6. 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 s, int numRows);

Example 1:

Input: s = "PAYPALISHIRING", numRows = 3
Output: "PAHNAPLSIIGYIR"

Example 2:

Input: s = "PAYPALISHIRING", numRows = 4
Output: "PINALSIGYAHRPI"
Explanation:

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

---

估计大多数人看到这题都不知道Zigzag具体是怎样一个pattern，题目也只给了一个例子，不好找规律，这是维基百科上介绍Zigzag时给的一张图片： 也就是先下后上来回走两条路径，下去和上来的路径是各自平行的。这一题中，下去是竖直下去的，上来是45°斜着走上来的。使用数组模拟走路过程即可。 代码如下：

class Solution {
public:
    string convert(string s, int numRows)
    {
        int n = s.size();
        if (numRows >= n || numRows == 1)
            return s;
        vector<vector<char> > board(numRows);
        int k = 0, i = 0;
        bool up = false;
        while (k < n) {
            board[i].push_back(s[k]);
            if (i >= numRows - 1)
                up = true;
            else if (i <= 0)
                up = false;
            if (up)
                i--;
            else
                i++;
            k++;
        }
        string ret = "";
        for (int i = 0; i < numRows; i++)
            for (int j = 0; j < board[i].size(); j++)
                ret += board[i][j];
        return ret;
    }
};

本代码提交AC，用时48MS。