## Description

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


## Solutions

### 1. String

# Time: O(n^2)
# Space: O(n)
class Solution:
def convert(self, s: str, numRows: int) -> str:
if numRows == 1:
return s
n = len(s)
interval = 2 * (numRows - 1)
res = ''
# first row
for i in range(0, n, interval):
res += s[i]
# middle lines
for r in range(1, numRows - 1):
inter = 2 * r
i = r
while i < n:
res += s[i]
inter = interval - inter
i += inter

for i in range(numRows-1, n, interval):
res += s[i]
return res

# 1158/1158 cases passed (52 ms)
# Your runtime beats 86.83 % of python3 submissions
# Your memory usage beats 100 % of python3 submissions (12.9 MB)