<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>

// P A Y P A L I S H I R  I  N  G

// 0 1 2 3 4 5 6 7 8 9 10 11 12 13
// P       A       H         N 
//   A   P   L   S   I    I     G
//     Y       I       R

// -->

// 0 1 2 3 4 5 6 7 8 9 10 11 12 13
// P A H N 
//         A P L S I I G
//                        Y  I  R

// P A H N A P L S I I G  Y  I  R

class Solution {
public:
    std::string convert(const std::string& s, int numRows) {
        if(numRows == 1) {
            return s;
        }
        // prepare string for output and reserve sufficient space in advance
        std::string result;
        result.resize(s.size());
        
        // fill output line by line
        auto maxStep = (numRows - 1) << 1;
        auto outIter = result.begin();
        for(int i = 0; i < numRows; ++i) {
            bool goingDown = true;
            for(auto rowIter = s.begin() + i; rowIter < s.end();) {
                *outIter = *rowIter;
                
                auto step = std::abs((maxStep * goingDown) - (i<<1));
                
                rowIter += step;
                outIter += bool(step);
                goingDown = !goingDown;
            }
        }
        return result;
    }
};
9706