<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>

class Solution {
private:
    class Trie {
    private:
        struct Node {
            Node *next[26];
            bool last;
            
            Node() {for (int i = 0; i < 26; i++) next[i] = nullptr; last = 0;}
        };
        Node *head = new Node;

    public:
        void insert(string str) {
            Node *cur = head;
            for (int i = 0; i < str.size(); cur = cur->next[str[i]-'a'], i++) {
                if (cur->next[str[i]-'a'] == nullptr) cur->next[str[i]-'a'] = new Node;
            }
            cur->last = 1;
        }

        vector<string> search(string str) {
            Node *cur = head;
            vector<string> ret;
            for (int i = 0; i < str.size(); cur = cur->next[str[i]-'a'], i++) {
                if (cur->next[str[i]-'a'] == nullptr) return {};
            }

            int cnt = 3; dfs(str, cur, cnt, ret);
            return ret;
        }

        void dfs(string& str, Node *cur, int& cnt, vector<string>& ret) {
            if (cur->last == 1) {
                ret.push_back(str);
                cnt--;
            }

            for (int i = 0; i < 26; i++) {
                if (cur->next[i] == nullptr or cnt == 0) continue;
                str.push_back('a' + i);
                dfs(str, cur->next[i], cnt, ret);
                str.pop_back();
            }
        }
    };

public:
    vector<vector<string>> suggestedProducts(vector<string>& prod, string word) {
        vector<vector<string>> ans;
        Trie *obj = new Trie;
        for (int i = 0; i < prod.size(); i++) obj->insert(prod[i]);

        string cur = "";
        for (int i = 0; i < word.size(); i++) {
            cur.push_back(word[i]);
            ans.push_back(obj->search(cur));
        }

        return ans;
    }
};
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