leetcode 13:zigzag conversion

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".

class Solution {
public:
    string convert(string s, int nRows) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function    
        int pattern_size = (nRows-1) * 2;
        string rel;
        const int len = s.size();
        
        //first line
        for( int i=0; i<len; i+=pattern_size){
            rel.push_back( s[i]);
        }
        
        //middle lines;
        for( int i=1; i< nRows-1; i++){
            for( int j=i; j<len; j+=pattern_size ) {
                rel.push_back( s[j] );
                int k = j+(nRows-1-i)*2;  
                if(k<len) {
                    rel.push_back( s[k] );
                }
            }
        } 
        
        //last line;
        for( int i=nRows-1; i<len; i+=pattern_size ) {
            rel.push_back( s[i] );
        }
        
        return rel;
    }
};

public class Solution {
    public String convert(String s, int nRows) {
        // Start typing your Java solution below
        // DO NOT write main() function        
        if(s==null) return null;
        int sz = s.length();
        
        if(nRows<=1) return s;
        //int i=0;
        
        StringBuilder sb = new StringBuilder();
        
        for(int i=0; i<nRows; i++) {
            int j=i;
            while(j<sz) {
                sb.append( s.charAt(j) );
                
                if( (i% (nRows-1)) != 0) {
                    int k = j + (nRows-1-i)*2;         //define new int k and save the old value in j for next loop
                    if(k<sz) sb.append(s.charAt(k) );  //must check k<sz; may be exceed string length.
                }
                j+=2*(nRows-1);
            }
        } 
        return sb.toString();
    }
}