<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 Solution {
private:
    struct Node
    {
        char val;
        unordered_map<char, Node*> children;
        Node(char c = '\0') {val = c;}
    };
    Node* root;
public:
    string replaceWords(vector<string>& dictionary, string sentence) {
        if (sentence.length() == 0)
            return sentence;
        
        root = new Node();
        for (string s : dictionary)
            insert(s);
        vector<string> words;
        string s = "";
        for (char c : sentence)
        {
            if (c != ' ')
                s += c;
            else
            {
                words.push_back(s);
                s = "";
            }
        }
        words.push_back(s);
        
        for (string& word : words)
        {
            string prefix = "";
            for (int j = 0; j < word.length()-1; j++)
            {
                prefix += word[j];
                if (startsWith(prefix))
                {
                    if (search(prefix))
                    {
                        word = prefix;
                        break;
                    }
                }
                else
                    break;
            }
            
            
            
        }
        string result = words[0];
        for (int i = 1; i < words.size(); i++)
            result += " " + words[i];
        return result;
    }
    
    void insert(string word) {
        Node* traverse = root;
        for (char c : word)
        {
            if (traverse->children.count(c) > 0)
                traverse = traverse->children[c];
            else
            {
                Node* child = new Node(c);
                traverse->children.insert(make_pair(c, child));
                traverse = child;
            }
        }
        traverse->children.insert(make_pair('0', nullptr));
    }
    
    bool search(string word) {
        Node* traverse = root;
        for (char c : word)
        {
            if (traverse->children.count(c) > 0)
                traverse =  traverse->children[c];
            else
                return false;
        }
        return traverse->children.count('0') > 0;
        
    }
    
    bool startsWith(string prefix) {
        Node* traverse = root;
        for (char c : prefix)
        {
            if (traverse->children.count(c) > 0)
                traverse =  traverse->children[c];
            else
                return false;
        }
        return true;
    }
    
    ~Solution()
    {
        queue<Node*> deleteNodes;
        deleteNodes.push(root);
        while (deleteNodes.size()>0)
        {
            Node* d = deleteNodes.front();
            deleteNodes.pop();
            for (auto& p : d->children)
            {
                if (p.second)
                    deleteNodes.push(p.second);
            }
            delete d;
        }
    }
};
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