Word Ladder I and II 🎯

Welcome to an exciting journey into the world of Word Ladders I and II! These are fascinating problems that test both your programming skills and your linguistic prowess. Let's dive in!

What are Word Ladders? 📝

Word Ladders are word puzzles where you're given two words and the challenge is to find a sequence of words (a ladder) where each word differs from the previous one by exactly one letter. For example, given the words CAT and DOG, a valid word ladder would be:

CAT
CATS
DOGS
DOG

In this case, we changed CAT to CATS by adding one letter, then changed CATS to DOGS by replacing one letter, and finally changed DOGS to DOG by removing one letter.

Word Ladder I 📝

Word Ladder I is a classic problem where you're given two words and you have to find the shortest possible ladder between them. Let's write a Python solution for this!

python

# A simple function to check if two words differ by exactly one letter
def neighbor(word1, word2):
    return len(word1) == len(word2) and abs(ord(word1[0]) - ord(word2[0])) == 1

# Main function to find the shortest word ladder between two words
def word_ladder(start, end):
    # We'll use a dictionary to store all words that are one letter away from our current word
    neighbors = {}

    # Let's populate the dictionary for the starting word
    for word in words:
        if neighbor(start, word):
            neighbors[word] = 1

    # Now we'll explore the ladder
    steps = 0
    current = start
    while current != end:
        next_words = neighbors.copy()
        neighbors.clear()

        # Find words that are one letter away from the current word
        for word in words:
            if neighbor(current, word):
                if word not in next_words:
                    next_words[word] = 1

        # Check if we found the next word in the ladder
        next_word = None
        for word in next_words:
            if not neighbor(word, current[1:-1]) and word != current:
                next_word = word
                break

        # If we didn't find the next word, we've hit a dead-end, so we'll backtrack
        if not next_word:
            current = current[:-1]
            steps -= 1
            if steps == 0:
                break

        # Move forward in the ladder
        current = next_word
        steps += 1

    # If we reached the end word, we've found the shortest ladder
    return current == end and steps

💡 Pro Tip: The above solution assumes that you have a list of words available called words. You can get this list from a dictionary file, for example.

Word Ladder II 📝

Word Ladder II is a slightly more challenging problem where you're given two words and a list of other words. The goal is to find the shortest ladder between the two given words that contains every word from the list exactly once.

Let's modify our previous solution to accommodate this new requirement:

python

# A simple function to check if a word is in the given list of words
def in_list(word, words):
    return word in words

# Main function to find the shortest word ladder between two words that contains a given list of words
def word_ladder_ii(start, end, words):
    # Let's populate the dictionary for the starting word
    neighbors = {}

    # Find words that are one letter away from the starting word and are in the given list
    for word in words:
        if neighbor(start, word) and in_list(word, words):
            neighbors[word] = 1

    # Now we'll explore the ladder
    steps = 0
    current = start
    while current != end:
        next_words = neighbors.copy()
        neighbors.clear()

        # Find words that are one letter away from the current word and are in the given list
        for word in words:
            if neighbor(current, word) and in_list(word, words):
                if word not in next_words:
                    next_words[word] = 1

        # Check if we found the next word in the ladder
        next_word = None
        for word in next_words:
            if not neighbor(word, current[1:-1]) and word != current:
                next_word = word
                break

        # If we didn't find the next word, we've hit a dead-end, so we'll backtrack
        if not next_word:
            current = current[:-1]
            steps -= 1
            if steps == 0:
                break

        # Move forward in the ladder
        current = next_word
        steps += 1

    # If we reached the end word and all words from the list are in the ladder, we've found the shortest ladder
    if current == end and set(current.split('-')) == set(words):
        return current
    return None

Practice Time! 🎯

Now that you've learned the basics, let's put your skills to the test! Try solving the following problems:

That's all for today! Keep practicing and soon you'll be solving complex Word Ladders like a pro. Happy coding! 💡 📝 ✅