<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>

#include <string>
#include <map>
#include <vector>
#include <algorithm>

class Solution {
public:
    string sortString(string s) {
        map<char, int> frequency_map;
        for (char c: s){
            frequency_map[c]++;
        }

        vector<char> asc_list,desc_list;
        for (const auto& entry:frequency_map){
            asc_list.push_back(entry.first);
        }

        desc_list=asc_list;
        sort(asc_list.begin(),asc_list.end());
        sort(desc_list.begin(),desc_list.end(),greater<char>());

        string res;
        while (!frequency_map.empty()){
            for (char c : asc_list) {
                if (frequency_map.count(c) && frequency_map[c] > 0) {
                    res += c;
                    frequency_map[c]--;
                    if (frequency_map[c] == 0) {
                        frequency_map.erase(c);
                    }
                }
            }

            // Add characters in descending order
            for (char c : desc_list) {
                if (frequency_map.count(c) && frequency_map[c] > 0) {
                    res += c;
                    frequency_map[c]--;
                    if (frequency_map[c] == 0) {
                        frequency_map.erase(c);
                    }
                }
            }
        }

        return res;
    }
};
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