C++中的Z字形变换问题

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

string convert(string s, int numRows);

class Solution {
public:
    string convert(string s, int numRows) {
        int rows = numRows;
	    int columns = ((s.length() / (2 * rows - 1)) + 1) * rows;//尽可能缩小所使用的空间，这里columns可优化，并未精确求解
	    std::vector<std::vector<char>> arrs(rows, std::vector<char>(columns));

	    //初始化
	    for (int i = 0; i < rows; i++)
		    for (int j = 0; j < columns; j++)
			    arrs[i][j] = '0';

	    int x = 0, y = 0;
	    int index = 0;
	    while (index < s.length())
	    {
		    if (index < s.length() && x < rows)
			    arrs[x++][y] = s[index++];

		    if (index < s.length() && x == rows)
		    {
                 //更新x和y
			    y++;
			    x -= 2;
			    while (index < s.length() && x > 0)
				    arrs[x--][y++] = s[index++];
			    x = 0;//重置x
		    }
	    }

	    std::string res;
	    for (int i = 0; i < rows; i++)
	    {
		    for (int j = 0; j < columns; j++)
		    {
			    if (arrs[i][j] != '0' && arrs[i][j] != '\0')
				    res.push_back(arrs[i][j]);
		    }
	    }
	    return res;
    }
};