Search Suggestions System
<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; Array; String; Binary Search; Sorting; Heap (Priority Queue)
class Trie {
public:
    void insert(string& w, int i) {
        Trie* node = this;
        for (int j = 0; j < w.size(); ++j) {
            int idx = w[j] - 'a';
            if (!node->children[idx]) {
                node->children[idx] = new Trie();
            }
            node = node->children[idx];
            if (node->v.size() < 3) {
                node->v.push_back(i);
            }
        }
    }

    vector<vector<int>> search(string& w) {
        Trie* node = this;
        int n = w.size();
        vector<vector<int>> ans(n);
        for (int i = 0; i < w.size(); ++i) {
            int idx = w[i] - 'a';
            if (!node->children[idx]) {
                break;
            }
            node = node->children[idx];
            ans[i] = move(node->v);
        }
        return ans;
    }

private:
    vector<Trie*> children = vector<Trie*>(26);
    vector<int> v;
};

class Solution {
public:
    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        sort(products.begin(), products.end());
        Trie* trie = new Trie();
        for (int i = 0; i < products.size(); ++i) {
            trie->insert(products[i], i);
        }
        vector<vector<string>> ans;
        for (auto& v : trie->search(searchWord)) {
            vector<string> t;
            for (int i : v) {
                t.push_back(products[i]);
            }
            ans.push_back(move(t));
        }
        return ans;
    }
};