<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>

import math
class Solution:
    def convert(self, s: str, numRows: int) -> str:
        if numRows == 1 or numRows >= len(s):
            return s

        n = len(s)
        num_sections = math.ceil(n/(2*numRows-2))
        numCols =  num_sections * (numRows-1)

        matrix = [[""] * numCols for row in range(numRows)]

        # Boolean to encode whether we are placing value on diagnol
        on_diagnol = False # False first

        current_row = 0
        current_col = 0

        for char in s:
            # Placing character in matrix
            matrix[current_row][current_col] = char

            if current_row == (numRows-1) and on_diagnol==False:
                on_diagnol = True
            
            if current_row == 0 and on_diagnol==True:
                on_diagnol = False

            # if on diagnol, the row and col index change
            if on_diagnol:
                current_row -= 1
                current_col += 1

            else:
                current_row += 1

        answer = ""
        for row in matrix:
            answer += "".join(row)
        return answer

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