ZigZag Conversion

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:

string convert(string text, int nRows);
convert("PAYPALISHIRING", 3) should return "PAHNAPLSIIGYIR".

class Solution(object):
    def convert(self, s, numRows):
        """
        :type s: str
        :type numRows: int
        :rtype: str
        """
        rows = ["" for x in range(numRows)]
        count = 0
        start = 0
        end = numRows
        inc = 1

        # while we dont run out of letters
        while count < len(s):
            # count from index 0 -> numRows -> numRows
            for i in range(start, end, inc):
                if count < len(s):
                    rows[i] += s[count]
                    count += 1

            if inc == 1:
                inc = -1
                start = numRows-2
                end = 0
            else:
                inc = 1
                start = 0
                end = numRows
        return "".join(rows)


sol = Solution()
s = "PAYPALISHIRING"
numRows = 3
print sol.convert(s, numRows)

This solution goes through the string once, using a loop that changes direction when it hits the number of rows. Then, this simply joins the separated rows of strings into one, which makes an O(n) complexity.