Zigzag Conversion

Problem Description

The string PAYPALISHIRING is written in a zigzag pattern on a given number of rows like this:

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.

Solution Approach

The problem asks us to reconstruct a string that is formed by reading a zigzag pattern row by row. We can solve this by simulating the placement of each character into its corresponding row.

The core idea is to maintain a list of strings, where each string represents a row in the zigzag pattern. We iterate through the input string, character by character, and append each character to the correct row.

To determine the correct row for each character, we can track the current row number and the direction of movement (down or up).

1. Initialize an array of empty strings, with the size equal to numRows.
2. Initialize a currentRow index to 0 and a step variable to 1 (indicating we are moving down).
3. If numRows is 1, the zigzag pattern is just a single line, so the direction never changes. This is an important edge case to handle, where we can simply return the original string.
4. Iterate through each character of the input string: a. Append the character to the string at rows[currentRow]. b. If we reach the top (currentRow == 0) or bottom (currentRow == numRows - 1) row, we must reverse the direction. This can be done by changing the sign of our step variable. c. Update currentRow by adding the step to it.
5. After iterating through all characters, the rows array will contain the strings for each row of the pattern. Concatenate these strings to get the final result.

This approach directly builds the rows of the zigzag pattern, making it straightforward to get the final output string.

Code

# The user has opted to not include a code block.
# The solution involves iterating through the string once,
# placing each character in the correct row based on the zigzag pattern.

Complexity Analysis

• Time: O(n), where n is the length of the input string s. We iterate through the string once to place each character in its respective row. Concatenating the final rows also takes O(n) time.
• Space: O(n). We use additional space to store the characters in the numRows rows. In the worst case, the total space required for these rows is proportional to the length of the input string.

Notes & Learnings

• This problem is a great example of simulation. The key is to find a simple rule to describe the zigzag movement.
• Using a step or direction variable simplifies the logic for moving up and down the rows.
• Handling edge cases like numRows = 1 is crucial for a correct solution.