6 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.

Solution:

class Solution {
public:
    string convert(string s, int numRows) {
        /*
        T = numRows*2-2
        0     6   T*i
        1   5 7   d1 = T-2, d2 = 2
        2 4   8   d1 = T-4, d2 = 4
        3     9   numRows-1 + T*i
        */
        if ( numRows == 1 ) return s;
        int T = numRows*2-2, n = s.size();
        string res = "";
        for ( int i = 0; i <= numRows-1; i++ ) {
            int d1 = T-2*i;
            if ( i == 0 ) {
                for ( int j = 0; j*d1 <= n-1; j++ ) res += s[j*T];
                continue;
            }
            if ( d1 == 0 ) {
                for ( int j = 0; numRows-1+j*T <= n-1; j++ ) res += s[numRows-1+j*T];
                continue;
            }
            int j = 0;
            while (true) {
                if ( i + j*T>= n ) break;
                res += s[i + j*T];
                if ( i + j*T + d1 >= n ) break;
                res += s[i + j*T + d1];
                j += 1;
            }
        }
        return res;
    }
};