<p>You are given a string <code>s</code>. Reorder the string using the following algorithm:</p>

<ol>
	<li>Remove the <strong>smallest</strong> character from <code>s</code> and <strong>append</strong> it to the result.</li>
	<li>Remove the <strong>smallest</strong> character from <code>s</code> that is greater than the last appended character, and <strong>append</strong> it to the result.</li>
	<li>Repeat step 2 until no more characters can be removed.</li>
	<li>Remove the <strong>largest</strong> character from <code>s</code> and <strong>append</strong> it to the result.</li>
	<li>Remove the <strong>largest</strong> character from <code>s</code> that is smaller than the last appended character, and <strong>append</strong> it to the result.</li>
	<li>Repeat step 5 until no more characters can be removed.</li>
	<li>Repeat steps 1 through 6 until all characters from <code>s</code> have been removed.</li>
</ol>

<p>If the smallest or largest character appears more than once, you may choose any occurrence to append to the result.</p>

<p>Return the resulting string after reordering <code>s</code> using this algorithm.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aaaabbbbcccc&quot;
<strong>Output:</strong> &quot;abccbaabccba&quot;
<strong>Explanation:</strong> After steps 1, 2 and 3 of the first iteration, result = &quot;abc&quot;
After steps 4, 5 and 6 of the first iteration, result = &quot;abccba&quot;
First iteration is done. Now s = &quot;aabbcc&quot; and we go back to step 1
After steps 1, 2 and 3 of the second iteration, result = &quot;abccbaabc&quot;
After steps 4, 5 and 6 of the second iteration, result = &quot;abccbaabccba&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;rat&quot;
<strong>Output:</strong> &quot;art&quot;
<strong>Explanation:</strong> The word &quot;rat&quot; becomes &quot;art&quot; after re-ordering it with the mentioned algorithm.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 500</code></li>
	<li><code>s</code> consists of only lowercase English letters.</li>
</ul>

class Solution {
public:
    string sortString(string s) {

        string res;
        std::map<int,int> freq_map;

        for (auto c : s) {
            auto itr = freq_map.find(static_cast<int>(c));
            
            if (itr == freq_map.end()) {
                freq_map.insert(std::make_pair<int,int>(c,1));
            } else {
                itr->second++;
            }
        }

        while(res.size() != s.size()) {
            // grab the smallest
            auto itr = freq_map.begin();
            while (itr != freq_map.end()) {
                while (itr->second == 0 && itr != freq_map.end()) itr++;
                if (itr != freq_map.end()) {
                    res.push_back(static_cast<char>(itr->first));
                    itr->second--;
                    itr++; // increment once so we don't get the same char
                }
            }

            auto ritr = freq_map.rbegin(); // now start from end end and work backwards
            while (ritr != freq_map.rend()) {
                while (ritr->second == 0 && ritr != freq_map.rend()) ritr++;
                if (ritr != freq_map.rend()) {
                    res.push_back(static_cast<char>(ritr->first));
                    ritr->second--;
                    ritr++; // increment once so we don't get the same char
                }
            }
        }

        return res;
        
    }

};
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