# 6. ZigZag Conversion

## 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
```

## Complexity

* Time complexity: O(n)
* Space complexity: O(n)

## Code

```python
def convert(self, s: str, numRows: int) -> str:
    if numRows > len(s) or numRows == 1: #single string vertically or horizontally
        return s
    res = [''] * numRows #init space for storing each row
    row, step = 0, 1 #step positive if going up, negative if going down
    for i, c in enumerate(s):
        res[row] += c #add char to corresponding row
        if row == 0: #change direction to go up
            step = 1
        if row == numRows - 1: #change direction to go down
            step = -1
        row += step
    return "".join(res)
```


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