### Problem Statement

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 = 3Output:"PAHNAPLSIIGYIR"

**Example 2:**

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

### Video Tutorial

You can find the detailed video tutorial here### Thought Process

It's a very good implementation problem, by simply simulating each character in the string to each row, it would take extra O(N) space to hold up the array where N is the string size. However, there is definitely a difference between a good and poor implementation.There is also a math formula we can use, please see attached pdf for solutions.

### Solutions

#### Simulation poor implementation

Time Complexity: O(N) where N is the string sizeSpace Complexity: O(N) since we used an extra array to store each character in the string

#### Simulation good implementation

Time Complexity: O(N) where N is the string sizeSpace Complexity: O(N) since we used an extra array to store each character in the string

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