# 6. ZigZag Conversion

**<font color=red>难度: Medium</font>**

## 刷题内容

> 原题连接

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

> 内容描述

```
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
```

## 解题方案

> 思路 1

参考大神[pharrellyhy](https://leetcode.com/problems/zigzag-conversion/discuss/3404/Python-O(n)-Solution-in-96ms-(99.43)?page=2)的思路,
纵向思维考虑，```index```从```0```开始，我们要一直***自增***直到```numRows-1```，此后又一直***自减***到```0```，重复执行。
给个例子容易懂一些：```s = “abcdefghijklmn”```, ```numRows = 4```
```
a   g   m
b f h l n
c e i k
d   j
```
看明白了吗，下来上去，下来上去，zigzag


```python
class Solution(object):
    def convert(self, s, numRows):
        """
        :type s: str
        :type numRows: int
        :rtype: str
        """
        if numRows == 1 or numRows >= len(s):
            return s
        res = [''] * numRows
        idx, step = 0, 1
    
        for x in s:
            res[idx] += x
            if idx == 0:  ## 第一行，一直向下走
                step = 1
            elif idx == numRows - 1: ## 最后一行了，向上走
                step = -1
            idx += step
        return ''.join(res)
```
假设用我上面给的例子，并且在```L[index] += x```这一行后面打印出index, step, L的值, 输出结果如下：
```
(0, 1, ['a', '', '', ''])
(1, 1, ['a', 'b', '', ''])
(2, 1, ['a', 'b', 'c', ''])
(3, 1, ['a', 'b', 'c', 'd'])
(2, -1, ['a', 'b', 'ce', 'd'])
(1, -1, ['a', 'bf', 'ce', 'd'])
(0, -1, ['ag', 'bf', 'ce', 'd'])
(1, 1, ['ag', 'bfh', 'ce', 'd'])
(2, 1, ['ag', 'bfh', 'cei', 'd'])
(3, 1, ['ag', 'bfh', 'cei', 'dj'])
(2, -1, ['ag', 'bfh', 'ceik', 'dj'])
(1, -1, ['ag', 'bfhl', 'ceik', 'dj'])
(0, -1, ['agm', 'bfhl', 'ceik', 'dj'])
(1, 1, ['agm', 'bfhln', 'ceik', 'dj'])
```

