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 {
    Trie[] children = new Trie[26];
    List<Integer> v = new ArrayList<>();

    public void insert(String w, int i) {
        Trie node = this;
        for (int j = 0; j < w.length(); ++j) {
            int idx = w.charAt(j) - 'a';
            if (node.children[idx] == null) {
                node.children[idx] = new Trie();
            }
            node = node.children[idx];
            if (node.v.size() < 3) {
                node.v.add(i);
            }
        }
    }

    public List<Integer>[] search(String w) {
        Trie node = this;
        int n = w.length();
        List<Integer>[] ans = new List[n];
        Arrays.setAll(ans, k -> new ArrayList<>());
        for (int i = 0; i < n; ++i) {
            int idx = w.charAt(i) - 'a';
            if (node.children[idx] == null) {
                break;
            }
            node = node.children[idx];
            ans[i] = node.v;
        }
        return ans;
    }
}

class Solution {
    public List<List<String>> suggestedProducts(String[] products, String searchWord) {
        Arrays.sort(products);
        Trie trie = new Trie();
        for (int i = 0; i < products.length; ++i) {
            trie.insert(products[i], i);
        }
        List<List<String>> ans = new ArrayList<>();
        for (var v : trie.search(searchWord)) {
            List<String> t = new ArrayList<>();
            for (int i : v) {
                t.add(products[i]);
            }
            ans.add(t);
        }
        return ans;
    }
}