<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 {
public:
    struct TrieNode {
        map<char, TrieNode*> children;
        bool isEndOfWord = false;
    };

    class Trie {
    public:
        TrieNode* root;
        
        Trie() {
            root = new TrieNode();
        }
        
        void insert(const string& word) {
            TrieNode* node = root;
            for (char c : word) {
                if (!node->children[c]) {
                    node->children[c] = new TrieNode();
                }
                node = node->children[c];
            }
            node->isEndOfWord = true;
        }
        
        vector<string> getWordsStartingWith(const string& prefix) {
            vector<string> words;
            TrieNode* node = root;
            for (char c : prefix) {
                if (!node->children[c]) {
                    return words;
                }
                node = node->children[c];
            }
            dfs(node, prefix, words);
            return words;
        }
        
    private:
        void dfs(TrieNode* node, string currentWord, vector<string>& words) {
            if (words.size() == 3) return; // limit to 3 suggestions
            if (node->isEndOfWord) {
                words.push_back(currentWord);
            }
            for (auto& child : node->children) {
                dfs(child.second, currentWord + child.first, words);
            }
        }
    };

    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        sort(products.begin(), products.end());
        Trie trie;
        for (const string& product : products) {
            trie.insert(product);
        }
        
        vector<vector<string>> result;
        string prefix = "";
        for (char c : searchWord) {
            prefix += c;
            result.push_back(trie.getWordsStartingWith(prefix));
        }
        
        return result;
    }
};
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