<p>In English, we have a concept called <strong>root</strong>, which can be followed by some other word to form another longer word - let&#39;s call this word <strong>derivative</strong>. For example, when the <strong>root</strong> <code>&quot;help&quot;</code> is followed by the word <code>&quot;ful&quot;</code>, we can form a derivative <code>&quot;helpful&quot;</code>.</p>

<p>Given a <code>dictionary</code> consisting of many <strong>roots</strong> and a <code>sentence</code> consisting of words separated by spaces, replace all the derivatives in the sentence with the <strong>root</strong> forming it. If a derivative can be replaced by more than one <strong>root</strong>, replace it with the <strong>root</strong> that has <strong>the shortest length</strong>.</p>

<p>Return <em>the <code>sentence</code></em> after the replacement.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> dictionary = [&quot;cat&quot;,&quot;bat&quot;,&quot;rat&quot;], sentence = &quot;the cattle was rattled by the battery&quot;
<strong>Output:</strong> &quot;the cat was rat by the bat&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> dictionary = [&quot;a&quot;,&quot;b&quot;,&quot;c&quot;], sentence = &quot;aadsfasf absbs bbab cadsfafs&quot;
<strong>Output:</strong> &quot;a a b c&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= dictionary.length &lt;= 1000</code></li>
	<li><code>1 &lt;= dictionary[i].length &lt;= 100</code></li>
	<li><code>dictionary[i]</code> consists of only lower-case letters.</li>
	<li><code>1 &lt;= sentence.length &lt;= 10<sup>6</sup></code></li>
	<li><code>sentence</code> consists of only lower-case letters and spaces.</li>
	<li>The number of words in <code>sentence</code> is in the range <code>[1, 1000]</code></li>
	<li>The length of each word in <code>sentence</code> is in the range <code>[1, 1000]</code></li>
	<li>Every two consecutive words in <code>sentence</code> will be separated by exactly one space.</li>
	<li><code>sentence</code> does not have leading or trailing spaces.</li>
</ul>

class TrieNode:
    def __init__(self):
        self.children = {}  # Dictionary to store child nodes for each character
        self.is_end = False  # Boolean to mark the end of a word
        self.word = None  # To store the root word when we reach the end of a word

class Trie:
    def __init__(self):
        self.root = TrieNode()  # Initialize the root node of the Trie
    
    def insert(self, word):
        node = self.root  # Start from the root node
        for char in word:  # Iterate over each character in the word
            if char not in node.children:  # If the character is not already a child
                node.children[char] = TrieNode()  # Create a new TrieNode for the character
            node = node.children[char]  # Move to the next node (child)
        node.is_end = True  # Mark the end of the word at this node
        node.word = word  # Store the word at the end node to retrieve it later
    
    def find_root(self, word):
        node = self.root  # Start from the root node
        for char in word:  # Iterate over each character in the word
            if char not in node.children:  # If the character is not found in the Trie
                return word  # Return the original word as no root exists
            node = node.children[char]  # Move to the next node (child)
            if node.is_end:  # If this node marks the end of a root word
                return node.word  # Return the root word
        return word  # If no root is found, return the original word

class Solution:
    def replaceWords(self, dictionary: List[str], sentence: str) -> str:
        trie = Trie()  # Create a new Trie
        for root in dictionary:  # Insert all root words from the dictionary into the Trie
            trie.insert(root)  # Call the insert method to add the root word
        
        words = sentence.split()  # Split the sentence into words
        for i, word in enumerate(words):  # Iterate over each word in the sentence
            replacement = trie.find_root(word)  # Find the root word for the current word
            words[i] = replacement if replacement is not None else word  # Replace with root or keep the original word
        
        return " ".join(words)  # Join the words back into a sentence and return the result

# Example usage
dictionary = ["cat", "bat", "rat"]  # List of root words
sentence = "the cattle was rattled by the battery"  # Sentence to be processed
sol = Solution()  # Create a solution instance
print(sol.replaceWords(dictionary, sentence))  # Call the method and print the result

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