<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;
      }
      bool r_growing = true; 
      // TODO(caml): need ceil of double
    //   int num_cols = std::ceil(s.size() / (numRows + numRows - 2)) * (numRows - 1);
      int num_cols = std::ceil(static_cast<double>(s.size()) / (numRows + numRows - 2)) * (numRows - 1);
      std::vector<std::vector<char>> matrix(/*size=*/numRows, 
        /*val=*/std::vector<char>(/*size=*/num_cols, /*val=*/' ')); 
      
    //   std::cout << "num_cols: " << num_cols << std::endl;
      int r = 0; 
      int c = 0; 
      for (int i = 0; i < s.size(); ++i) {
        // std::cout << "r: " << r << ", c: " << c << std::endl;
        matrix[r][c] = s[i]; 
        if (r == numRows - 1) {
          r_growing = false; 
          r -= 1; 
        } else if (r == 0) {
          r_growing = true;
          r += 1; 
        } else {
          r += (r_growing ? 1 : -1);
        }
        if (!r_growing) {
          c += 1; 
        }
      }
      std::string out; 
      out.reserve(matrix.size() * matrix[0].size()); 
      for (const auto& row : matrix) {
        for (const char c : row) {
          if (c != ' ') {
            out.push_back(c); 
          }
          
        }
      }
      return out; 
    }
};
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