<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 {
public:
    char data;
    TrieNode* children[26];
    bool isTerminal;
    
    TrieNode(char ch) {
        data = ch;
        isTerminal = false;
        for (int i = 0; i < 26; i++) {
            children[i] = NULL;
        }
    }
};

class Trie {
public:
    TrieNode* root;
    
    Trie() {
        root = new TrieNode('\0');
    }
    
    void insertUtil(TrieNode* root, string word) {
        if (word.length() == 0) {
            root->isTerminal = true;
            return;
        }
        int index = word[0] - 'a';
        TrieNode* child;
        
        if (root->children[index] != NULL) {
            child = root->children[index];
        } else {
            child = new TrieNode(word[0]);
            root->children[index] = child;
        }
        insertUtil(child, word.substr(1));
    }
    
    void insertWord(string word) {
        insertUtil(root, word);
    }
    
    bool searchUtil(TrieNode* root, string word) {
        if (word.length() == 0) {
            return root->isTerminal;
        }
        
        int index = word[0] - 'a';
        TrieNode* child;
        
        if (root->children[index] != NULL) {
            child = root->children[index];
        } else {
            return false;
        }
        return searchUtil(child, word.substr(1));
    }
    
    bool searchWord(string word) {
        return searchUtil(root, word);
    }
};

class Solution {
public:
    string replaceWords(vector<string>& dictionary, string sentence) {
        Trie t;
        for (const string& word : dictionary) {
            t.insertWord(word);
        }
        string result;
        int start = 0;
        for (int i = 0; i < sentence.length(); i++) {
            if (sentence[i] == ' ') {
                string word = sentence.substr(start, i - start);
                string root = getRoot(t, word);
                result += root + ' ';
                start = i + 1;
            }
        }
        
        string lastWord = sentence.substr(start);
        result += getRoot(t, lastWord);
        
        return result;
    }
    
    string getRoot(Trie& t, const string& word) {
        TrieNode* node = t.root;
        string root;
        for (char ch : word) {
            int index = ch - 'a';
            if (node->children[index] == NULL) {
                return word; 
            }
            node = node->children[index];
            root += ch;
            if (node->isTerminal) {
                return root;
            }
        }
        return word;
    }
};

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