<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) {
        if (numRows == 1) {
            return s;
        }

        int sections = ceil(s.length() / (2 * numRows - 2.0));
        int numCols = sections * (numRows - 1);

        vector<vector<char>> matrix(numRows, vector<char>(numCols, string::npos));
        int x = 0;
        int y = 0;
        int i = 0;
        while (i < s.length()) {
            while (y < numRows && i < s.length()) {
                matrix[y][x] = s[i];
                i++;
                y++;
            }

            y -= 2;
            x++;

            while (y > 0 && i < s.length()) {
                matrix[y][x] = s[i];
                y--;
                x++;
                i++;
            }
        }

        string zigzagged;
        for (auto& row : matrix) {
            for (auto& c : row) {
                if (c != string::npos) {
                    zigzagged += c;
                }
            }
        }

        return zigzagged;
    }
};
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