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".

分析：之字形扫描，有一个特点，如下图所示，每一层的下一个坐标和上一个坐标有递推关系，并设置一个标志是先往下再往上还是先向下再往上。

代码如下：

class Solution {
public:
    string convert(string s, int nRows) {
        string result;
        if(s.length()<1 || nRows <= 0){
            return result;
        }else if(nRows == 1){
            return s;
        }
        result = s;
        bool isDownUp = true;
        for(int i=0,j=0,k=0; i<nRows && j<s.length();++j){
            result[j] = s[k];
            if(i == 0 || i == nRows-1){
                 k += (nRows-1)*2;
            }else{
                if(isDownUp){
                    k += (nRows-i-1)*2;
                    isDownUp = false;
                }else{
                    k += i*2;
                    isDownUp = true;
                }
            }
            if(k > s.length()-1){ //层数加1
                ++i;
                k = i;
                isDownUp = true;
            }
        }
        return result;
    }
};