LeetCode 6: Zigzag Conversion — Python Solution

Solve LeetCode 6: Zigzag Conversion in Python with a row simulation approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Walk down and up across row buffers, reversing direction at the first and last row, then concatenate the rows.

Algorithm

1. Walk down and up across row buffers, reversing direction at the first and last row, then concatenate the rows.
2. Maintain this invariant: Each processed character is appended to the row visited by the zigzag cursor.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def convert(self, s, numRows):
        if numRows == 1 or numRows >= len(s):
            return s
        rows = ["" for _ in range(numRows)]
        row, direction = 0, 1
        for char in s:
            rows[row] += char
            if row == 0:
                direction = 1
            elif row == numRows - 1:
                direction = -1
            row += direction
        return "".join(rows)

Why this is correct

The proof follows the maintained state: Each processed character is appended to the row visited by the zigzag cursor. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(n) space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

One row or at least as many rows as characters returns the original string.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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