<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>

// Trie Node
struct Node {
    Node* next[26];
    priority_queue<string, vector<string>> maxHeap;

    Node() {
        for (int i = 0; i < 26; i++) {
            next[i] = nullptr;
        }
    }
};

class Solution {
public:
    // Keep track of the number suggestions currently made
    int curSuggestionCnt;

    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        vector<vector<string>> res;
        Node* root = new Node();

        // Add all the product names into the Trie
        for (string product: products) {
            Node* curNode = root;
            for (char c: product) {
                if (curNode->next[c - 'a'] == nullptr) {
                    curNode->next[c - 'a'] = new Node();
                }
                curNode = curNode->next[c - 'a'];

                // Ensure there are always at most 3 suggestions and lexicographically minimums 
                if (curNode->maxHeap.size() < 3) {
                    curNode->maxHeap.push(product);
                } else {
                    if (curNode->maxHeap.top() > product) {
                        curNode->maxHeap.pop();
                        curNode->maxHeap.push(product);
                    }
                }
            }
        }

        // Iterate through the search word character by character
        Node* curNode = root;
        for (char c: searchWord) {
            if (curNode == nullptr) {
                res.push_back({});
            } else {
                vector<string> curSuggestions;
                curNode = curNode->next[c - 'a'];
                if (curNode == nullptr) {
                    res.push_back({});
                    continue;
                } else {
                    while (!curNode->maxHeap.empty()) {
                        curSuggestions.push_back(curNode->maxHeap.top());
                        curNode->maxHeap.pop();
                    }
                    reverse(curSuggestions.begin(), curSuggestions.end());
                    res.push_back(curSuggestions);
                }
            }
        }

        return res;
    }
};
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