<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>

#define N ('z' - 'a' + 1)
class T {
public:
bool leaf;
T* child[N];
    T() {
        for (int i = 0; i < N; ++i)
            child[i] = 0;
        leaf = false;
    }
    void insert(string& w) {
        T* node = this;
        for (int i = 0; i < w.size(); ++i) {
            if (!node->child[w[i] - 'a']) {
                node->child[w[i] - 'a'] = new T();
            }
            node = node->child[w[i] - 'a'];
        }
        node->leaf = true;
    }
    vector<string> sub(string w) {
        T* node = this;
        for (int i = 0; i < w.size(); ++i) {
            if (!node->child[w[i] - 'a']) return {};
            node = node->child[w[i] - 'a'];
        }
        vector<string> ans;
        queue<T*> q;
        queue<string> qs;
        q.push(node);
        qs.push("");
        while (!q.empty()) {
            if (q.front()->leaf) {
                ans.push_back(w + qs.front());
            }
            for (int i = 0; i < N; ++i) {
                if (q.front()->child[i]) {
                    q.push(q.front()->child[i]); 
                    qs.push(qs.front() + (char)('a' + i));
                }
            }
            q.pop();
            qs.pop();
        }
        sort(ans.begin(), ans.end());
        vector<string> ret;
        for (int i = 0; i < (3 < ans.size() ? 3 : ans.size()); ++i) 
            ret.push_back(ans[i]);
        return ret;
    }
};
class Solution {
public:
    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        T t;
        for (int i = 0; i < products.size(); ++i) {
            t.insert(products[i]);
        } 
        vector<vector<string>> ans;
        for (int i = 1; i <= searchWord.size(); ++i) {
            ans.push_back(t.sub(searchWord.substr(0, i)));
        }
        return ans;
    }
};
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