<p>The string <code>&quot;PAYPALISHIRING&quot;</code> is written in a zigzag pattern on a given number of rows like this: (you may want to display this pattern in a fixed font for better legibility)</p>

<pre>
P   A   H   N
A P L S I I G
Y   I   R
</pre>

<p>And then read line by line: <code>&quot;PAHNAPLSIIGYIR&quot;</code></p>

<p>Write the code that will take a string and make this conversion given a number of rows:</p>

<pre>
string convert(string s, int numRows);
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;PAYPALISHIRING&quot;, numRows = 3
<strong>Output:</strong> &quot;PAHNAPLSIIGYIR&quot;
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;PAYPALISHIRING&quot;, numRows = 4
<strong>Output:</strong> &quot;PINALSIGYAHRPI&quot;
<strong>Explanation:</strong>
P     I    N
A   L S  I G
Y A   H R
P     I
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;A&quot;, numRows = 1
<strong>Output:</strong> &quot;A&quot;
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists of English letters (lower-case and upper-case), <code>&#39;,&#39;</code> and <code>&#39;.&#39;</code>.</li>
	<li><code>1 &lt;= numRows &lt;= 1000</code></li>
</ul>

class Solution {
public:
    string convert(string s, int numRows) {
        string *ret  = new string(s.length(),'a');
        if(numRows == 1 || numRows == s.length()){
            return s;
        }
        int colDis = numRows-2;
        int numCols = s.length()/(2*numRows-2)*(colDis+1)+s.length()%(2*numRows-2);
        int row = 0;
        int col = 0;
        int direction = 1;
        int count = 0;
        string mat(numCols*numRows,'$');
        for(int i=0;i<s.length();i++){
            mat[row*numCols+col] = s[i];
            row+=direction;
            if(direction < 1){
                col++;
            }
            if(row == numRows){
                direction*=-1;
                col++;
                row-=2;
            }
            if(row == 0){
                direction*=-1;
            }
        }
        for(int i=0;i<numCols*numRows;i++){
            if(mat[i]!= '$'){
                if(count < (*ret).length())
                    (*ret)[count] = mat[i];
                count++; 
            }
        }
        return (*ret);
    }
};
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