Zigzag String

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

**Example 2 : **
ABCD, 2 can be written as

A....C
...B....D

and hence the answer would be ACBD.

Method:

We notice that for the first row, the gap between words is 2 * (B - 1), in the example, if B = 5, then it's 8. For the second row, the gap is 6,2,6,2,6,2, etc.. For the third row, it's 4,4,4,4,4... Fourth row: 2,6,2,6,2,6. Fifth row: 8,8,8,8,8,8.

Solution:

Time: O(n)
Space: O(1)

public class Solution {
    public String convert(String A, int B) {
        if (B == 1) return A;
        StringBuilder sb = new StringBuilder();
        char[] arr = A.toCharArray();
        int cap = 2 * (B - 1);
        int gap = cap;
        boolean flip = false;
        int start = 0;
        int i = 0;
        while (sb.length() < A.length()) {
            sb.append(arr[i]);
            if (i + gap <= A.length() - 1) {
                i += gap;
            } else {
                i = ++ start;
                flip = false;
            }
            int nextGap = cap - ( (start * 2) % cap );
            if (start != 0 && start != B - 1) {
                if (!flip) {
                    gap = nextGap;
                    flip = true;
                } else {
                    gap = cap - nextGap;
                    flip = false;
                }
            } else {
                gap = nextGap;
            }
        }
        return sb.toString();
    }
}

class Solution {
    public String convert(String s, int numRows) {
        if (numRows == 1) return s;
        StringBuilder sb = new StringBuilder();
        int maxGap = 2 * (numRows - 1);
        int gap = maxGap;
        int start = 0;
        int i = 0;
        boolean flip = false;
        while (sb.length() < s.length()) {
            sb.append(s.charAt(i));
            if (i + gap < s.length()) {
                i += gap;
            } else {
                start ++;
                i = start;
                flip = false;
            }
            int nextGap = maxGap - ( 2 * start ) % maxGap;
            if (start != 0 && start != numRows - 1) {
                if (flip) {
                    gap = maxGap - nextGap;
                    flip = false;
                } else {
                    gap = nextGap;
                    flip = true;
                }
            } else {
                gap = nextGap;
            }
        }
        return sb.toString();
    }
}