LeetCode 6 ZigZag Conversion(Z字转换)

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 = 3
Output: "PAHNAPLSIIGYIR"

Example 2:

Input: s = "PAYPALISHIRING", numRows = 4
Output: "PINALSIGYAHRPI"
Explanation:

P     I    N
A   L S  I G
Y A   H R
P     I

解：

/*
 * @lc app=leetcode id=6 lang=cpp
 *
 * [6] ZigZag Conversion
 */
class Solution {
public:
    string convert(string s, int nRows) {
        if(nRows <= 1) return s;
        string result = "";

        /*
        P   A   H   N
        A P L S I I G
        Y   I   R

        P   | A   | H   | N
        A P | L S | I I | G
        Y   | I   | R   |
         */

        // 假设一个竖线和一个斜线（不包括斜线和下一个线的交集）是个循环
        // 那么循环的公式就是
        // cycle = (2*nRows - 2), nRows > 1.
        int cycle = 2 * nRows - 2;
        for(int i = 0; i < nRows; ++i)
        {
            for(int firstJ = i; firstJ < s.length(); firstJ = firstJ + cycle){
                // firstJ为该行该循环的第一个字母index
               result = result + s[firstJ];
                // secondJ 该行该循环的第二个字母index
                // firstJ - i 当前循环开始的index
                // cycle - i  循环内同一行的第二个字母
               int secondJ = (firstJ - i) + cycle - i;
               if(i != 0 && i != nRows-1 && secondJ < s.length())
                   result = result + s[secondJ];
            }
        }
        return result;
    }
};