<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>

struct TrieNode {
    TrieNode *child[26];
    bool is_word;
    TrieNode() {
        for (auto &a : child) {
            a = NULL;
        }
        is_word = false;
    }
};

class Solution {
    TrieNode *root;
    public:
    void insert(string word) {
        if (root == NULL)
            root = new TrieNode();
        TrieNode *p = root;
        for (auto &w : word) {
            int i = w - 'a';
            if (!p->child[i]) {
                p->child[i] = new TrieNode(); 
            }
            p = p->child[i];
        }
        p->is_word = true;
    }
    
    void backtrack(TrieNode *p, string &replaced, string word, int i) {
        if (i == word.size() || !p || p->is_word) {
            replaced = p && p->is_word ? replaced : ""; 
            return;
        }
        int l = word[i] - 'a';
        if (p->child[l]) {
            replaced.push_back(word[i]);
            backtrack(p->child[l], replaced, word, i + 1);
            return;
        }
        replaced = "";
    }

    string replaceWords(vector<string>& dictionary, string sentence) {
        for (int i = 0; i < dictionary.size(); i++) {
            insert(dictionary[i]);
        } 
        int i = 0, n = sentence.size();
        string result = "";
        while (i < n) {
            string word;
            if (sentence[i] == ' ') {
                result += sentence[i];
                i++;
                continue;
            }
            while (i < n && sentence[i] != ' ') {
                word.push_back(sentence[i]);
                i++;
            }
            string replaced = "";
            backtrack(root, replaced, word, 0);
            if (replaced == "")
                result += word;
            else
                result += replaced;
            //cout<<word<<":"<<replaced<<"\n";
        } 
        return result;
    }
};
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