<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>

from collections import defaultdict
class Solution:
    def convert(self, s: str, numRows: int) -> str:
        if numRows<=1:
            return s
        rows = defaultdict(list)

        dir_map = {
            'down': (0,1),
            'up': (1,-1)
        }
        direction = 'up'
        stop_after = 0
        x,y = 0,0
        for ii in range(len(s)):
            if stop_after<=0:
                stop_after = numRows-1
                direction = 'down' if direction=='up' else 'up'
            dx,dy = dir_map[direction]
            lst = rows[y]
            while len(lst)<= x+1:
                lst.append(' ')
            lst[x] = s[ii]
            stop_after -= 1
            x += dx
            y += dy
        # for y,lst in rows.items():
        #     print(''.join(lst))
        return ''.join([val for y,lst in rows.items() for val in lst if val!=' '])
17700