<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 Node {
public:
    bool flag;
    Node* links[26] = {NULL};
    Node(){
        flag = false;
    }
};

class Solution {
    void add_word(Node* root, string &word){
        Node* curr = root;
        for(auto it: word){
            int ch = it-'a';
            if(!curr->links[ch]) curr->links[ch] = new Node();
            curr = curr->links[ch];
        }
        curr->flag = true;
    }

    void dfs(Node* curr, int &it, vector<string> &res, string s){
        if(it == 3) return;
        if(curr->flag) {
            it++;
            res.push_back(s);
        }
        if(it == 3) return;
        
        for(int i = 0; i<26; i++){
            if(curr->links[i]){
                s += char(i+'a');
                dfs(curr->links[i],it,res,s);
                s.erase(s.size()-1,1);
            }
        }
    }

    vector<string> compile(Node* root, char ch){
        Node* curr = root->links[ch-'a'];
        vector<string> res;
        string s = "";
        int it = 0;
        dfs(curr,it,res,s);
        return res;
    }

public:
    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        Node* root = new Node();
        for(auto it: products) add_word(root,it);

        int n = searchWord.size();
        vector<vector<string>> ans(n);
        for(int i = 0; i<n; i++){
            char ch = searchWord[i];
            if(!root->links[ch-'a']) break;
            
            vector<string> res = compile(root,ch);
            for(int j = 0; j<res.size(); j++){
                res[j] = searchWord.substr(0,i+1)+res[j];
            }
            root = root->links[ch-'a'];
            ans[i] = res;
        }

        return ans;
    }
};
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