<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) {
        map<char,int> mp;
        string ans = "";
        int n = s.size();
        for(char ch : s)
        {
            mp[ch]++;
        }
        int i = 0;
        bool check = true;
        while(i < n)
        {
            if(check)
            {
                for(auto it = mp.begin(); it != mp.end(); it++)
                {
                    if(it-> second >= 1)
                    {
                        ans += it-> first;
                        it-> second--;
                        i++;
                    }
                }
                check = false;
            }
            else if(!check)
            {
                auto it = mp.end();
                do
                {
                    it--;
                    if(it-> second >= 1)
                    {
                        ans += it-> first;
                        it-> second--;
                        i++;
                    }
                } while(it != mp.begin());
                check = true;
            }
        }
        return ans;
    }
};
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