<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>

struct rowGap {
    int first;
    int second;
};

/* 3:
4, 0
2, 2
0, 4
*/

/* 4:
6, 0
4, 2
2, 4
0, 6
*/

class Solution {
public:

    rowGap getRowGap(string s, int rowNum, int numRows) {
        if (numRows == 1) {
            return {.first = 0, .second = 1};
        } else {
            return {
                .first = (numRows - 1 - rowNum) * 2,
                .second = rowNum * 2
            };
        }
    }

    string convert(string s, int numRows) {
        string newS = "";
        for (int rowNum = 0; rowNum < numRows; rowNum++) {
            rowGap gap = getRowGap(s, rowNum, numRows);
            bool onFirst = true;
            bool changed = true;
            int charOn = rowNum;
            while (charOn < s.size()) {
                if (changed) {
                    newS += s[charOn];
                }
                int gapSize = onFirst ? gap.first : gap.second;
                charOn += gapSize;
                changed = gapSize > 0;
                onFirst = !onFirst;
            }
        }
        return newS;
    }
};
40643