https://leetcode.com/problems/zigzag-conversion/

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"

primitive idea: 模拟把这些character填进去一个char[] array里，最后逐行输出非空的character. (default value for char is '\u0000')

Space 其实有很多浪费，空字符

How to improve:

我们并不需要保存空字符，其实只要按照zigzag 的规律不断地把字符放进相应的行去 （就相当于把空字符压缩）

==> what is the DS => StringBuilder is enough (or k list)

/*n=numRows
Δ=2n-2     1                           | 2n-1                        | 4n-3
Δ=2n-4     2                     2n-2  | 2n                    4n-4  | 4n-2
Δ=2n-6     3               2n-3        | 2n+1              4n-5      | .
Δ=         .           .               | .               .           | .
Δ=         .       n+2                 | .           3n              | .
Δ=2n-2(n-1)n-1 n+1                     | 3n-3    3n-1                | 5n-5
Δ=2n-2     n                           | n-2                         | 5n-4

I separate this pattern into smaller part as 1 to 2n - 2

filling the numbers in following steps:

1. vertical down n - 1 times （1 .. n - 1）
2. diagonal up n - 1 times （n .. 2n - 2）
3. goto 1 again until reach to the end of string