<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:
    struct Node {
        unordered_map<char, unique_ptr<Node>> children;
        bool isEnd;
        Node() : isEnd(false) {}
    };

    unique_ptr<Node> root;

    void insert(const string& word) {
        Node* node = root.get();
        for (char ch : word) {
            if (!node->children.count(ch)) {
                node->children[ch] = make_unique<Node>();
            }
            node = node->children[ch].get();
        }
        node->isEnd = true;
    }

    void dfs(Node* node, const string& word, priority_queue<string>& pq) {
        if (node->isEnd) {
            pq.push(word);
            if (pq.size() > 3) pq.pop();
        }

        for (auto& [key, value] : node->children) {
            dfs(value.get(), word + key, pq);
        }
    }

    vector<string> startWith(const string& word) {
        Node* node = root.get();
        priority_queue<string> pq;
        for (char ch : word) {
            if (!node->children.count(ch)) return {};
            node = node->children[ch].get();
        }
        dfs(node, word, pq);

        vector<string> generatedWords;
        while (!pq.empty()) {
            generatedWords.insert(generatedWords.begin(), pq.top());
            pq.pop();
        }

        return generatedWords;
    }

public:
    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        root = make_unique<Node>();
        int length = searchWord.size();
        vector<vector<string>> words;

        for (const string& product : products) {
            insert(product);
        }

        string word = "";
        for (int i = 0; i < length; i++) {
            word += searchWord[i];
            words.push_back(startWith(word));
        }

        return words;
    }
};

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