题目：

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"
.

思路：

假设有ABCDEFG这样的字符串，我们可以表示为如下格式。即分为上行和下行两列，考虑上行下行两种情况以及对应的游标跳转的表达式。
A    G
B F
C E
    D

代码：

方法1：

class Solution {
public:
    string convert(string s, int nRows) {
        if(nRows==1)
        {
            return s;
        }
        else
        {
            string str;
            for(int i=0;i<nRows;i++)
            {
                str += convertLine(i, nRows, s, i!=(nRows-1));
            }
            return str;
        }
    }
    
    string convertLine(int num, int nRows, string s, bool downstair)
    {
        int cur = num;
        string str;
        
        while(cur<s.size())
        {
            str.push_back(s[cur]);
            
            if(downstair)
            {
                cur+= 2*(nRows-1-cur%(nRows-1));
            }
            else
            {
                cur+=2*(nRows-1-cur%(nRows-1));
            }
        };
        return str;
    }
};

方法2：

class Solution {
public:
    string result;
    string convert(string s, int nRows) {
        if(nRows <= 1){
            return s;
        }
        
        int unit = 2 * nRows - 2;
        int n = s.size() / unit;
        for(int i = 0; i < nRows; i++){
            for(int j = 0; j <= n; j++){
                if(j * unit + i < s.size() && (i == 0 || i == nRows - 1))
                    result.push_back(s[j * unit + i]);
                else{
                    if(j * unit + i < s.size())
                        result.push_back(s[j * unit + i]);
                    if(j * unit + unit - i < s.size())
                        result.push_back(s[j * unit + unit - i]);
                } 
            }
        }
        return result;
    }
};