# Question

The string “`PAYPALISHIRING`

” 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 A H N
A P L S I I G
Y I R
```

And then read line by line: “`PAHNAPLSIIGYIR`

”

Write the code that will take a string and make this conversion given a number of rows:

```
string convert(string s, int numRows);
```

Example 1:

```
Input: s = "PAYPALISHIRING", numRows = 3
Output: "PAHNAPLSIIGYIR"
```

Example 2:

```
Input: s = "PAYPALISHIRING", numRows = 4
Output: "PINALSIGYAHRPI"
Explanation:
P I N
A L S I G
Y A H R
P I
```

# Solution

\(O(n)\) time and space complexity solution by rearranging characters into the final string.

Each row’s character starts at \(r\)th character in the string. The gap between two columns are \(2*(N_r-1)\). Between two columns there will be one or two gaps. If there’s only one gap, the gap size is \(2*(N_r-1)\). If there are two gaps, the first gap is of size \(2*(N_r - r - 1)\) and the second gap is of size \(2*r\), where \(N_r\) is total number of rows and \(r\) is the 0-based row number.

```
class Solution:
def convert(self, s, numRows):
"""
:type s: str
:type numRows: int
:rtype: str
"""
if numRows == 1:
return s
gap = 2 * (numRows - 1)
out = list()
for row in range(0, numRows):
firstGap = gap - 2 * row
secondGap = 2 * row
i = row
round = 0
while i < len(s):
out.append(s[i])
if firstGap == 0 or secondGap == 0:
i += max(firstGap, secondGap)
elif round % 2 == 0:
i += firstGap
else:
i += secondGap
round += 1
return ''.join(out)
```