<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 Solution {
public:
    //key 값과 같거나 큰 값이 처음으로 나오는 위치 반환
    int bs_lowerbound(string typing, vector<string> products, int len){
        int l = 0, r = products.size();
        while(l < r){
            int m = l + (r - l)/2;
            string cmp = products[m].substr(0, len);
            //curr 값이 key값과 같거나 크다면 왼쪽 부분만 탐색 
            if(typing <= cmp){
                r = m;
            }
            else{
                l = m + 1;
            }
        }
        //cout << "\n";
        return l;
    }

    vector<vector<string>> suggestedProducts(vector<string>& products, string searchWord) {
        vector<vector<string>> suggests;
        sort(products.begin(), products.end());
        string typing = "";
        int len = 1;

        for(auto c : searchWord){
            typing += c;
            vector<string> tmp;
            int target = bs_lowerbound(typing, products, len);

            while(target < products.size() && !products[target].compare(0, len, typing) && tmp.size() < 3){
                tmp.push_back(products[target++]);
            }
            suggests.push_back(tmp);
            len++;
        }
        return suggests;
    }
};
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