=0; i<A.Length; i++){
        if(A[i] != B[i]){
            if(singleMismatch) return false;
            singleMismatch = true;
        }
    }

    return singleMismatch;
}

bool FindSequenceWithSingleCharacterChanges(string next, List<string> list){
    foreach(var item in list){
        if(HasExactlyOneCharacterDifference(next, item)){
            var listCopy = new List<string>(list);
            Console.WriteLine($"Matched: {next} to {item}");
            if(listCopy.Count == 2) return true;
            Console.WriteLine(listCopy.Count);
            listCopy.Remove(next);
            if(FindSequenceWithSingleCharacterChanges(item, listCopy)){
                return true;
            }
        }
    }
    return false;
}

bool HasValidSequence(string[] inputArray) {
    foreach(var item in inputArray){
        if(FindSequenceWithSingleCharacterChanges(item, inputArray.ToList())){
            return true;
        }
    }
    return false;
}

The core of the algorithm works in three parts:

1. HasExactlyOneCharacterDifference Function:

   • Compares two strings character by character.
   • Returns true if there’s exactly one mismatched character, false otherwise.

2. FindSequenceWithSingleCharacterChanges Function:

   • Recursively explores possible chains of strings.
   • Takes a next string and a list of remaining strings as input.
   • For each remaining string, checks if it has a single mismatch with next.
   • If a match is found:
     • Prints the matched pair.
     • Creates a copy of the remaining list, removing the matched string.
     • Recursively calls FindSequenceWithSingleCharacterChanges with the matched string and the reduced list.
     • If the recursive call returns true, the entire chain is valid.
     • If the recursive call returns false, the function backtracks and explores other possibilities.

3. HasValidSequence Function:

   • Iterates through each string in the input array.
   • Calls the FindSequenceWithSingleCharacterChanges function with the current string and the remaining list.
   • If any chain is found, the function returns true.
   • If no chain is found after checking all strings, the function returns false.

Example: Let’s take an example with input:

string[] inputArray = { "abc", "abx", "abz", "xyz", "zyx" };
bool result = HasValidSequence(inputArray);
Console.WriteLine($"Result: {result}");

If there are strings in the list that only have one mismatch with each other, the algorithm will print the matched pairs and return true when a valid match is found.

Key Points:

• Recursive Approach: The FindSequenceWithSingleCharacterChanges function employs recursion to efficiently explore all possible combinations of string pairings.
• Backtracking: The recursive nature allows the algorithm to backtrack when a dead-end is reached, ensuring all possibilities are considered.
• Early Termination: The function returns true as soon as a valid chain is found, optimizing the search process.
• Time Complexity: The time complexity of this algorithm is exponential in the worst case, as it explores all possible permutations. However, in practical scenarios, the average case performance might be significantly better due to early termination and pruning.