<p>You are given an array of strings <code>products</code> and a string <code>searchWord</code>.</p>

<p>Design a system that suggests at most three product names from <code>products</code> after each character of <code>searchWord</code> is typed. Suggested products should have common prefix with <code>searchWord</code>. If there are more than three products with a common prefix return the three lexicographically minimums products.</p>

<p>Return <em>a list of lists of the suggested products after each character of </em><code>searchWord</code><em> is typed</em>.</p>

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

<pre>
<strong>Input:</strong> products = [&quot;mobile&quot;,&quot;mouse&quot;,&quot;moneypot&quot;,&quot;monitor&quot;,&quot;mousepad&quot;], searchWord = &quot;mouse&quot;
<strong>Output:</strong> [[&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;],[&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;],[&quot;mouse&quot;,&quot;mousepad&quot;],[&quot;mouse&quot;,&quot;mousepad&quot;],[&quot;mouse&quot;,&quot;mousepad&quot;]]
<strong>Explanation:</strong> products sorted lexicographically = [&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;,&quot;mouse&quot;,&quot;mousepad&quot;].
After typing m and mo all products match and we show user [&quot;mobile&quot;,&quot;moneypot&quot;,&quot;monitor&quot;].
After typing mou, mous and mouse the system suggests [&quot;mouse&quot;,&quot;mousepad&quot;].
</pre>

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

<pre>
<strong>Input:</strong> products = [&quot;havana&quot;], searchWord = &quot;havana&quot;
<strong>Output:</strong> [[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;],[&quot;havana&quot;]]
<strong>Explanation:</strong> The only word &quot;havana&quot; will be always suggested while typing the search word.
</pre>

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

<ul>
	<li><code>1 &lt;= products.length &lt;= 1000</code></li>
	<li><code>1 &lt;= products[i].length &lt;= 3000</code></li>
	<li><code>1 &lt;= sum(products[i].length) &lt;= 2 * 10<sup>4</sup></code></li>
	<li>All the strings of <code>products</code> are <strong>unique</strong>.</li>
	<li><code>products[i]</code> consists of lowercase English letters.</li>
	<li><code>1 &lt;= searchWord.length &lt;= 1000</code></li>
	<li><code>searchWord</code> consists of lowercase English letters.</li>
</ul>

auto init = [](){
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    return 'c';
}();

class Trie {
public:
    bool ed[20007];
    int child[26][20007], num;
    Trie() {
        memset(ed, 0, sizeof(ed));
        memset(child, 0, sizeof(child));
        num = 0;
    }
    
    int getChild(int cur, char c)
    {
        return child[c - 'a'][cur];
    }

    bool isEd(int cur)
    {
        return ed[cur];
    }

    void insert(string word) {
        int cur = 0;
        for (char c : word)
        {
            if (!child[c - 'a'][cur]) child[c - 'a'][cur] = ++num;
            cur = child[c - 'a'][cur];
        }
        ed[cur] = 1;
    }

    void dfs(int u, string sug, vector<string>& suggestions)
    {
        if (suggestions.size() == 3) return;
        if (isEd(u)) 
        {
            suggestions.push_back(sug);
        }
        for (int i = 0; i < 26; i++)
        {
            int v = getChild(u, i + 'a');
            if (v) dfs(v, sug + char(i + 'a'), suggestions);
        }
    }   
};

class Solution {
public:
    Trie* trie;
    Solution() {
        trie = new Trie();
    }

    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        for (string product : products) {
            trie->insert(product);
        }
        vector<vector<string>> ans;
        string tmp;
        int cur = 0;
        for (char ch : searchWord) {
            tmp += ch;
            cur = trie->getChild(cur, ch);
            if (cur == 0) break; 
            vector<string> suggestions;
            trie->dfs(cur, tmp, suggestions);
            ans.push_back(suggestions);
        }
        while (ans.size() < searchWord.size()) {
            ans.push_back({});
        }
        return ans;
    }

    ~Solution() {
        delete trie;
    }
};
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